Acme Mathematics 8

Acme Mathematics 8 301Item Bricks Cement Steel Labour MiscellaneousExpenditure (in percentage) 15% 20% 10% 25% 30%Represent the above data by a pie-chart.Solution : Here, total value = 100 Central angel for a component = value of the component total value × 360 ° Calculation of central anglesItem Expenditure (in percentage) Central anglesBricks 15% 15 100 × 360 ° = 54°Cement 20% 20 100 × 360 ° = 72°Steel 10% 10 100 × 360 ° = 36°Labour 25% 25 100 × 360 ° = 90°Miscellaneous 30% 30100 × 360 ° = 108°Construction of the pie-chart Steps of construction1. Draw a circle of any convenient radius.2. Within this circle, draw a horizontal radius.3. Starting with the horizontal radius drawn in step 2, form sectors with central angles of 54°, 72°,36°,90° and 108°. 4. Shade the sectors differently and label them. Thus, we obtain the required pie-graph, shown in the adjoining figure. c. Reading a pie chart We know thatIn the circle central angle for a component = value of the component 360° × total value∴ Value of component = its central angle 360° × total valueBricksCementSteel LabourMisc.

302 Acme Mathematics 8Solved ExamplesExample 1 : The adjoining pie-chart shows the annual agricultural production of Chitwan. If the total production of all the given commodities is 8100 tonnes, find the production (in tonnes) of (i) wheat, (ii) sugar, (iii) rice, (iv) maize, and (v) gram.Solution : Using the formula Value of a component = its central angle 360° × total valueWe can find the production of each commodity, as shown in the following table.Commodity Central angle Annual Production (in tonnes)(i) Wheat 120° 120360 × 8100 = 2700(ii) Sugar 100° 100360 × 8100 = 2250(iii) Rice 60° 60360 × 8100 = 1350(iv) Maize 30° 30360 × 8100 = 675(v) Gram 50° 50360 × 8100 = 1125Thus, we have the annual production as given below:Commodity Wheat Sugar Rice Maize GramAnnual Production (in tonnes) 2700 2250 1350 675 1125 Example 2 : The pie-chart alongside shows the monthly expenditure of a family on food, clothing, rent, miscellaneous expenses and savings. Read the pie-chart carefully and answer the following questions: (i) What is the central angle for savings ? (ii) What is the ratio of expenditure on food to that on rent? (iii) If the family spends Rs 825 on clothing, what is its total monthly income ? Wheat 120°Gram 50°Maize 30°Rice 60°Sugar 100°Misc. 72°Food 108°Rent 90° SavingClothing 36°

Acme Mathematics 8 303(iv) What percent of the total income does the family save ? Solution : Central angle for savings = 360° – (108° + 90° + 36° + 72°) = 54° (i) Ratio of expenditure on food to that on rent = ratio of their central angles = 108: 90 = 6:5. (iii) Central angle for clothing = money spent on clothing total value × 360or, 36 = 825 total value × 360or, total value = 82536 × 360= 8250∴ The total monthly income is Rs 8250.(iv) Saving % = central angle for saving 360° × 100 %= 54360 × 100 % = 15% The family saves 15% of the total income.Classwork1. Number of tourist that visited nepal in last 5 years is given below.Year (in AD) 2021 2022 2023 2024 2025No. of tourists ('000) 40 55 60 30 20(a) Which was the year in which tourist visited the most in the last 5 years?(b) Draw a pie chart to represent the above information. 2. In the given pie chart, 1° represents 2 students. Then,(a) Find the total number of students.(b) How many students are there in class VII? (c) Which class has highest number of students? Find it.55°70° 80°viiixv viivi65°

304 Acme Mathematics 83. (a) A man spends Rs. 3600 on food out of total expenditure Rs. 10800. Find the angle to draw a pie chart.(b) Marks obtained by 5 students is given below. Compute arithmetic mean of the marks. Marks 20 40 60 80 100Roll Number of students 15 5 8 3 14. Here is a pie chart prepared on the basis of answer asked as which subject do you like among 480 students enrolled in Janata Secondary School. Study the pie-chart carefully and answer the following question.(a) Find the number of students who liked each subject.(b) What is the difference between the number the most liked subject and the least liked subject? Find out. (c) What percentage of students liked mathematics? 5. The monthly budget of a family is given below.Food Rs. 2100Rent Rs. 2250Clothing Rs. 3300Saving Rs. 3150(a) What is the total budget?(b) Represent the above data in a pie chart. Exercise 6.11. (a) The monthly income of a family is Rs 9000. Its monthly budget is given below: Item Rent Food Children's education Misc. SavingExpenses (in Rs) 1878 3250 1125 1500 1250Represent the above data by a pie-chart. (b) There are 1440 creatures in a zoo as per the list given below: Insects Other land animals Birds Water animals Reptiles340 360 260 300 180Draw a pie-chart to represent the above data. SocialMath ScienceNepali108°81° 57°114°

Acme Mathematics 8 305(c) There are 168 workers in a factory as per the list given below:Rank Labour Mechanics Filters Supervisors ClerksNumber of workers 63 56 28 14 7Represent the above data by a Pie-chart.2. (a) The marks obtained by Sujan in an examination are given below: Subjects English Nepali Mathematics Science Social studiesMarks 95 75 100 90 90Represent the above data by a Pie- diagram. (b) The following table gives the number of different fruits that have been kept in a shop:Type of fruit Mangoes Apples Orange Coconuts PomegranatesNumber of fruits 26 30 21 5 8Represent the above data by a pie-diagram. 3. (a) Draw a pie-chart to represent the following data on money spent during the Fourth five Year plan:Item Money spent (in crores of rupees)Agriculture 6000Industries 4000Energy 2500Communications 4500Miscellaneous 3000(b) The following data shows the agricultural production in a country during a certain year.Food grain Rice Wheat Coarse cereals PulsesProduction (in millions of tones) 57 76 38 19 Represent the above data by a pie-chart. 4. (a) The annual examination results declared by a school show the grade of students in each category as given below:A+ A B+ B NG5% 25% 45% 20% 5% Represent the above data by a pie-chart.

306 Acme Mathematics 8(b) The following table shows the percentages of buyers of five different brands of bathing soaps:Brand A B C D EPercent of buyers 20% 35% 25% 15% 5% Draw a pie chart to represent the above information.(c) The following table shows the expenditure invested by a publisher in bringing out a book:Item Paper Printing Binding Advertising Misc.Expenditure (in percentage) 35% 20% 10% 5% 30%Represent the above data by a pie-chart. (d) The following table gives the monthly expenditure of a family under different heads as a percentage of their income.Item Food Housing Clothing Education Misc.Expenditure 30% 25% 10% 20% 15%Draw a pie-chart to represent the above data.(e) The table below gives the percentages of car drivers of various age groups involved in accidents during a year.Age of drivers (in years) Under 20 20 - 40 40 - 60 Over 60 Percentage of accidents 20% 45% 30% 5%Represent the above data by a pie-chart. 5. (a) The pie-chart given in the figure represents the marks obtained by a student in various subjects. Read it carefully. If the student obtained 3600marks in all, calculate the marks obtained by him in each of the given subject. (b) The adjoining pie-chart shows the marks obtained by a student in an examination. If the student secures 300 marks in all, calculate his marks in each of the given subjects. [use 3 dp]Social Studies 72°English 62°Mathematics90°Nepali 60°Science76°Math. 108°Science 81°Social Studies 45°Nepali 54°English72°

Acme Mathematics 8 307(c) The adjoining pie-chart shows the expenditure incurred by a publisher in bringing out a book. If a book costs Rs 120 to the publisher, calculate the expenditure involved under each of the given categories. 6. (a) Monika spends Rs 16000 per month. Her expenses on various items are represented by the pie diagram alongside. Read the diagram and answer the questions given below: (i) How much does Monika spend on rent? (ii) What is the central angle for miscellaneous expenses?(iii) How much is spent on education? (iv) What is the ratio of expenses between food and rent? (b) The adjoining circular diagram shows the number of students of a school using different mode of travel to school. If 360 students come to the school on bicycle, answer the questions given below: (i) How many students come to the school by school bus? (ii) How many students travel by taxi to reach the school? (iii) What is the ratio of students coming by school bus to those who come on foot? (iv) How many students are there in the school?Printing72° Paper 108°Misc. 90° Royalty36°Binding54°Food 135°Rent 81°Education36°Misc.Bicycle144°Taxi48°School Bus112°Walking56°

308 Acme Mathematics 86.3 Mean, Median, Mode A. Arithmetic mean(a) Arithmetic mean in case of individual dataArithmetic mean of a set of observations is their sum divided by number of observations. The arithmetic mean is denoted by X . The arithmetic mean X of n observation x1, x2, x3 ………. xn is given by Arithmetic Mean = x1 + x2 + x3 + .......... + xn N∴ X = ∑x NWhere, X = mean, ∑x = sum of n terms and N = Number of observationsSolved ExamplesExample 1 : Find the arithmetic mean of 20, 22, 25, 28, 30 Solution : Here, 20, 22, 25, 28, 30 are givenThe sum of the terms = 20 + 22 + 25 + 28 + 30∴ ∑ X = 125 ∴ The number of terms (N) = 5 We know that, Arithmetic mean (X) = ∑x N= 1255= 5∴ Arithmetic mean (X) = 25 Example 2 : Find the mean of all factors of 12. Solution : Here the factors of 12 are 1, 2, 3, 4, 6, 12 The sum of the terms (∑x) = 1 + 2 + 3 + 4 + 6 + 12 ∴ ∑x = 28 ∴ The number of terms (N) = 6

Acme Mathematics 8 309We know that; Arithmetic mean (X) = ∑x N= 28 6= 14 3= 4.67∴ Arithmetic mean (X) = 4.67Example 3 : The arithmetic mean of 6, 10, x, 12 and 16 is 11. Find the value of x. Solution : Here, given terms are, 6, 10, x 12 and 16.Arthmetic mean (X) = 11The sum of the terms (∑X) = 6 + 10 + x + 12 + 16∴ The sum of the terms (∑X) = 44 + xThe number of terms (N) = 5We know that,Arithmetic mean (X) = ∑x Nor, 11 = 44 + x 5or, 44 = x = 55or, x = 55 – 44or, x = 11Thus, the value of x is 11Classwork1. Find the arithmetic mean of following: (a) 2, 4, 6, 8, 10 (b) 10, 14,16, 20, 22 (c) 3, 8, 10, 15, 18 (d) 20, 50, 30, 40, 60, 80 (e) 25, 35, 55, 65, 75, 95(f) 45, 25, 35, 10, 15, 5

310 Acme Mathematics 8Exercise 6.21. Find the mean of following numbers: (a) Wt in kg: 2, 8, 6, 4, 3, 5, 7, 1 (b) Marks: 15, 1, 13, 9, 7, 5, 3, 17, 11, 19 (c) Ht in cm: 20, 30, 50, 70, 110 (d) Numbers: 2, 8, 12, 10, 6, 4 (e) Our notes: 1, 5, 10, 20, 50, 100, 500, 1000(f) Factors of 20: 1, 2, 4, 5, 10, 202. The monthly expenditure of Mr A's family is given below in the table.Baishakh Jestha Ashar SawonRs. 30000 Rs. 20000 Rs. 25000 Rs. 28000 What is the monthly average expenditure of Raman's family? 3. In an exam, 11 students got the following marks. 19, 15, 18, 14, 12, 13, 11, 16, 17,20 What is the average mark ?4. In the exam the marks obtained by a student are as follows. Subject Math Science Social Nepali EnglishMarks 70 80 85 60 65Find the mean score. 5. In the table given below, the expenses have done by a family in a month on food, education, health, transportation and miscellaneous are given. Titles Amount (Rs.)Food 12000Education 8000Health 6000Transportation 10000Miscellaneous 6000The average expenditure of the family according to the above table is Rs. 7000. How much money should be reduced from miscellaneous expenses to make average expense Rs. 6500 ?

Acme Mathematics 8 3116. In the first term examination Kenjal got the following marks.Subject English Maths Science Social HPEMarks 40 45 40 30 25The average marks of Kunjan is 37.Is the average marks of Kenjal is greater than Kunjal's marks ? 7. The weight in kg of the children who came for treatment in health post is given below. 22, 20, 15, 21, 18, 19, 18(a) What is the mean weight of children ? Find it.(b) 2 more children came for the treatment on the same day. What should be their weight to be the mean weight as in question (a).8. The average expenditure of Anup's family is shown in the table below. Item Food Education Rent OthersExpenditure 20000 275000 30000 32500(a) What is the total expenditure of Anup's family ?(b) Show that average expenditure of Anup's family is equal to expenditure on Education.9. Calculate the value of 'x' in the following condition. (a) When ∑X= 93 + x, X = 15 and N = 7. (b) When ∑X= 651 + x, X = 92 and N = 8. (c) When ∑X= 44 + x, X = 11 and N = 510. In each of the following conditions find the value of x.(a) The mean of 6, 10, x and 12 is 18.(b) The mean of 6, 8, 9, x and 13 is 10 (c) The mean of 20, 22, x, 28 and 30 is 25. (d) The mean of 12, 3, 4, x and 12 is 7.4. (e) The mean of x, x + 3, x + 6, x + 9, x + 12, x + 15 is 18 (f) The mean of P, P + 2, P + 4, P + 6 and P + 8 is 13.

312 Acme Mathematics 8C. Median (a) Mean in case of individual data Look at the following set of numbers. (a) 2, 3, 4, 5, 7, 9, 11 (b) 6, 8, 10, 12, 14, 16Answer the following questions with respect to above data. (i) Are the given data in increasing order ? (ii) Which is the middle term in (a) ? (iii) Which is the middle term in (b) ?Given data are in increasing order of magnitude. In (a) the middle term is 5. But in (b) there is not single middle term. To find middle term add the middle two and divide by 2 that is called the median of the data.Thus, median, is the value of the variable which exactly lies in the middle position when the data is arranged in the increasing (or decreasing) order. For example in the sequence of data 4, 7, 9 the value of the variable in the middle position is 7. Hence, 7 is the median. We can calculate the median of an individual data by applying following steps. Steps: 1. Arrange the variable in increasing or decreasing order. 2. Count the number of observation and find N.3. Apply the formula, Median = N + 1 2th item.Solved ExamplesExample 1 : Find the median of the following data: 6, 7, 8, 11, 18, 13, 15 Solution : Here, 6, 7, 8, 11, 13, 15, 18 ∴ The number of observation (N) = 7 We know that; Median = size of N + 1 2th item = size of N + 1 2th item= size of 4th item = 11 [by counting) Thus, the median of given data is 11

Acme Mathematics 8 313Note: In computing the arithmetic mean we use every item of the distribution, whereas in computing the median we use only the position of a particular observation. It is because of this basic difference that the median (and also mode) are called positional averages.Example 2 : A student secured the following marks in seven subjects: 50, 53, 61, 49, 45, 63, 48. Find the median score. Solution : Here arranging the marks in increasing order, we have45, 48, 49, 50, 53, 61, 63 Since the series contains seven items, N = 7 Now, Median = size of N + 1 2th item= size of 7 + 1 2th item= size of 4th item∴ Median = Size of 4th item = 50 marks.Example 3 : Find the median of the following set of numbers: 10, 75, 3, 81, 18, 27, 4, 48, 12, 47, 9, 15 Solution : Here, arranging the numbers in increasing order, we have 3, 4, 9, 10, 12, 15 ↓ 18 , 27, 47, 48, 75, 81∴ No of terms (N) = 12 Now, Median = size of N + 1 2th item = size of 12 + 1 2th item= size of 6.5th item In this case 6.5th item lies midway between 6th and 7th terms, as shown by the box above. ∴ Median = Size of 6.5th item = Average of (6th terms + 7th terms)= 15 + 18 2= 16. 5 Hence, median is 16.5

314 Acme Mathematics 8Classwork1. Find the median of the following data:(a) 2, 3, 5, 7, 9(b) 4, 8, 12, 16, 20, 23, 28, 32 (c) 60,33, 63, 61, 44, 48, 51(d) 13, 22, 25, 8, 11, 19, 17, 31, 16, 10 (e) First ten prime numbers (f) Prime numbers between 51 and 80 Exercise 6.31. Find the arithmetic mean and median of the first 11 natural numbers. What do you notice ?2. Find the median for the following data : 46, 64, 87, 41, 58, 77, 35, 90, 55, 33, 92 If in the data, the observation 92 is replaced by 29, determine the new median.3. The following data have been arranged in ascending order. Determine the median. 24, 27, 28, 31, 34, 35, 37, 40, 42, 45 In the above data, if 45 changed to 54, find the new median. 4. The median of the following observation arranged in ascending order is 24. 11, 12, 14, 18, x + 2, x + 4, 30, 32, 35, 41(a) Find the value of x.(b) Find the median of the data.5. In an exam, 11 students got the following marks. 19, 15, 18, 14, 12, 13, 11, 16, 17,20(a) What is the median mark ?(b) Find the number of students above and below the median mark.6. The obtained marks of a students in an exam are as follows. Subject Maths Science Social Nepali EnglishObtained Marks 70 80 85 60 65Find the median marks of the given data.7. The weight in kg of the children who came for treatment in health post is given below. 22, 20, 15, 21, 18, 19, 18 (a) What is the median weight of children ? Find it.(b) 2 more children came for the treatment on the same day. What should be their median weight ?

Acme Mathematics 8 315D. ModeAnother method of getting a measure of central value, which is not upset by extreme values in this distribution, is to use the most commonly occurring value. This is the most fashionable. It is called the mode or modal value. The item which is repeated the maximum number of times is the mode. We often hear; (a) average height of a Nepalese boy is 160 cm.(b) average man wears 90 cm long vest.It is not necessary that in a series there must be only one mode. A distribution having only one mode is called unimodal, having two bimodal, and more then two, multimodal. For example,(a) The set of numbers 2, 3, 4, 7, 4, 5, 4, 9, 4 has mode 4, as it occurs the maximum number of times. (b) The set of numbers 5, 7, 6, 9, 1, 2, has no mode, as no number occurs more numbers of times than the other numbers.(c) The set 2, 2, 2, 3, 5, 6, 6, 6, 4, 4, 9 has two modes, namely, 2 and 6 as each of 2 and 6 occurs equal number of times, i.e., 3 times. This series is bimodal.(d) The set 25, 15, 23, 40, 27, 25, 23, 25, 20 has 25 as the mode as it repeats the largest number of times, i.e., 3 times, whereas 23 repeats only twice. So far as we have shown how to find mode in a simple distribution.Solved ExamplesExample 1 : Let us suppose that 10 students obtained the following marks in science.2, 3, 9, 8, 12, 7, 9, 13, 9, 17Calculate the model marks.Solution: Arrange the data in ascending order:2, 3, 7, 8, 9, 9, 9, 12, 13, 17Here, 9 marks is secured by 3 students. So the model marks obtained in science by the 10 students is 9 marks. Note The mode is always identified by the observation.

316 Acme Mathematics 8Example 2 : The weight of 15 students is given below:Weight (in kg) : 35, 36, 40, 38, 42, 45, 41, 40, 39, 38, 40, 33, 29,36,40.Calculate the model weight.Solution: Arrange the data in ascending order:Weight (in kg) : 33,35, 36, 36, 38, 38,39,40, 40, 40, 40, 41, 41, 42, 45.Here, 2 students have 36 kg weight,2 students have 38 kg weight4 students have 40 kg weight and2 students have 41 kg weight. So the model weight is 40 kg Classwork1. Find the mode of the following data: (a) 8, 5, 6, 8, 8, 4, 6, 10, 8, 2(b) 1, 2, 3, 3, 3, 5, 6, 8, 8, 8, 9, 8 (c) 3, 5, 6, 6, 5, 3, 5, 3, 5, 3, 6, 5, 3, 5, 7, 6, 5, 7, 5 (d) 3, 4, 7, 11, 4, 3, 4, 5, 6, 4, 1, 4, 2, 4, 4 2. A boy scored the given marks in various class-tests during a term, (each test being marked out of 20): 15, 17, 7, 16, 10, 12, 14, 16, 19, 12, 16 a. What is his modal marks ?b. What is his median marks ?Exercise 6.41. The weight (in kg) of 10 students of grade-8 of a school are as follows:30, 35, 31, 40, 38, 37, 39, 36, 39, 39 Arrange the data in ascending order and find:(a) The least weight.(b) The highest weight.(c) The model weight.

Acme Mathematics 8 3172. The following data shows the number of children in 30 families.2, 2, 5, 4, 2, 2, 1, 3, 2, 2,5, 3, 1, 3, 1, 2, 4, 1, 3, 4,4, 3, 2, 3, 4, 5, 2, 3, 1, 4Arrange the data in ascending order and find the model number children in the family3. Following are the number of members in 25 families in a village:6, 8, 6, 3, 2, 5, 7, 8, 6, 5,5, 7, 4, 8, 6, 6, 7, 4, 6, 5,3, 4, 2, 4, 3Arrange the data in ascending order and answer the following questions:(a) What is the smallest family size? (b) What is the model family size?(c) How many families are of the big size?4. In a study of number of accidents per day the observations for 30 days were obtained as following:4, 3, 5, 6, 4, 3, 2, 5, 4, 2,5, 2, 1, 2, 2, 0, 5, 4, 6, 1,3, 0, 5, 3, 6, 1, 5, 5, 2, 6Find the model number of accidents per day.5. A die was thrown 30 times and the following scores were obtained:5, 4, 3, 2, 1, 1, 2, 5, 4, 6,6, 3, 2, 1, 4, 3, 2, 1, 5, 6,4, 3, 1, 1, 5, 6, 5, 2, 1, 3Find the mostly occurred number.

318 Acme Mathematics 81. The height (in cm) of 5 students of grade 8 are presented below:150, 149, 152, 147, 152(a) Write the mode from the above data.(b) Find mean from above data.2. In an exam, 9 students got the following marks.19, 15, 18, 14, 12, 13, 11, 16, 17(a) Find the median and number of students above and below the median.(b) What is the average marks?3. Study the gievn pie-chart whose index are defined as follows.150°Liked Maths 110° 100°Liked ScienceLiked NepaliIndex RepresentationIf there are 720 students in total then,(a) Find the number of students who liked each of the given subjects.(b) Find the average number of students who liked Maths and Science.4. Marks obtained in Mathematics by 10 students in third terminal examination of grade 8 are as follows:36, 39, 42, 47, 41, 42, 45, 40, 42, 46(a) Write the modal data of the students.(b) If mark 46 is removed from the above marks, what will be the average mark of the students?5. The expenditure of Hari's family of a month is given below.Items Food Rent Education MiscellaneousAmount (in Rs.) 1000 4000 2000 3000(a) Calculate the average.(b) Present the expenditures in a pie-chart.Mixed Exercise

Acme Mathematics 8 3196. Information about the number of students from class 5 to 8 of a school is given in the table.Class 5 6 7 8Number of students 45 55 40 60(a) Find the average number of students of the school from class 5 to 8.(b) Represent the above information in the pie chart.7. Solve the following questions on the basis of the date given below:Marks 15 25 35 45 20 45Roll Number 6 8 5 9 4 7(a) Find the mean of the given data.(b) Find the mode of the given data.8. The obtained marks of a students in an exam are as follows.Subject Maths Science Social Nepali EnglishObtained marks 70 80 85 60 65(a) Represent the given data in circular diagram.(b) Find the median obtained mark of the given data.9. In the table given below, the expenses have done by a family in a month on food, education, health and miscellaneous are given.Title Food Education Health MiscellaneousAmount of Expenditure in Rs. 12000 8000 6000 10000(a) Represent the above information in the pie-chart.(b) The average expenditure of the family according to the above table is Rs. 9000. How much money should be reduced from miscellaneous expenses to make average expenses Rs. 8500?10. Number of tourist that visited nepal in last 5 years is given below.Year (in AD) 2018 2019 2020 2021 2022No. of tourists ('000) 40 55 60 30 20(a) Which was the year in which tourist visited the most in the last 5 years?(b) Draw a pie chart to represent the above information.

320 Acme Mathematics 811. In the given pie chart, 1° represents 2 students. Then,(a) Find the total number of students.(b) How many students are there in class VII? (c) Which class has highest number of students? Find it.12. (a) A man spends Rs. 3600 on food out of total expenditure Rs. 10800. Find the angle to draw a pie chart.(b) Marks obtained by 5 students is given below. Compute arithmetic mean of the marks.Marks 20 40 60 80 100Roll Number of students 15 5 8 3 113. Here is a pie chart prepared on the basis of answer asked as which subject do you like among 480 students enrolled in Janata Secondary School. Study the pie-chart carefully and answer the following question.(a) Find the number of students who liked each subject.(b) What is the difference between the number the most liked subject and the least liked subject? Find out. (c) What percentage of students liked mathematics? 14. The monthly budget of a family is given below.Food Rs. 2100Rent Rs. 2250Clothing Rs. 3300Saving Rs. 3150(a) What is the total budget? (b) Represent the above data in a pie chart.55°70° 80°viiixv viivi65°SocialMath ScienceNepali108°81° 57°114°

Acme Mathematics 8 321EvaluationTime: 43 minutes Full Marks: 181. The monthly expenditure of Roman's family is given below.Month Mangsir Poush Magh FalgunExpenditure 8000 6000 4000 2000 (a) Find the average expenditure. [1](b) Construct a pie-chart. [2]2. The height (cm) of 5 students of grade 8 are presented below.: 150, 149, 152, 147, 152(a) Write the mode from the above data. [1](b) Find the mean from the above data. [2]3. The marks obtained in mathematics by 12 students of class 8 in their first terminal examination are given below. 23, 30, 25, 26, 24, 28, 29, 28, 31, 33, 34, 28(a) Find the mode of above data. [1](b) Find the median marks of the students of class 8. [2]4. Solve the following questions on the basis of the date given below: Marks 15 25 35 45 55 65Students Rita Kisu Bunu Bhanu Rakes Ronit(a) Find the mean of the given data. [2](b) Find the number of students who got more than mean marks. [1]5. Marks obtained in Mathematics by 10 students in third terminal examination of grade 8 are as follows: 36, 39, 42, 47, 41, 42, 45, 40, 42, 46 (a) Write the modal data of the students. [1](b) If mark 46 is removed from the above marks, what will be the average mark of the students ? [2]6. The pie chart is prepared on the basis of the details of animals of on Narayan's farm. Study the pie chart and answer the following questions. (a) What is the total number of animals all together? [1](b) Find the percentage of cow and hen are in the form. [2]Goats HensBuffaloCows200 15512075

322 Acme Mathematics 8Model QuestionClass - 8 F.M. 50Subject - Mathematics Time – 2 hrsAll the questions are compulsory.1. Given a Venn-diagram.(a) Define proper subset. [1K](b) Write the improper subset of L. [1U](c) If e, i, o, u are the members of set M only then what type of set are L and M, write with reason. [1HA]2. Ramdev went to the utensil shop to buy a presser cooker. The marked price of a pressercooker is Rs. 3900.(a) If marked price and discount are represented by MP and D respectively, write the formula to find the discount percent. [1K] (b) How much discount did Ramdev get while buying a pressure cooker on discount of 7%? [1U](c) The shopkeeper got 17% profit after selling them at 7% discount. What was the cost price of the pressure cooker? [2A]3. Sangita has deposited Rs, 1,00,000 in a commercial bank for 2 years at the rate of Rs. 5interest per annum for Rs.100.(a) At what percent of interest rate per annum had Sangita deposited the amount of money? [1K](b) How much interest will Sangita get in 2 years at the same rate of interest? [2A](c) The ages of elder and younger daughter of Sangita's are 12 years and 8 yearsrespectively If Sangita divides her Rs. 1,00,000 to her daughters based on the ratio of their ages, how much more money will the elder daughter get than the younger daughter? [2HA]4. The capacity of a water tank to supply water to a village is 37,200 l.(a) Write the capacity of the water tank in scientific notation? [1U](b) A family of that village has consumed 8520l of water in a month. If the cost of 1 liter water is 30 paisa, how much rupees have to be paid for the consumption of water in one month? [1A](c) Convert 0. 34 into fraction. [2U](d) If and denote 1 and 0 respectively, which of the given boxes will have to be shaded to denote 43 in binary number system? [1HA].c.b.a .i.e.oL MU.u

Acme Mathematics 8 32340m70m40m5. The trapezium shaped land shown in the figure, belongs to Bimala. She made the workers dig a well with diameter 1.4 m to irrigate her land.(a) Write the formula to find the area of well? [1K] (b) What is the area of the well? Find it out. [1U](c) What is the area of land except the well ? [2A](d) Bimala wanted to fence the wire at once on that land. If she asks you whether 190 meter wire is enough or not, write your answer with reasons. [1HA]6. (a) Expressxmxn as power of x. [1K](b) Simplify:x x–y – x x+y [2U]7. Two equations are given below.2x + y = 8 and x + y = 5(a) What are the system of equations called? [1K](b) Solve the above equations by using graph. [2A]8. (a) Find the highest common factors (HCF) of the given algebraic expressions. x2 – 5x + 6and x2 – 9. [2A](b) At what value of x, the value of x2 – 5x + 6 becomes zero? [2HA]9. In the adjoining figure, AB intersect straight lines LM and PQ at point E and F respectively. Observe the figure and answer the following questions.(a) Write a pair of co-interior angles in the figure. [1K](b) Find the value of x. [2U](c) At what value of ∠MEG, the line segments LM and PQ will become parallel? [1HA]10. (a) Construct a parallelogram LMNO with LM = 8 cm, MN = 6 cm and ∠LMN = 75º. [3A](b) Construct two triangles LMN and LON from the parallelogram LMNO. Prove that ∠LMN is congruent to ∠LON. [2HA]11. (a) Which type of triangle is used to make regular tessellation? [1K]O X' XYY'AB CMP QEFAB60°L x2x

324 Acme Mathematics 8(b) Answer the following questions on the basis of given figure:In given ∠ABC, if the bearing of point C from the point B is 090o then,find the bearing of point B from C. [2U](b) Rotate the ∠ABC at positive 90o about the centre at origin (0, 0). Write the coordinates of the image A', B' and C' after rotation. [3A]12. The monthly expenditure of Raman's family is given below in the table.Baishakh Jestha Ashar SawonRs. 25000 Rs. 19000 Rs. 28000 Rs. 18000(a) What is the monthly average expenditure of Raman's family? [1A](b) Present Raman's family expenditure in a pie chart? [2A]

Acme Mathematics 8 325MIXED Exercise 1. (a) {11, 13, 17, 19, 23} (b) {x : x is the multiple of 7 between 6 and 40} (c) Yes2. (a) STYT (b) Set A3. (a) A = { }, B{2, 3, 5, 7} (b) 4 (c) A is subset of B.4. (a) 5 (b) {2} (c) B is subset of A.5. (a) disjoint (b) STYT (c) STYT6. (a) {1, 2, 4, 8} and {2, 4, 6, ...} (b) Overlapping sets(c) STYT (d) {2, 4, 8}7. (a) {a, e, i, o, u}{a, e} (b) Yes (c) STYT8. (a) {3, 6, 9, 12, 15}, {6, 12, 18, 24} (b) STYT9. (a) STYT (b) STYT (c) Disjoint10. (a) {1, 3, 5, 15}, {1, 2, 3, 6, 9, 18} (b) Overlapping (c) STYT11. (a) overlapping sets (b) {a, b, c, d}, {c, d, e, f}(c) {a, b, c, d, e, f, g, h, i} (d) STYT12. (a) {1, 2, 4, 8} (b) {1, 2, 4} (c) Overlapping sets (d) STYT13. (a) {2, 3, 5, 7}, {2, 4, 6, 8, 10} (b) Overlapping sets (c) 1614. (a) {2, 3, 5, 7}, {2, 4, 6, 8} (b) STYT(c) STYT (d) Overlapping sets15. (a) STYT (b) (i) Overlapping sets (ii) No16. (a) STYT (b) STYT 17. (a) {1, 3, 5, 7, 9} (b) 5 (c) EquivalentExercise 1.1Exercise 1.2Show to your teacher.Show to your teacher.Exercise 2.11. Show to your teacher2. (a) 2 (b) 3 (c) 5 (d) 7 (e) 9 (f) 4(g) 11 (h) 14 (i) 21 (j) 170 (k) 85 (l) 23(m) 29 (n) 30 (o) 17 (p) 25 (q) 59 (r) 63(s) 53 (t) 55 (u) 61 (v) 62 (w) 33 ANSWER SHEET

326 Acme Mathematics 83. (a) 10002 (b) 110012 (c) 1010002(d) 1110002 (e) 10110102 (f) 11101102(g) 11110002 (h) 1000110012 (i) 1001110112(j) 1101111002 (k) 10000010112 (l) 111100000024. 11112 5. 100012 6. 12 7. 12 8. 12 9. 010. 1 and 0 11. 0 and 0 12. 1 and 1 13. 110102 and 1040514. 10101002 and 43 15. 84Exercise 2.21. Show to your teacher.2. (a) 86 (b) 58 (c) 67 (d) 69 (e) 117 (f) 551(g) 127 (h) 269 (i) 125 (j) 2586 (k) 3124 (l) 117183. (a) 335 (b) 10005 (c) 10305 (d) 20115 (e) 34305(f) 140035 (g) 1403005 (h) 440005 (i) 3040225 (j) 3044445(k) 1202345 (l) 13421054. (a) 105 (b) 205 (c) 305 (d) 415 (e) 11405(f) 1110102 (g) 11101012 (h) 110000102 (i) 11111012 (j) 1010000110112(k) 10011100002 (l) 110000110102 5. 23156. (a) 101445 (b) 5 (c) 97. (a) STYT (b) STYT (c) 39108. (a) STYT (b) 100101112 (c) 1519. (a) 424015 (b) Rs. 2851 (c) 101100100011210. (a) STYT (b) 54 (c) STYTExercise 2.31. Show to your teacher.2. (a) True (b) False (c) False (d) False3. (a) 54 (b) 4930 (c) 5936 (d) 17144. (a) 54 (b) 59 (c) 320 (d) 12255. (a) 1121 (b) 22063 (c) – 1 127221 6. – 12817 7. 328. (a) 92 (b) 3546 (c) – 354 (d) 6322 9. Show to your teacher. 10. – 932 11. Show to your teacher.

Acme Mathematics 8 327Exercise 2.41. (a) 49 (b) 1799 (c) 15299 (d) 318999 (e) 4599(f) 13 (g) 89 (h) 59 (i) 433 (j) 533(k) 833 (l) 12299 (m) 23399 (n) 53799 (o) 637992. (a) false (b) true (c) true3. (a) 1750 (b) 3190 (c) 19699 (d) 733 (e) 411(f) 41333 (g) 123449999 (h) 44333 4. Show to your teacher.Exercise 2.51. (a) 11 (b) 17 (c) – 2 (g) 7 (j) 1252. Show to your teacher 3. Show to your teacher 4. Show to your teacherExercise 2.61. (a) 2.5× 107 (b) 7 × 109 (c) 1.41 × 1012 (d) 2.73 × 1015 (e) 1.1×1015(f) 3.14 × 1017 (g) 7.32 × 108 (h) 7.89 × 1011 (i) 7 × 10-7 (j) 9 × 10-16(k) 5 × 10–5 (l) 1.8 × 10–82. (a) 200000 (b) 403000000 (c) 38000 (d) 700000000000000(e) 0.000025 (f) 0.00043 (g) 0.000000000567 (h) 1500000000(i) 4931506850 yrs3. (a) 1.5 × 108 km (b) 4.458 × 107 sq. km (c) 1.9967 × 108 km(d) 10-6 sq. m (e) 10-9 cubic m (f) 10-12 sq. km (g) 7.78 × 108 km4. (a) 2.4 × 104 (b) 1.01 × 107 (c) 2.7013 × 10-9 (d) 2.3 × 10–9 (e) 2.42 × 108 (f) 2.95 × 1055. (a) 4 × 103 (b) 9.9 × 106 (c) 3.996 × 10–9 (d) 1.11×105 (e) 7.23 × 10– 116. (a) 108 (b) 3.843 × 105 (c) 1.5 × 1012 (d) 1.25 × 104 (e) 8.33× 10 –3(f) 5 × 10–2 (g) 102Mixed Exercise1. STYT2. (a) 204,800,000 mm (b) 2.048 × 108 nm (c) 2.768 × 10–73. (a) 2400 liter  (b) 2260 liter (c) 3302054. (a) STYT   (b) 1,2,3   (c) 0,1,2,3…9   (d) STYT

328 Acme Mathematics 85. (a) 194   (b) 221   (c) 415 and (110011111)26. (a) B   (b) A   (c) 24267. (a) 11112   (b) 13   (c) 300 + 40 + 6   (d) 1258. (a) Yes   (b) STYT (c) 5 × 10³ m   (d) 23400009. (a) Yes   (b) (101101)2   (c) (11000010)210. (a) Yes, rational   (b) 0.75   (c) (d) STYT   11. (a) 7.5 × 10–³   (b) 3.75 × 10–5   (c) 1512. (a) 32415   (b) 446   (c) (110111110)213. (a) √25   (b) √24 (c) √25 > √2414. STYT 15. (a) rational   (b) 533   (c) STYT16. (a) (iii)   (b) 8.5 × 104   (c) 4 × 10817. (a) No   (b) STYT 18. (a) STYT    (b)43   (c) (d) STYT 19. (a) 45000000 mg   (b) 4.5 × 107   (c) 5 × 10720. (a) (b) STYT (c) (1010101100)221. STYT 22. (a) (b) STYT   (c) 0.00047  (d) 1.3 × 10³23. (a) 10   (b) 1   (c) STYT 24. (a) √9   (b) √10    (c) √10 > √925. (a) 586   (b) (1001001010)226. (a) 4.3689 × 104   (b) (2344224)5   (c)16750Exercise 2.71. (a) 1 : 2 (b) 1 : 4 (c) 1 : 2 (d) 1 : 3 (e) 2 : 5 (f) 1 : 3(g) 1 : 3 (h) 1 : 5 (i) 6 : 7 (j) 5 : 62. (a) 3 : 1 (b) 5 : 1 (c) 1 : 25 (d) 3 : 1 (e) 100 : 1 (f) 4 : 1(g) 5 : 1 (h) 1 : 5 (i) 1 : 3 (j) 3 : 13. (a) 9 : 4 (b) 2 : 1 (c) 4 : 3 (d) 2 : 1 (e) 60:7 (f) 6 : 1(g) 9 : 2 (h) 3 : 1 (i) 7 : 3 (j) 1 : 24. (a) 8 : 7 (b) 3 : 5 (c) 7 : 30 (d) 15 : 4 (e) 5 : 11 (f) 8 : 7(g) 3 : 5 (h) 1 : 4 (i) 15 : 4 (j) 10 : 3 (k) 8 : 5 (l) 2 : 15. (a) 4y5 (b) 5x4 (c) 6z7 (d) 24 : 35 6. 3 : 107. (a) 52 (b) 72 (c) 1 (d) 6008. (a) Rs. 10 and Rs. 5 (b) Rs. 12 and Rs. 4 (c) Rs. 25 and Rs. 100(d) 180 g and 120 g (e) 1000g and 2000g (f) 20 min and 25 min

Acme Mathematics 8 329(g) 5 km and 1 km 9. (a) Rs. 200 and Rs. 300 (b) 280 g and 420 g (c) 60 cm and 15 cm(d) 57 and 76 (e) 156 and 10410. (a) Rs. 5000 (b) Rs. 114 (c) 344 (d) 5511. (a) Rs. 300, Rs. 200 and Rs. 100 (b) 2468, 2468 and 6170 (c) Rs. 600, Rs. 300 and Rs. 10012. (a) 36 and 45 (b) 3 and 2 (c) 15 and 24(d) 40 and 8013. (a) 15 : 1 (b) 15 : 16 (c) 1 : 16 14. (a) 50 yrs and 30 yrs (b) 7 yrs and 1 year (c) 10 yrs and 15 yrs(d) 15 yrs and 20 yrs 15. (a) 8.75 km (b) 2 cm16. (a) 6 cm (b) 8 m 17. 2km, 5km 18. (a) 4 cm (b) 6 cm (c) 0.5 cm19. (a) Rs. 180000, Rs. 45000, Rs. 135000 (b) Rs. 6000, Rs. 3000, Rs. 200020. (a) 1311 (b) 27 (c) 82 : 921. (a) 12 years (b) 41:17 (c) 12 years22. (a) Rs. 12000 (b) Rs. 108000Exercise 2.81. (a) Yes (b) No (c) Yes (d) Yes (e) Yes (f) Yes2. (a) 6 (b) 8 (c) 4 kg (d) 45 m (e) 15 litres (f) 6003. (a) 7 (b) 56 (c) 420 (d) 2000 (e) 20 kg(f) 1200 (g) 1 (h) 6 (i) 44. (a) 9 (b) 30 (c) 25 (d) 21 (e) 25 (f) 2485. (a) 250 (b) 4 (c) 9 (d) 2 (e) 24 (f) 86. (a) 59.5 litres (b) 90 (c) Rs. 228 (d) 213 (e) 736.98 km 7. (a) 6 (b) 8 8. (a)274 (b) 12 (c) 25 days9. (a) A=Rs. 67500, B= Rs. 101250, C=Rs. 101250(b) A=Rs. 22500, B= Rs. 33750, C=Rs. 33750Exercise 2.91. (a) 0.44% (b) 7.75% 2. (a) 1.46% (b) 9.35% 3. (a) Rs. 3913.04 (b) Rs. 1020.404. (a) Rs. 4750 (b) Rs. 668.75 5. (a) Rs. 200 (b) Rs. 1888.89 6. (a) Rs. 425 (b) Rs. 72 (c) Rs. 4007. (a) Profit,1.49% (b) Rs. 108, 17.65% 8. (a) Rs. 20 (b) Rs. 22 9. (a) Rs. 1920 (b) 6.25%10. (a) Rs 1575 (b) Rs 2047.50 11. Profit, 55.85%

330 Acme Mathematics 812. (a) Rs. 181.44 (b) Rs. 3420 (c) Rs. 600(d) Rs. 4620 and Rs. 4400 (e) Rs. 88013. (a) 0.64%, Loss (b) Profit, 6.5% 14. (a) Rs. 704000 (b) Rs. 7739 15. (a) Profit, Rs. 150 (b) Profit, Rs. 44016. (a) Rs. 80000 (b) 900 (c) Rs. 87480 (d) Rs. 97.20Exercise 2.101. (a) Rs. 800, 20% (b) Rs. 4000, 20% (c) Rs. 6000, 25% 2. (a) Rs. 1000, 20% (b) Rs. 20000, 25% (c) Rs. 2500, 25%3. (a) Rs. 5200 (b) Rs. 6500 (c) Rs. 210004. (a) Rs. 4705.88 (b) Rs. 6250 (c) Rs. 100005. (a) Rs. 1500 (b) 8% (c) Rs. 729 (d) Rs. 19350.656. (a) Rs. 24, Rs. 136 (b) Rs. 360, Rs. 4140 7. (a) Rs. 4000 (b) Rs. 1200 (c) Rs. 450 (d) Rs. 75608. (a) Rs. 6000 (b) Rs. 10009. (a) Profit, 2% (b) 17% (c) 12.5% (d) 14% 10. (a) Rs. 531.96 (b) Rs. 100Mixed Exercise1. (a) STYT (b) Rs 150 (c) Rs 28502. (a) Rs 2500 (b) Rs 800, Rs 15,200 (c) Rs. 138183. (a) STYT (b) Rs 1,700   (c) profit, Rs 2004 (a) 5% (b) 4.83%    (c) 1.45 × 106   (d) Rs 335. (a) STYT    (b) Rs 5,000    (c) Rs 37,5006. (a) STYT (b) Rs 477.27  (c) Rs 24,18.187. (a) 9:1   (b) Rs 150  (c) Rs 122.228. (a) STYT    (b) 10%   (c) Rs 7,105.229. (a) STYT    (b) Rs 3,600   (c) Rs 32,000 (d) 2410. (a) Rs 120   (b) 450   (c) 10%   (d) Profit, 12.5%11. (a) STYT    (b) Rs 6,688   (c) Rs 6,150

Acme Mathematics 8 331Exercise 2.111. (a) Rs. 620 (b) Rs. 1020 (c) Rs. 33 (d) Rs. 250 (e) Rs. 250(f) 54 days (g) 33men2. (a) 45 (b) 266.67 kg (c) 80 kg (d) 18.75 days (e) 2.55 hours(f) 10 hours and 3 hours 3. (a) 8 (b) 250 (c) 184. (a) 3 (b) 6 5. (a) 3 (b) Rs. 120 (c) Rs. 420(d) Rs 150 (e) 75 6. (a) 18 (b) 10 (c) 30 (d) 20Exercise 2.121. (a) Rs 600 (b) Rs 1200 (c) Rs 30000 (d) Rs. 6000(e) Rs 250 (f) Rs 50 (g) Rs 312.50 (h) Rs. 219.372. (a) Rs 320 (b) Rs 3600 (c) Rs. 75 (d) Rs. 1603. (a) Rs 1000, Rs 1200 (b) Rs. 4000, Rs. 6000(c) Rs 24000, Rs 30000 4. (a) 10% (b) 25% (c) 10%5. (a) 2 yrs (b) 2 yrs (c) 5 yrs6. (a) Rs 130000 (b) Rs. 21888 (c) Rs. 10250 (d) Rs. 295007. (a) Rs 3050 (b) Rs. 3333.33 8. (a) 15% (b) 8%9. (a) 3.7 years (b) 5 years 10. (a) Rs 1728, 8yrs (b) Rs 432, 4 years11. (a) Rs 672 (b) Rs. 462 12. (a) 8%, 5 years (b) 4 years(c) Rs 4800, 2 years 13. (a) 4.35 yrs (b) 1.36 yrs 14. (a) Rs 500 (b) Rs. 5000 15. (a) Rs. 4500000 (b) Rs. 9500000(c) Rs. 950000016. (a) STYT (b) Rs. 3000 (c) 12.5%17. (a) STYT (b) STYT (c) Rs. 1584 (d) Rs. 11484Mixed Exercise1. (a)114 (b)12 work (c)67 work2. (a) 6.5%   (b) Rs 76,480   (c) Subodh = Rs 24,000, Arun = Rs 40,0003. (a) 12 days    (b) Rs.65,0004. (a) STYT    (b) Rs.1,600    (c) Rs.1,5205. (a) 8%  (b) Rs.72000  (c) Rs.1200006. (a) Rs.40,000 (b) Rs.6,000 (c) 3 years7. (a) STYT    (b) Rs.35,000   (c) Rs.5040 and Rs.7,5608. (a) STYT (b) Rs.2400000   (c) Rs.40,00000 9. (a) Rs 64000 (b) Rs 16000  (c) 10%10. (a) STYT (b) STYT    (c) Rs.2400   (d) 10%

332 Acme Mathematics 811. (a) Rs.70 per packet   (b) Rs.1050   (c) 30 packets12. (a) Rs.70   (b) Rs.50   (c) (i) Rs.3360   (ii) Rs.8960Exercise 3.11. (a) BD = 7.93 cm, BC = 11.53 cm (b) 138 cm22. (a) 173.2 cm2 (b) 83.13 cm2 3. (a) 6.92 cm2 (b) 18 cm 4. (a) 48 cm2 (b) 12 cm 5. (a) 6 cm2 (b) 960 cm2 (c) 532.25 cm26. (a) 36 cm2 (b) 160 cm2 (c) 50 cm27. (a) 24 cm2 (b) 280 cm2 (c) 192 cm2 (d) 96 cm2 (e) 40 cm2(f) 20 cm2 (g) 32.5 cm2 (h) 28 cm2 (i) 60 cm2 (j) 84 cm2(k) 16 cm2 (l) 30 cm28. (a) 63.58 cm2 (b) 56.94 cm29. (a) 68 cm2 (b) 84 cm2 (c) 45 cm2 (d) 30 cm2 (e) 26.25 cm2(f) 18 cm2 (g) 21 cm2 (h) 44 cm2 (i) 27.5 cm210. (a) 5.9 Dhur, 14.58 Dhur, 1.86 Dhur (b) 2.83 Aana, 6.79 Aana, 1.98 AanaExercise 3.21. (a) 1256 cm2 (b) 3846.5 cm2 (c) 254.34 cm2 (d) 200.96 m22. (a) 615.44 cm2 (b) 1962.5 cm2 (c) 122.65 cm2 (d) 12.56 cm23. (a) 14 cm, 43.96 cm, 153.86 cm2 (b) 10 cm, 62.8 cm, 314 cm2(c) 97.45 cm, 194.90 cm, 29819 cm2 (d) 7cm, 14cm, 44cm(e) 29.7 cm,59.42 cm, 186.5 cm4. 3881.04 m2 5. 7471.74 m2 6. (a) 168.56 cm2 (b) 58.875 cm2(c) 69.66 cm2 (d) 168.56 cm2 (e) 12.56 cm2 (f) 100.48 cm27. 300 8. (a) 32.26 cm2 (b) 44.13 ft29. (a) 42.14 cm2 (b) 42.14 cm2 (c) 42.14 cm2 (d) 11.75 cm2(e) 14.13 cm2 (f) 115.39 cm2 10. 314 m2Mixed Exercise1. (a) STYT (b) 192 cm² (c) 96 cm²   (d) Rs.3122. (a) 10 cm (b) 12 cm   (c) STYT    (d) 201cm²3. (a) STYT (b) 300 m   (c) 3338 m² (d) 1500 m²4. (a) STYT (b) 8 cm   (c) 48 cm²   (d) 32 cm5. (a) 7 cm (b) 154 cm² (c) 44 cm (d) 660 cm

Acme Mathematics 8 3336. (a) STYT (b) 6.25 m²   (c) 1043.75 m²7. (a) 81.27 cm²   (b) 200.96 m²   (c) 8127:200968. (a) 66 cm   (b) 792 cm   (c) 16.5 cm9. (a) STYT   (b) STYT   (c) (i) 4 cm  (ii) 25.12 cm10. (a) STYT   (b) 12 cm²   (c) 96 cm²11. (a) 14 m  (b) 88 m  (c) Rs.22000Exercise 4.11. (a) x6 (b) x7 (c) – x2 9 (d) (–3y)7(e) 1 (f) 5p3 (g) – 4a (h) 1x3 2. (a) x12 (b) 64125 (c) y–9 (d) a20b8(e) 4096x12531441z12 (f) x8y12z2016b4 (g)x664y6 (h) –1 (i)–2783. (a) 2x5 – 8 (b) x8 – x3 (c) x (d) x2y2(e) 1a2b (f) 14. (a) 0 (b) 0 (c) 43 , 51845. (a) 7 (b) 9 (c) 34 (d) 10 (e) 2 (f) 2 6. (a) 1 (b) 1 (c) 1 (d) 1 (e) 1 (f) 1Mixed Exercise1. (a) Barsha (b) STYT 2. (a) 0 (b) (113)²(m+n+l)3. (a) 6 (b) 14. (a) 5 (b) 9 4 (c) 15. (a) 1   (b) 64a³b6 (c) 16. (a) xa+b (b) xᵃᵇ and 1 (c) 17. (a) -2 (b) 48. (a) 0 (b) 19. STYT10. (a) 1   (b) 1 11. (a) 4x³ (b) 112. (a) 0 (b) x²

334 Acme Mathematics 813. (a) 35a (b) 114. (a) a5 (b) 115. (a) 0 (b) 1Exercise 4.21. (a) 2 (b) a2b2 (c) 21ab (d) 5x2 (e) 3abc (f) 12. (a) 3 × x × y (b) – 3 × 5 × x × y × y (c) 2×2×2×3×5×x×x×x×y×y×y×z(d) 5x(2 – x) (e) a(a – 2) (f) – 4a(2 – 3b)(g) 3(x – 3) (h) –5x2(4x – 5) (i) 3a2b2(2a – 3b)(j) 2ab(ax – 2cz) (k) –x3y(x + 1) (l) 12x2y3(2 – 3xy)3. (a) (a + 3) (x + 3) (b) (x + 3) (x – 2) (c) (a + 4) (3 – b)(d) (m + n) (a + b) 4. (a) 4(x2 – y2 + z2) (b) x(x2 + x + 1) (c) 3(x2 + 2x + 3)(d) 5(4 – 2x + x2) (e) 4x2(4x2 – 5x + 3) (f) y(y2 – 2y – 1) (g) 2y2(y – 3y2 – 5) (h) 3xy(5xy + 4y + 12x) (i) 6x2y2(2xy2 – 3x2y + 4) (j) x(2xy – 3y3 + 5yz + 4)5. (a) (2x + 1) (y + 5) (b) (y + 3) (x + y) (c) (x + 1) (y + 1)(d) (y2 + r2) (x + z) (e) (2y + 1) (5x + 1) (f) (a + 5) (x − y)(g) (4x2 − 5) (x + 2) (h) (zy + x) (zx + y) (i) (x − y) (x − z)(j) (3a + c) (a + 2b)Exercise 4.31. (a) (x + 5) (x – 5) (b) (2x + 1) (2x – 1) (c) (7p + q) (7p – q)(d) (4x + 5y) (4x – 5y) (e) (a – b + 3) (a + b – 3) (f) (x2+ 16) (x + 4) (x – 4)(g) 5x(x – 2y) (x + 2y) (h) (x2 + y2) (x + y) (x – y) (i) (b – c + a) (b – c – a) 2. (a) 2xz (b) –8a (c) 20y (d) –2x (e) 24xy (f) 20ab (g) 1 (h) 1 (i) 25y2 (j) 4 (k) x2 (l) a2b23. (a) (x + 4)2 (b) (x – 6)2 (c) (2x + 1)2(d) (8a – 3b)2 (e) (4x + 5y)2 (f) (a – 11b)2(g) (12 + x)2 (h) (11 – 3x)2 (i) (7a + 2b)2(j) (5a – 8b)2 (k) (y + 3)2 (l) (x – 4)2(m) (a – 3)2 (n) (a + 4)2 (o) (x – 3)24. (a) 2,400 (b) 14,200 (c) 5,000 (d) 9,900 (e) 9,800 (f) 2,55,000(g) 9991 (h) 8091 (i) 80.99

Acme Mathematics 8 3355. (a) 12 cm2 (b) 3x2 cm2 (c) (16y2 – 4x2) cm26. (a) S = 27 cm, D = 9 cm, A = 763 cm2 (b) S = 12 m, D = 4 m, A = 150. 72 m2(c) S = 10.5 cm, D = 3.5 cm, A = 115.4 cm2Exercise 4.41. (a) (a – 3) (a – 3) (b) (a – 36) (a – 1) (c) (a – 13) (a – 3)(d) (a – 5) (a – 1) (e) (a + 3) (a – 2) (f) (a + 5) (a – 3) (g) (a + 4b) (a – 3b) (h) (a + 5b) (a – 4b) (i) (a – 7) (a + 6) (j) (a – 8) (a + 7) (k) (a – 16b) (a + 4b) (l) (a – 5b) (a + 3b)2. (a) (2y + 1) (y + 1) (b) (y + 1) (2y + 11) (c) (y + 4) (2y + 5)(d) (4y + 3) (y + 3) (e) (4y + 1) (3y + 2) (f) (5y – 8) (y – 2)(g) (7y – 1) (y – 7) (h) (3y – 4) (3y – 4) (i) (3y + 20z) (y – z)(j) (10y – z) (y + 6z) (k) (y + 2z) (2y – z) (l) (y + 1) (3y – 4)(m) (6y + 5z) (y – 2z) (n) (3y + 2) (y – 1) (o) (3y – 4z) (5y + 2z)(p) (y + 1) (2y – 5)Exercise 4.51. (a) 4xy (b) 2a (c) 5a2b2 (d) 5x2(e) 5 (f) 7xyz2. (a) 2x (b) 3x2 (c) (x – 2) (d) (x + 4)(e) (a + b) (f) (x + 5) (g) x(x2 + y) (h) (x + 3)3. (a) (x + 2) (b) (x + 5) (c) (x – 7) (d) (2x – y)(e) (x – 3) (f) (x – 4) (g) (x + 4) (h) (x + 1)(i) (x – 2) (j) (x – 2) (k) (x + 3)4. (a) x(x + 2) (b) x(3x – 2) (c) x(x –7) Exercise 4.61. (a) 4x2y3 (b) 84x2 (c) x3y2 (d) x4y (y – x)(e) 14 (x – y)2 (f) 6x2 (x + 2) (g) (x + 2) (x + 3) (x – 1)(h) (x – 2) (x – 6) (x + 1) (i) (x + 1) (x + 2) (x – 2)2. (a) LCM = (x – 1)2 (b) LCM =(x – 2)2 (c) LCM= (y + 3x)2(d) LCM= (x + 4)2 (e) LCM= (5x + y)2 (f) LCM= (7x – 4y)23. (a) 3x (x – 1) (x – 2) (b) 6(x + 1) (x – 1) (x + 2)(c) (x – 2)2 (d) (2x – 3) (3x – 4)(e) (x + 2) (x + 1) (x – 2) (f) (x – 5) (x + 5) (x – 4) (g) (x + 3) (x + 2) (x – 2) (h) (x – 11) (x + 2) (x + 3)4. (a) HCF =(x–1) and LCM=(x + 1) (x – 1)2 (b) HCF =(x+y) and LCM=2(x – y) (x + y)

336 Acme Mathematics 8(c) HCF =(x–5) and LCM=(x + 5) (x – 5) (x – 3)(d) HCF =(x+2) and LCM=2(x + 2) (x – 1) (x – 2)(e) HCF =(x+2) and LCM=(x + 2) (x – 2) (2x – 1)(f) HCF =(x+4) and LCM=(x + 4) (x – 2) (x – 1)(g) HCF =(x+1) and LCM=(x + 1) (x + 3) (x + 2)(h) HCF =(x+2) and LCM=(x + 2) (x + 4) (x + 5)5. (a) x(x + 2) (x + 1) (x – 3) (b) x(2x + 3) (3x – 2) (x – 2) (3x + 1)(c) x(x – 7) (x + 2) (x + 6) Exercise 4.71. & 2. Show to your teacher.3. (a) y2x (b) x2y22 (c) y2x (d) y33x3(e) a – b (f) 12 (g) x + 2 (h) x (i) x – 2x4. (a) x + 2x (b) x + 74 (c) 2x + 1x – 3 (d) 2x – 1y (e) 2x x + 1(f) x + y x – 2y (g) 3 + a6 – a (h) x + 4x – 4 (i) x – 8x – 3 (j) – x2y25. (a) 1 (b) – 5 (c) – 7 (d) 3 (e) +2, –2 (f) + 3, – 36. Show to your teacherExercise 4.81. (a) x + 2y4x – 3y (b) 4 – xx – 1 (c) 1x – y (d) x2 + y2(x + y)22. (a) x – y (b) 7x – y2x + 3y (c) 4(x + y)x – y (d) 1x – 23. (a) 2xx2 – 1 (b) x2 + y2+x2 – y2 (c) 10x – 21x2 – 4 (d) x2(x + y)2(e) 8x – 8x(x –2) (f) 3112(x – 2)4. (a) x + 2x + 4 (b) x2 + 2x – 10(x + 1)(x – 2) (c) x2 + 5x + 3(x – 1)(x + 3)(d) x2 – 3x – 2x(x + 1)(x– 2) (e) – 12x – 25x(x – 5)(x + 5) (f) 4x2 + 7x – 122(x – 1)(2x – 1)(g) 2 (2x+1)(3x + 4)(x – 2) (h) x(x – 2)(x – 3) (i) 2x2 + xy x2 – y2(j) 8xy + 3y2x2 – y2 (k) a(x + 4)(2 – x)2 (l) 3x2 – 2x + 1(x – 1)(x2 + 1)

Acme Mathematics 8 337Exercise 4.91. Show to your teacher.2. (a) 3(x – 2)2 (b) 1 (c) xyz3 (d) b2yzax3. (a) 1 (b) (x – 1) (x – 2)3(x2 + 2) (c) (x – 5)(3x + 2)7x (d) x(x + 2)6(x – 3) 4. (a) y (b) −1 (c) 2axz2 (d) 8x3z2 (e) bc36a4x3y6z (f) x2(x + 2)5. (a) (x – 3)(x + 2) (b) 8x(x + 2)(x + 3) (c) (x + 4)(x – 5) (d) 1(e) x2y2 (f) 16. (a) (x + 2)(x – 1) (b) (x + 6)(x – 3) (c) 2(x + 1)(x +4) (d) (x + 5)(x – 1)(e) x – 1x + 5 (f) x + 1x – 1 (g) x + 1x – 27. (a) 33x50 (b) 2x(x2 + 1)(x – 1)2 (x + 1) (x – 2) (c) 28. (a) x3 + x2 – 2x + 3x2 – 3x (b) x3 – x2 + 6x – 3x2 – 3x (c) x3 – x2 + 2x – 2x2 – 3x (d) x3 + 2xx2 – 4x + 3Mixed Exercise1. (a) (x²+2) (x²-2) (b) (x− 4) (2x+ 5) (c) (3 − x) (3 + x) (9 + x²)(d) (a − b) (x − y) (e) (a + 2b) (4a − 3b)2. (a) (a − b) (a + b) (b) 2100 m²3. (a) a² + 6a + 9 (b) length = (x + 3)m and breadth = (x − 5)m4. (a) 16 (b) (x − y) (x + 1)5. (a) 19 and 25   (b) − 8 a6. (a) (x − 5) (x − 1) and x (x + 5) (x − 5) (b) x (x − 5)(x − 1)(x + 5)7. (a) STYT (b) 3 (c) (x³ + 2) (x² + x + 1)8. (a) (ab − cd) cm²    (b) STYT9. (a) x2y  (b) (3x − 4y) (3x + 4y)   (c) 8x10. (a) −3 and −2   (b) (x − 3)(x − 2)11. (a) 3a(a + 2b) and (x + 4) (x − 2)   (b) x² − 412. (a) HCF = (x − 2) (b) (x+3)2(x−3)13. (a) (x3 − x) → Numerator and x² + x → denominator   (b) (x − 1)

338 Acme Mathematics 814. (a) (a + b)(a − b) and (x² − y²)   (b) x–yy15. (a) a² + 2ab + b² (b) (x + 4)(x + 4)16. (a) STYT    (b) 7 and 917. (a) (x − 1)(x − 2) (x − 3) (b) STYT18. (a) xyx+y (b) STYT19. (a) STYT (b) (x – 1) (c) 1 or 320. (a)x+6x+3 (b) (x – 3)(x + 3) (x + 6)21. (a) (x – y – 11)(x – y + 2) (b) a+2a–122. (a) Length = (x + 3) and Breadth = (x + 1) (b) STYT (c) (x² + 4x + 3) sq. unit23. (a) 220 cm² (b) STYTExercise 4.101. (a) – 34 (b) – 2312 (c) 0 (d) 5 (e) – 2116 (f) – 6 (g) 2 (h) 0 (i) 2912 (j) 4 2. (a) 4 (b) 2 (c) – 5 (d) 8 (e) 8 (f) 32Exercise 4.111. Show to your teacher.2. (a) 1 and 3 (b) 3 and 1 (c) 1 and –1 (d) 6 and 1(e) –1 and 5 (f) 2 and 5 (g) 3 and 4 (h) 6 and 10 3. (a) 2 and 6 (b) 6 m and 2 m (c) 5 gel pen and 17 fountain pen (d) 14 and 6 (e) 25 and 10 (f) 7° and 2° (g) 6° and 3°(h) 10 m and 2 m (i) 9 and 11Exercise 4.121. (a) 7, – 7 (b) 0, 3 (c) 0, –1 (d) 0, –5 (e) 0, 3 (f) 5, –5 (g) 1, –12. (a) 2, –1 (b) 4, –7 (c) –3 (d) 10 (e) 5 (f) 8, –4 (g) –3, –93. (a) 0, – 83 (b) 0, 72 (c) –1, – 12 (d) 12,14 (e) 53 ,– 13(f) 1, – 95 (g) – 13 ,– 43 (h) 52,– 23 (i) 74,– 43 (j) 57 ,– 23

Acme Mathematics 8 3394. (a) 1, –5 (b) 0, 3 (c) 0, – 6 (d) 7, –1(e) 73 ,– 53 (f) 215 ,– 2215 (g) 2, 13 (h) 2 3 , –2 35. (a) (x2–16) m2 , x2–16=84, 14 m, 6 m (b) (2x2–x–15) m2 , 2x2–x–15=765, 45 m , 17 m 6. 26.9 mMixed Exercise1. (a) STYT (b) x = 3, y = 12. (a) x = 3, y = 3 (b) 1x3. (a) x = 2, - 2 (b) x = 3, y = 24. (a) x = 4, y = 5 (b) x = –1 or –135. (a) STYT (b) x = 6, y = 16. (a) STYT (b) x = 3, y = 27. (a) 4x + 3y = 230, 2x=3y + 70, x (pen) = Rs.50, y (pencil) = Rs.108. (a) +5, –5 (b) 3, –1Exercise 5.11. Show to your teacher.2. (a) 70°, 110°, 70° (b) 70°, 128°, 128° (c) 100°, 80° (d) 30° (e) 60° (f) 15°(g) 32.7° (h) 36° (i) 12°(j) 60°, 20°, 160°3. (a) 102.8°, 77°, 51.4° (b) 46.7°, 50°, 40° (c) 32°, 45°(d) 89°, 29.7°, 29.7°, 34.7° (e) 40°, 70°, 70°, 70° (f) 80°, 125°, 55°4. (a) 27° (b) 17° (c) 6° (d) 7.5°5. (a) 78° (b) 10° (c) 60° (d) 22° 6. 31.3°7. (a) 67° (b) 23°8. (a) a + b + c = 180° (b) 90°9. (a) STYT (b) 113°10. (a) V.O.A (b) STYT (c) x = 17°, y = 51°11. (a) STYT (b) 144° and 36°12. (a) 90° (b) 100° (c) 110°Exercise 5.21. (a) 70° (b) 30° (c) 150° (d) 50° (e) 75° (f) 50°

340 Acme Mathematics 82. (a) Yes (b) No (c) Yes (d) No (e) Yes (f) Yes 3. (a) a = 60°, b = 60°, x = 60°, y = 120°, z = 120° (b) a = 45°, x = 70°, y = 65°(c) 46.7° (d) x = 60°, y = 50°, z = 70°(e) a = 70°, b = 110° (f) x = 50°, y = 60°, a = 70°, b = 70°(g) x = 50° (h) a = 35°, x = 24°, y = 24°, z = 70°(i) x = 90°, y = 30°, z = 60° (j) x = 40°, y = 70°, z = 70°, a = 70°, b = 70°(k) a =60°, x = 30°, y = 120° (l) a = 20°, b = 35°, x = 15°(m) a = 125°, b = 60°, x = 60°, y = 125° (n) x = 30.7°, b = 137.3°, a = 75°, y = 62.3°, z = 75°(o) x = 60°, z = 50°, b = 22°, a = 50°, y = 130°4. (a) STYT (b) x = 140°, z = 40°, y = 40°,5. (a) STYT (b) Corresponding angles (c) 120°6. (a) STYT (b) STYT (c) 55°7. (a) 180° (b) ∠PQR (c) x = 40°, y = 45°8. (a) ∠CRP (b)180°9. (a) STYT (b) a = 140°, x = 70°10. (a) STYT (b) STYT (c) STYT11. (a) STYT (b) 10° (c) 20°, 20°12. (a) STYT (b) 35°13. (a) ∠EGB and ∠EHD (b) Yes (c) x = 30°, y = 30°14. (a) Corresponding angles (b) x = 110°, y = 110° (c) z = 70°15. (a) STYT (b) x = 20° (c) 110°16. (a) x = 48°, y = 120° (b) y = 70°, z = 60°Exercise 5.31. (a) 49° (b) x = 90°, y = 90° (c) 30°(d) x = 90°, y = 120° (e) x = 65°, y = 65° (f) x = 22°(g) x = 70°, y = 60° (h) x = 60°, y = 120° (i) x = 31°, y = 60°, a = 29°(j) x = 20° and y = 70° (k) x = 45°, y = 90° (l) x=43.3°,y = 43.3°(m) a = 30°, b = 70°, c = 80° (n) a = 40°, b = 140°, c = 90° (o) a = 40°, x = 40°2. 36°, 72°, 72° 3. 65°, 95° 4. STYT 5. STYT 6. STYT7. (a) 60° (b) 60° 8. (a) 180° (b) 90° 9. (a) 20° (b) STYT10. (a) 60° (b) STYT 11. (a) (ii) (b) x= 70°, y= 60°, z= 50° (c) STYT

Acme Mathematics 8 341Exercise 5.41. (a) x = 80°, y = 100°, z = 80° (b) x = 20°, y = 80°, z = 80° (c) x =120°, y =120°, z = 60°(d) x = 70°, y = 110°, z = 110° (e) x = 25°, y = 20°, z = 70° (f) x = 40°, y = 100°, z = 40°(g) x = 4°, y = 172°, z = 172° (h) x = 110°, y = 60°, z = 70° (i) x = 110°, y = 70°, z = 70°2. (a) x = 5cm, y = 4cm (b) x = 4cm, y = 5cm (c) x = 2cm, y = 8cm3. (a) y = 7cm, x = 6cm (b) x = 4cm, y = 9cm (c) x = 4cm4.-6. STYT 7. (a) STYT (b) x = 15, y = 50° 8. STYT9. (a) x = 5cm, y = 8.54cm and AC= 12 cm, BD=6cm(b) x = 7.1cm, y = 12cm and AC= 17 cm, BD=10cmExercise 5.5Show to your teacherExercise 5.61. (a) 36°, 72°, 108°, 144° (b) 40°, 80°, 100°, 140° 2. (a) 120° (b) 43° (c) 100° (d) 95° (e) 30° (f) 90°(g) 70° (h) 130° (i) 95°3. (a) x = 60°, y = 120° (b) x = 60°, y = 120° (c) x = 135°, y = 45°(d) x = 45°, y = 90° (e) x = 72°, y = 108° (f) x = 36°, y = 144°4. (a) 5 (b) 108° (c) 72° Exercise 5.71. Show to your teacher 2. Show to your teacher3. (a) 3 cm (b) x = 2.5 cm 4. 3 cm5. 70°, 70°, 50°, 4 cm and 6 cm 6. 90° 7. 40°Exercise 5.81. (a) x = 16 cm, y = 20 cm (b) x = 53°, y = 4 cm (c) x = 80°, y = 15 cm(d) x = 2.3 cm, y = 5.7 cm (e) x = 5.3 cm (f) x = 5.6 cm, y = 9 cm Mixed Exercise1. (a) ∠EAB (b) 38° (c) 127°2. (a) STYT (b) 12° (c) 48°3. (a) STYT (b) STYT 4. (a) STYT (b) 290° (c) 15°5. (a) STYT (b) STYT (c) STYT

342 Acme Mathematics 86. (a) STYT (b) x = 70°, y = 60°7. (a) V.O.A (b) 110° (c) 60°8. (a) ∠EHD (b) 25° (c) 40°9. (a) Alternate angle (b) 40°10. (a) ASA, x = 4 (b) STYT11. (a) 180° (b) 90° (c) Side AB12. (a) ∠MFC (b) 70° (c) 125°13. (a) STYT (b) STYT14. (a) STYT (b) 40° (c) 80°15. (a) STYT (b) STYT16. (a) STYT (b) STYT17. (a) STYT (b) STYT18. (a) ∠CBD (b) 103° (c) STYT19. (a) STYT (b) STYT20. (a) STYT (b) STYT (c) 31 unit21. (a) 45° (b) 50°, 100° (c) STYT22. (a) STYT (b) 4 cm (c) 8 cm23. (a) STYT (b) STYT (c) x = 27 cm, y = 16 cm24. (a) 108° (b) STYT25. (a) STYT (b) STYT Exercise 5.9Show to your teacherExercise 5.101. (a) 5 units (b) 3.6 units (c) 13.45 units (d) 4 units 2. (a) 8 units (b) 17 units (c) 15 units 3. (a) 7.6 units (b) 12.8 units(c) 12 units (d) 10 units (e) 15 units (f) 5.8 units 4. 6 units, 9.49 units, 9.49 units. It is isosceles triangle.5. 4.47 units, No 6. 5.65 units7. (a) Isosceles (b) Scalene (c) Isosceles (d) Scalene8. - 10. Show to your teacher 11. (a) 7 or – 1 (b) 0 or 16 (c) 1 or 3 12. STYT13. (a) STYT (b) 8m

Acme Mathematics 8 343Exercise 5.11 to Exercise 5.17Show to your teacher.Mixed Exercise1. (a) STYT (b) ±2√62. (a) STYT (b) A'(3, –2), B'(4, –5), C'(–2, –3)3. (a) STYT (b) ±3√24. (a) North direction (b) 3-digits (c) 240°5. (a) STYT (b) M'(5, 2) and N'(–2, –1)6. (a) STYT (b) STYT (c) A'(1, –2), B'(5, –2), C'(3, –4)7. (a) STYT (b) P'(–2, 3), Q'(–5, 2), R'(–3, –2) (c) (d) STYT 8. (a) √(a² + b²) units (b) 240° (c) STYT 9. (a) STYT (b) 115° (c) A'(–5, –4), B'(–3, 6), C'(0, 4)10. (a) STYT (b) P'(5, –4), Q'(6, –7), R'(9, 1) (c) 150°11. (a) P'(x + a, y – b) (b) STYT 12. (a) A'(–3, 6), B'(2, 4), C'(–5, 1) (b) STYT 13. (a) 113° (b) A'(0, 6), B'(3, 7), C'(1, 1)14. (a) A'(–1, 1), B'(–3, 1), C'(–3, 4) (b) STYT (c) 6 units 15. (a) 13 (b) P'(–3, 4), Q'(–7, 3), R'(–4, 3) (c) STYT 16. (a) 240° (b) STYT (c) 45°, 60°, 75°Exercise 6.11-4. Show to your teacher.5. (a) Subjects Social Studies English Mathematics Nepali ScienceMarks Obtained 72 62 90 60 76 (b) Subjects Mathematics English Nepali Social Studies ScienceMarks Obtained 90 60 45 37.5 67.5 (c) Item Paper Printing Binding Royalty Misc.Expenditure (in Rs.) 36 24 18 12 306. (a) (i) Rs. 3600 (ii) 108° (iii) Rs. 1600 (iv) 5:3 (b) (i) 280 (ii) 120 (iii) 2:1 (iv) 900

344 Acme Mathematics 8Exercise 6.21. (a) 4.5 (b) 10 (c) 56 (d) 7 (e) 210.75 (f) 72. Rs. 24333.33 3. 15 4. 72 5. (a) No (b) Rs 20006. No 7. (a) 19 kg (b) 38 kg 8. (a) Rs 87500 (b) STYT9. (a) 12 (b) 85 (c) 1110. (a) 44 (b) 14 (c) 25 (d) 6 (e) 10.5 (f) 9Exercise 6.31. 6, mean and median are equal 2. 58 and 55 3. 34.5 and 34.5 4. 21 and 245. (a) 15 (b) below →4, above →4 6. 70 7. (a) 19kg (b) 19kgExercise 6.41. (a) 37 kg (b) 40 kg (c) 39 kg2. 2 children 3. (a) 2 (b) 6 (c) 34. 5 accidents per day 5. 1Mixed Exercise1. (a) 152 cm (b) 150 cm2. (a) 15, above → 4, below → 4  (b) 153. (a) Maths = 300, Science = 220 and Nepali = 200 students.4. (a) 42 marks (b) 41.65. (a) Rs 2500 (b) STYT6. (a) 50 (b) STYT7. (a) 30.8   (b) 458. (a) STYT   (b) 709. (a) STYT (b) Rs 200010. (a) 2020 (b) STYT11. (a) 720 (b) 160   (c) Class – 812. (a) 120° (b) 6013. (a) Nepali → 144, Science → 76, Maths → 108, Social → 152 (b) 7614. (a) Rs 10800 (b) STYT