64 Perfect Mathematics Class 8 a) Find the cost price of the mobile for Sailendra. b) Find the cost price of the mobile for Sunita. Solution: a) Let the cost price of the mobile for Sailendra be Rs. x Now, CP = SP – Profit or, x = Rs. 6,750 – 25% of x or, x = Rs. 6,750 – 25 100 × x or, x = Rs. 6,750 – x 4 or, x + x 4 = Rs. 6 ,750 or, 5x 4 = Rs. 6,750 or, x = Rs.6,750 × 4 5 or, x = Rs. 5,400 ⸫ CP of Sailendra = Rs. 5,400 b) Again, CP of Sailendra = SP of Sunita = 5,400 Let CP of Sunita be y. Now, CP = SP + Loss y = Rs. 5,400 + 10% of y or, y = Rs. 5,400 + 10 100 × y or, y = Rs. 5,400 + y 10 or, y – y 10 = Rs. 5,400 or, 9y 10 = Rs. 5,400 or, y = Rs.5,400 × 10 9 or, y = Rs. 6,000 ⸫ C.P of Sunita is Rs.6,000. Example 7: A milkman bought 20 litres of milk at Rs. 87 per litre and 40 litres of milk at Rs. 54 per litre. He mixed them together and sold at Rs.80 per litre. Find his profit or loss percent.
Percentage 65 Solution: Here, cost of the first 20 litres of milk = Rs.87 × 20 = Rs. 1740 Cost of the next 40 litres of milk = Rs.54 × 40 = Rs. 2160 Total cost price (CP) = Rs.1740 + Rs. 2160 = Rs. 3900 When he mixed both kinds of milk, the amount of mixture = 20 litres + 40 litres = 60 litres Selling price of the mixture (SP) = Rs. 80 × 60 = Rs. 4800 Since selling price > cost price, there is profit. \ Profit = SP – CP = Rs.4800 – Rs.3900 = Rs.900 Now, Profit percent = Profit CP × 100% = Rs.900 Rs.3900 × 100% = 900 39 % = 300 13 % = 23 1 13% Hence, his profit percent is 23 1 13%. Example 8: A man sold two bicycles at Rs.3960 each. If he gained 10% on one and lost 10% on the other, find the total gain or loss percentage he made. Solution: Here, Selling price of both bicycles = Rs.3960 × 2 = Rs.7920 As a bicycle was sold at 10% profit, When SP is Rs.110, CP is Rs. 100 When SP is Re.1, CP is Rs. 100 110 When SP is Rs.3960, CP = Rs. 100 110 × 3960 = Rs. 3600 Again as another bicycle was sold at 10% loss, When SP is Rs.90, CP = Rs.100 When SP is Re.1, CP is Rs. 100 90 When SP is Rs.3960, CP = 100 90 × 3960 = Rs.4400 Total cost price of both bicycles = Rs.3600 + Rs. 4400 = Rs. 8000 Since, SP < CP, there is a loss. \ Loss amount = Cost price – Selling price = Rs.8000 – Rs.7920 = Rs. 80
66 Perfect Mathematics Class 8 Now, loss percentage = Loss Cost Price × 100% = Rs. 80 Rs. 8000 × 100% = 1% \ Loss percentage = 1% Example 9: The selling price of a dozen of exercise books is equal to the cost price of 15 exercise books. Find the profit or loss percentage. Solution: Let the selling price of a dozen of exercise books (SP) = Rs.x Then,cost price of 15 exercise books = Rs. x or, cost price of 1 exercise book = Rs. x 15 or, cost price of 12 exercise books (CP) = Rs. x 15 × 12 = Rs. 4x 5 Since SP > CP, there is profit. \ Profit = SP – CP = Rs. x – Rs. 4x 5 = Rs. 5x – 4x 5 = Rs. x 5 \ Profit percentage = Profit CP × 100% = Rs.(x/5) Rs.(4x/5) × 100% = x 5 × 5 4x × 100% = 25% Exercise 2.5.1 1. A shopkeeper sold the following articles on a particular day. Find the unknown values for each article. Also, find the actual profit or loss. Name of items Cost price Selling price Profit Loss a) Laptop Rs.40000 Rs.42000 ? – b) Mobile Rs.25000 ? – Rs.1500 c) Printer ? Rs.15000 Rs. 2200 – d) Television ? Rs.20500 – Rs.2700 e) Washing machine Rs.87500 ? Rs. 3700 –
Percentage 67 2. a) A shopkeeper sold 120 books at Rs. 250 each, which he had bought at Rs. 225 each. Find his profit amount. b) Rabina bought 70 pens at Rs.90 each and sold them at Rs. 85 each. Find the loss amount. 3. a) A person bought a mobile phone for Rs.92000. He/she sold it at a loss of 12% after two years. What was its selling price? b) A person bought a piece of land for Rs.75,00,000. He/she sold it at a profit of 40% after 1 year. What was its selling price? 4. a) A businessman bought three machines at Rs. 5400 each and spent Rs. 4000 on their repairing. If he sold the machines for Rs. 7000 each, how much profit did he make? b) Rajani bought a scooter for Rs. 180000 and spent Rs.18000 on its repairing. If she sold it for Rs. 184140, find her loss percentage. c) A dealer bought 5 quintals of rice at Rs.95 per kg and paid Rs.500 on transportation. If he had sold the rice at Rs.100 per kg, find his profit. 5. The following table shows the sales of a furniture on a particular day. Fill in the table the missing value for each article. SN Items Cost price Selling price Profit% Loss% a) Table Rs. 12000 Rs. 12840 ? – b) TV rack Rs. 23500 Rs. 22795 – ? c) Showcase Rs. 25400 ? 12% – d) Chair ? Rs. 7350 – 2% e) Bed ? Rs. 27772 6% – 6. a) A man bought 600 glasses at Rs. 300 per dozen. 30 glasses were broken and he sold the remaining glasses at Rs.30 each. Find his profit or loss. b) Roshan bought 260 apples at Rs. 40 each and 20 of them were bad. If he sold all the remaining apples at Rs.540 per dozen, find his profit or loss. 7. a) A fruit-seller bought 200 oranges and 20 of them were bad. If he sold the remaining oranges at Rs. 25 each and made a profit of Rs.500, at what rate did he buy them? b) Radha bought 100 kg of fruit at Rs.220 per kg in which 12kg of them were bad. If she sold the remaining fruit at Rs.280 per kg, find her profit percentage. c) Milan bought 340 oranges at Rs. 20 each and 60 of them were bad. If he lost
68 Perfect Mathematics Class 8 Rs. 640 by selling all the remaining oranges, at what rate did he sell them? 8. a) A man makes a loss of Rs.270 by selling an article for Rs. 2430. For what price should he sell it to make a profit of Rs.300? b) A shopkeeper sold a bag for Rs. 950 with a loss of Rs. 75. For how much should the bag be sold to make a profit of Rs.75? 9. a) A business person makes a profit of 12% by selling an article for Rs.6272. At what price should he sell to get a profit of 25%? b) By selling a table for Rs.2760, a man gains 15%. What percent would he have gained if he had sold it for Rs.2520? 10. a) Anita bought a bag for Rs.4,000 and sold to Shova at 20% profit. Again, Shova sold it to Laxmi at 10% profit. (i) Find the SP of Anita (CP of Shova) (ii) Find the SP of Shova (CP of Laxmi). b) A dealer bought a laptop for Rs.45,000 and sold it to retailer at 12% profit. The retailer again sold it to a customer at 25% profit. (i) Find the SP of dealer. (ii) Find the C.P of customer. 11. a) A person bought 20 litres of milk at Rs.75 per litre and 30 litres of milk at Rs. 90 per litre. He/she mixed it together and sold at the rate of Rs.88.20 per litre. Find his profit or loss percent. b) Raju bought 200 apples at Rs. 25 each and 250 apples at Rs. 35 each. He mixed both together and sold all of them at Rs.30 each. Find his total loss. 12. a) A man bought 500 pens at Rs. 27 each. He sold 300 of them at Rs.34 each and remaining at Rs.35 each. Find his total profit. b) A man bought 30 litres of milk and mixed 5 litres of water. If he made a profit of Rs.575 by selling them at Rs. 85 per litre, what would be the cost price of milk per litre? 13. a) A dealer sold two motor bikes at Rs.247500 each. If he gained 10% of the cost price on one and lost 10% on the other, what would be his total gain or loss percent? b) A business person sold his two mobiles for Rs.24000 each. If he gained 20% on one and lost 20% on the other, what would be the total gain or loss percentage? 14. Find the percentage profit or loss in the following conditions.
Percentage 69 a) SP of 5 pens = CP of 6 pens b) SP of 36 books = CP of 32 books c) SP of 4 calculators = CP of 5 calculators 15. a) A man bought two motorbikes for Rs. 160000. He sold one of them at 5% profit and the other one at 5% loss. Calculate his total gain or loss percentage if the selling price of both the motorbikes is the same. b) A man sold two TV sets for Rs.27600 each. If he gains 15% on one and lost 8% on the other, what will be his total gain or loss percent? 16. a) Sunayana bought a mobile phone and sold to Pratik at 8% loss. Pratik sold it to Debansu for Rs.11,040 and made 20% profit. (i) Find the cost price of the mobile to Pratik. (ii) Find the cost price of the mobile to Sunayana. b) A wholesaler sold an electric heater to a retailer at 20% profit. The retailer sold it for Rs. 2,052 to a customer at 5% loss. (i) How much did the retailer pay for it? (ii) How much did the wholesaler pay for it? Exercise 2.5.1 Profit and Loss 1. a) Rs. 2000 1. b) Rs. 23500 1. c) Rs.12800 1. d) Rs. 23200 1. e) Rs. 91200 2. a) Rs.3000 2. b) Rs.350 3. a) Rs. 80960 3. b) Rs. 10500000 4. a) Rs.800 4. b) 7% 4. c) Rs. 2000 5. a) 7% 5. b) 3% 5. c) Rs.28448 5. d) Rs. 7500 5. e) Rs. 26300 6. a) Profit = Rs.2100 6. b) Profit = Rs. 400 7. a) Rs. 20 7. b) 12% 7. c) Rs.22 8. a) Rs. 3000 8. b) Rs. 1100 9. a) Rs.7000 9. b) 5% 10. a) (i) Rs.4,800 10. a) (ii) Rs.5,280 10. b) (i) Rs.50,40010. b) (ii) Rs. 63,00011. a) 5% profit 11. b) Rs. 250 12. a) Rs.3700 12. b) Rs.80 /litre 13. a) Loss = 1% 13. b) Loss = 4% 14. a) Profit = 20% 14. b) Loss = 11.11% 14. c) Profit = 25% 15. a) 0.25% loss 15. b) 2.22% 16. a) (i) Rs.9,200 16. a) (ii) Rs.10,000 16. b) (i) Rs. 2,160 16. b) (ii) Rs.18,00
70 Perfect Mathematics Class 8 2.5.2 Discount While selling any item, a shopkeeper may deduct a certain percentage from the marked price of the item. The deducted amount is called discount. The price after deducting the discount is the selling price of the item. Hence, the discount is always calculated from the marked price. 1. Amount of discount = Discount % of MP 2. Discount amount = MP – SP 3. Discount percent = Discount MP × 100% 4. SP = MP – Discount 5. SP = 100 – D% 100 × MP Rs. 85000 5% Discount Rs. 15000 8% Discount Example 1: The marked price of a sweater is Rs. 2400. If a discount of 10% is offered, find the selling price of the sweater. Solution: Given : Marked price (MP) = Rs.2400 Discount percentage = 10% To find : Selling price (SP) Here, Discount amount = 10% of MP = 10 100 × Rs. 2400 = Rs.240 Now, SP = MP – Discount = Rs. 2400 – Rs. 240 = Rs. 2160 \ The selling price of the sweater is Rs.2160. Example 2: A shopkeeper allowed 15% discount in a watch. If a customer pays Rs.1360 for the watch, find its marked price. Solution: Given : The selling price of the watch (SP) = Rs. 1360 Discount percentage = 15% To find : Marked price (MP) Let the mark price (MP) be Rs. x. Discount amount = 15% of MP = Rs.3x 20 Now, SP = MP – Discount or, Rs. 1360 = x – 3x 20
Discount 71 or, Rs. 1360 = 20x – 3x 20 = 17x 20 or, 17x = Rs. 1360 × 20 or, x = Rs.1360 × 20 17 = Rs. 1600 Hence, the marked price of the watch is Rs.1600. Example 3: Jujuman buys a computer at Rs. 36,000. The marked price of the computer is 25% above the cost price. If he sells the computer at 25% discount then, a) What is the marked price of the computer? b) What is the discount amount? c) What is the selling price of the computer? d) What is his profit or loss percent from that computer? Find it. Solution: Here, cost price of the computer (CP) = Rs.36,000 By the question, a) Marked price (MP) = ? Marked price (MP) = CP + 25% of CP = 36000 + 36000 × 25 100 = 36000 + 9000 = Rs. 45000 b) Discount = ? We know that, Discount = discount % of MP = 45,000 × 25 100 = Rs. 11,250 c) Selling price (SP) = ? By formula, SP = MP – Discount = 45000 – 11250 = Rs. 33,750 d) Since, the selling price of the computer is less than cost price so there is loss. Loss= CP – SP = 36,000 – 33,750 = Rs. 2,250 Loss percent = Loss CP × 100% = 2250 36000 × 100% = 6.25%
72 Perfect Mathematics Class 8 Example 4: The marked price of an article is Rs.3,200 and 10% discount is allowed on it. a) Find the discount amount. b) Find the selling price of the article after discount. c) If 13% VAT is charged on SP, find the VAT amount. d) How much should a customer pay for it with VAT? Solution: Here, MP of the article Rs.3,200 Discount percent 10% a) Discount amount 10% of Rs. 3,200 = 10% of Rs. 3,200 = 10 100 × Rs. 3,200 = Rs. 320 b) SP of the article = MP – Discount = Rs. 3,200-Rs.320 = Rs.2,880 c) Again VAT amount = 13% of SP = 13 100 × Rs. 2,880 = Rs. 374.40 d) Now, SP with VAT = SP + VAT amount = Rs. 2,880 + Rs. 374.40 = Rs. 3,254.40 Hence, the customer should pay Rs. 3,254.40. Example 5: A retailer bought a woolen jacket for Rs. 4,000 and fixed its price 30% above the cost price. He/she then allows 10% discount and sold it. a) Find the marked price of the jacket. b) Calculate the discount amount. c) How much did a customer pay for it? Solution: Here, CP of the jacket Rs.4,000 a) Now, MP of the jacket, MP = (100 + 30)% of C. P = 130% of Rs. 4,000 = 130 100 × Rs. 4000 = Rs. 5,200
Discount 73 Hence, the required MP is Rs. 5,200. b) Again, discount amount = 10% Rs. 5,200 = 10 100 × Rs. 5,200 = 10 × Rs.52 = Rs.520 Hence, the required discount amount is Rs.520, c) Then, SP of the jacket = MP – Discount = Rs. 5,200 – Rs.520 = Rs.4,680 Hence, a customer paid Rs.4,680 for it. Exercise 2.5.2 1. The following table shows the articles sold from a shop. Find the missing values in different columns. S.N Name of items MP SP Discount amount Discount percent a) Mobile Rs. 17000 Rs.16150 ? ? b) Laptop Rs. 56000 Rs.54880 ? ? c) Camera Rs. 22000 ? Rs.2000 ? d) Television ? Rs.40500 Rs.4500 ? e) Printer ? Rs.13500 ? 10% 2. a) The marked price of a washing machine is Rs. 90000. If a discount of 5% is offered, find its selling price. b) The marked price of a calculator is Rs.2000. If it is sold at 8% discount, find the discount amount and selling price. 3. a) The marked price of a calculator is Rs.900. If the shopkeeper sells it for Rs. 810, find the discount percentage. b) A shopkeeper sold a watch for Rs. 13600 whose marked price was Rs. 16000. Find the discount percentage. 4. a) Rojan sold a mobile phone for Rs. 14790 allowing Rs. 2210 discount, find the discount percentage.
74 Perfect Mathematics Class 8 b) Radhika sold a money bag for Rs. 1512 allowing discount Rs.288. Find the discount percentage. 5. a) A business person allowed 8% discount in a shirt. If a customer pays Rs. 1334 for the shirt, find its marked price. b) A shopkeeper sold a pair of pants for Rs.1056 allowing 12% discount on marked price. What was its marked price? 6. A shopkeeper allowed a 10% discount on a watch of marked price of Rs.600. If he got 8% profit, find the cost price of the watch. 7. Pramod sold a watch at a gain of 20% after allowing a discount of 15%. Had it been sold after allowing a 30% discount, there would have been a loss of Rs. 400. Find the marked price of the watch. 8. When an article is sold at a discount of 10% on its marked price, a profit of Rs. 8 is earned by the seller. If the same article is sold without allowing a discount, there will be a profit of Rs.20. What should be the cost price of the article? 9. An article is sold at a certain discount on its marked price. The marked price of the article is 25% above the selling price and the cost price is 20% below the selling price. Find the rate of discount and the profit percentage. 10. Urmila offers her customers a discount of 10% on her beauty products and she still makes a profit of 20%. What is her actual cost of that beauty product marked Rs.400? 11. Pemba offers a 10% discount on his goods and he offers a further discount of 5% on the reduced price to those customers who pay cash. What does a customer have to pay in cash for a cricket bat of Rs.20000? 12. A shopkeeper offers 20% discount and still makes profit of 25%. Calculate the cost of article which has a marked price of Rs.200. 13. A shopkeeper marked the price of a calculator as Rs. 1,600 and she/he sold it allowing a discount of 10%. Then, she/he made a profit of Rs. 140. a) Find the amount of discount. b) Find the selling price after allowing discount. c) Find the cost of price of the calculator.
Discount 75 14. Mr. Muhammad fixed the marked price of a cycle as Rs.6,000. He sold it after allowing a discount of 15% and made a profit Rs.500. a) Find the amount of discount. b) Find the selling price after allowing discount. c) Find the cost of cycle. 15. The marked price of a fan is Rs. 1,500. The shopkeeper allows 20% discount on it. a) Find the amount of discount. b) Find the selling price after allowing discount. c) If 13% VAT is charged on the selling price, find the amount of VAT. d) Find the selling price with VAT. 16. A retailer bought a watch for Rs. 800 and fixed its price 25% above the cost price. He then allows 10% discount. a) Find the marked price of the watch. b) Find the discount amount. c) Find the selling price of the watch. d) How much should a customer pay for it with 13% VAT? 17. A gift house allowed 20% discount on the marked price of a doll. Then, 13% VAT was levied on it and the doll was sold at Rs.1,808. a) Find the selling price of the doll without VAT. b) Find the marked price of the doll. Exercise 2.5.2 Discount 1. a) Rs. 850, 5% 1. b) Rs. 1120, 2% 1. c) Rs.20000, 9.09% 1. d) Rs. 45000, 10% 1. e) Rs.15000, Rs.1500 2. a) Rs. 85500 2. b) Rs.160, Rs.1840 3. a) 10% 3. b) 15% 4. a) 13% 4. b) 16% 5. a) Rs. 1450 5. b) Rs. 1200 6. Rs.500 7. Rs.48000 8. Rs.100 9. Discount = 20% and Profit = 25%. 10. Rs.300 11. Rs.17100 12. Rs.128 13. a) Rs. 160 13. b) Rs.1,440 13. c) Rs. 1,300 14. a) Rs.900 14. b) Rs.5,100 14. c) Rs.4,600 15. a) Rs. 300 15. b) Rs.1,200 15. c) Rs. 156 15. d) Rs.1,356 16. a) Rs. 1,000 16. b) Rs.100 16. c) Rs. 900 16. d) Rs.1,017 17. a) Rs. 1,600 17. b) Rs.2000
76 Perfect Mathematics Class 8 Mixed Exercise A Profit, Loss and discount 1. Ramdev went to utensil shop to buy a pressure cooker. The marked price of a pressure cooker is Rs.3900. a) If the marked price and the discount are represented by MP and D respectively, write the formula to find the discount percent. b) How much discount did Ramdev get while buying a pressure cooker on discount of 7%? c) The shopkeeper got 17% profit after selling it at 7% discount. What was the cost price of the pressure cooker? 2. Raman visited a furniture store to get a set of table and some chairs. A set of table and four chairs are available for Rs.16,000. a) If the price of a table is Rs. 6000, then how much does a chair cost? b) How much discount did Raman get while purchasing a set of table and chairs at 5% discount? Also, find the price after discount. c) If the shopkeeper earned 10% profit even after offering 5% discount, at what price did the shopkeeper purchase the set of a table and chairs? 3. Sony visited a computer store to get 2 laptops and a printer. A set of two laptops and a printer is available for Rs. 2,00,000. a) If the price of a laptop is Rs.80,000, then how much does a printer cost? b) How much discount did Sony get while purchasing a set of 2 laptops and a printer at 10% discount? c) If the shopkeeper earned 20% profit even after offering 10% discount, at what price did the shopkeeper purchase the set of laptops and printer? 4. A shopkeeper marked the price of a monitor as Rs.5000. He sold it allowing a discount of 10% and made a profit Rs. 500. Hint : MP – Discount = CP + Profit a) Write the formula for finding the rate of discount when discounted amount and marked price are given. b) What is the selling price of the monitor? c) Find the cost price of the monitor. d) If the discount was not allowed, then what would be the profit? e) If the profit in a monitor is Rs. 800 then how many radios should be sold to
Discount 77 make a profit of Rs. 40,000? 5. The marked price of a book is Rs.500. If 30% discount is allowed then a loss of Rs.100 is made. a) If marked price (MP), selling price (SP) and discount (D) then write the relation among MP, SP and D. b) What is the selling price of the book? c) What is the cost price of the book? d) If the discount was not allowed, then what would be the profit or loss in the book? 6. Nikunja marked the price of a watch as Rs. 1000. He sold it allowing a discount of 15% and the profit of Rs.100 is made. a) If marked price (w), cost price (x), loss (y) and discount (z) then write the relation among w, x, y and z. b) Find the selling price of the watch. c) Find the cost price of the watch. d) If the discount was not allowed, then what would be the profit or loss in the watch? 7. A shopkeeper marked the price of a radio as Rs. 840. He sold it allowing a discount of 5% and made a profit Rs.70. a) What do you understand by 5% discount? b) Find the discount amount. c) Find the cost price of the radio. d) If the discount was not allowed, then what would be the profit or loss in the radio? 8. The ratio of the marked price of a T-shirt and a shirt of a certain brand in a shop is 3 : 5. a) If the marked price of a shirt is Rs.5000, find the marked price of the T–shirt. b) If 10% discount is allowed on the marked price of T–shirt, what is the discount amount? c) Find the cost to be paid by the customer for T–shirt is 13% VAT is levied on it. 9. The cost price of a mobile is Rs.21,000. The marked price of the mobile is 30% above the cost price. If the shopkeeper sold the mobile after 20% discount then, a) What is the marked price of the mobile? b) What is the selling price of the mobile? c) What is the profit percent of the shopkeeper after selling the mobile? Find it.
78 Perfect Mathematics Class 8 10. The marked price of an iron is Rs.3000. The shopkeeper sold it for Rs. 2700 after allowing some discount. a) What percent of discount was allowed? b) If the cost of the iron is Rs.2000, how much did the shopkeeper gain? Find it in percent. c) How much should a customer pay for the radio if 13% VAT is added? 11. Samir marked Rs. 180,000 for an i-phone. He gives 10% discount on the i-phone and suffers with a loss of Rs. 20,000. a) Find the selling price of the i-phone after applying the discount. b) Find the cost price of the i-phone. c) Calculate his loss percent in the sale of the i-phone. 12. An electric scooter costs Rs. 270,000 when it is bought after 10% discount. a) The marked price of electric scooter is Rs. x and discount of Rs. y is allowed on it. What is the discount percent? Write. b) Find the marked price of the electric scooter. c) What is the discount amount that he gets? Mixed Exercise A Profit, Loss and Discount 1. a) D MP × 100% 1. b) Rs.273 1. c) Rs.3100 2. a) Rs.2,500 2. b) Rs.800, Rs. 15,200 2. c) Rs.13818.18 3. a) Rs.40,000 3. b) Rs.20,000 3. c) Rs.1,50,000 4. a) D MP × 100% 4. b) Rs.4,500 4. c) Rs.4,000 4. d) Rs.1,000 4. e) 50 5. a) SP = MP – d 5. b) Rs.350 5. c) Rs.450 5. d) Profit; Rs.50 6. a) w – z = x – y 6. b) Rs.850 6. c) Rs.750 6. d) Rs. 250 7. b) Rs.42 7. c) Rs.728 7. d) Rs.112 8. a) Rs.3000 8. b) Rs.300 8. c) Rs.30511 9. a) Rs.27300 9. b) Rs. 21840 9. c) 4% 10. a) 10% 10. b) Rs.4500 10. c) Rs.3051 11. a) Rs.162,000 11. b) Rs.182,000 11. c) 10.99%. 12. a) Discount percent = y x × 100% 12. b) Rs.3,00,000 12. c) Rs.30,000
Discount 79 2.6 Unitary Method Introduction In unitary method, we first find the value of 1 unit and then the value of the required number of units. This method is the application of direct and indirect proportion. Direct Variation or Direct Proportion The price of an exercise book is Rs.120. Complete the following table. No. of exercise book Price in Rs. 3 360 4 600 2 720 Activity - 1 Two quantities are said to be in direct variation if the increase in the value of one increases the other. For example, the cost of 3 books = Rs.120, the cost of 15 books = Rs. 600. The ratio of the number of books = 3 : 15 = 1 : 5. The ratio of the costs of books = Rs. 120 : Rs. 600 = 1 : 5. Here, as the number of books increases, the price also increases in the same ratio. Study the given table. No. of pens Price in Rs. 3 60 1 20 7 140 12 240 4 80 20 400 6 120 Example 1: If the cost of 7 pen-drives is Rs.4200, how many pen-drives can be bought for Rs.9600?
80 Perfect Mathematics Class 8 Solution: Here, No. of pen-drives Cost (Rs.) 7 450 0 ? 9600 For Rs.4200, we can buy 7 pen-drives. or, For Re.1, we can buy 7 4200 pen-drives. or, For Rs.9600, we can buy 7 4200 × 9600 pen-drives i.e., 16 pen-drives Thus, we can buy 16 pen-drives for Rs.9600. Alternately, Let the required number of pen-drives be x, then by direct variation, 7 x = 4200 9600 or, 4200x = 7 × 9600 or, x = 7 × 9600 4200 = 16 Thus, we can buy 16 pen-drives for Rs.9600. Example 2: Mr. Thapa bought 4 packets of DDC milk for Rs. 220 from a grocery shop. a) At what rate of cost did he buy the milk? b) Find the cost of 10 packets of milk at the same rate. c) How many packets of milk can be bought for Rs.385? Solution: a) Let the cost of 1 packet be Rs.x, No. of packets of milk Cost (Rs.) 4 220 1 ? (x) Here, then by ratio and proportion, we have i.e. 4 1 = 220 x or, 4x = 220 × 1 or, x = 220 × 1 4 = 55 Hence, the cost of 1 packet of milk is Rs.55. b) Let the cost of 10 packet be Rs.y, No. of packets of milk Cost (Rs.) 1 55 10 ? (y)
Discount 81 Here, then by ratio and proportion, we have i.e. 1 10 = 55 y or, y = 10 × 55 or, y = 550 Hence, the cost of 10 packet of milk is Rs.550. c) Let Rs. 55 is the cost of z packets of milk, No. of packets of milk Cost (Rs.) 1 55 z 385 Here, then by ratio and proportion, we have i.e. 1 z = 55 385 or, z = 1 × 385 55 or, z = 7 Hence, the required number of packets of milk is 7. Indirect Variation or Indirect Proportion When two quantities vary inversely in the same ratio, we can find the value of required number of units using unitary method. See the following situations of indirect variations. 1. If 12 men can do a work in 10 days, how many men can do it in 8 days? 2. If 20 men have provisions for 15 days, for how many days will the same provision be enough for 2 men? There is a stock of food in the store of a canteen enough for 200 students for 20 days. If the number of students varies from 200, complete the following table. Number of students Days enough for 200 20 100 ? 50 ? 20 ? Project Work Two quantities are said to be in indirect variation when the increase in the value of one in a certain ratio decreases the value of the other in the same ratio and vice versa.
82 Perfect Mathematics Class 8 For example, 5 men can do a piece of work in 40 days, then 20 men will be able to do that work in 10 days. The ratio of number of men = 5 : 20 = 1 : 4 The ratio of number of days = 40 : 10 = 4 : 1 Study the given table. Number of workers Number of days 20 15 10 30 2 150 1 300 60 5 75 4 To do the same work, more men take less time and less men take more time. In the above table, the number of workers and the number of days are changed in the same ratio towards the opposite directions. The product of the number of workers and the corresponding number of days is always the same i.e. 300. This type of variation is called Indirect Variation or Indirect Proportion or Inverse Proportion. Example 3: If the ratios 3 : 5 and x : 21 are in indirect proportion, find the value of x. Solution: Here, 3 : 5 and x : 21 are in indirect proportion. 3 : 5 = 21 : x or, 3 5 = 21 x or, 3x = 5 × 21 or, x = 5 × 21 3 \ x = 35 Example 4: If 15 men can do a piece of work in 20 days, in how many days can 10 men do it? Solution: No. of men No. of days 15 20 10 ? 15 men can do a piece of work in 20 days.
Discount 83 or, 1 men can do the work in 20 × 15 days. or, 10 men can do the work in 20 × 15 10 days i.e. 30 days. Hence, 10 men can do the work in 30 days. Example 5: 18 men can complete a piece of work in 20 days. How many men can complete the work in 15 days? Solution: Here, No. of men No. of days 18 20 ? (x) 15 18 men can complete a piece of work in 20 days. or, 18 × 20 men can complete a piece of work in 1 day. or, 18 × 20 15 men i.e., 24 men can complete a piece of work in 15 days. Thus, 24 men can complete a piece of work in 15 days. Alternately, Let x men can complete the work in 15 days. The men and days are inversely proportional. So, 18 x = 20 15 or, 15x = 18 × 20 \ x = 18 × 20 15 = 24 Hence, 24 men can complete the work in 15 days. Example 6: 6 workers can do a piece of work in 15 days working 7 hours a day. a) In how many days would 1 worker complete the same work with the same working hours? b) In how many days would 5 workers complete the work with the same working hours? c) In how many days would 5 workers complete the work working 6 hours a day?
84 Perfect Mathematics Class 8 Solution: a) Let, in x days 1 worker can complete the work with the same working hrs. No. of workers Time (hrs.) No. of days 6 7 15 1 7 x The number of workers and the number of days are in inverse proportion, we have 15 x = 1 6 or, x = 15 × 6 or, x = 90 \ The required number of days = 90. b) Let, in x days 5 workers can complete the work with the same working hrs. No. of workers Time (hrs.) No. of days 6 7 15 5 7 x The number of worker and the number of days are in inverse proportion, we have 15 x = 5 6 or, 5x = 15 × 6 or, x = 90 5 or, x = 18 \ The required number of days = 18. c) Let, in x days 5 workers can complete the work with the 6 working hrs. No. of workers Time (hrs.) No. of days 6 7 15 5 6 x The number of workers and time and the number of days are in inverse proportion, we have 15 x = 5 6 × 6 7 or, 30x = 15 × 6 × 7 or, x = 360 30 or, x = 21 \ The required number of days = 21.
Discount 85 Example 7: Ram can do a piece of work in 12 days and Shyam can do it in 20 days. If both of them work together, in how many days will they finish it? Solution: Here, In 12 days, Ram can do 1 work. or, In 1 day, Ram can do 1 12 work. or, In 20 days, Shyam can do 1 work. or, In 1 day, Shyam can do 1 20 work. When both of them work together, Ram and Shyam can do 1 12 + 1 20 work in 1 day. or, Ram and Shyam can do 5 + 3 60 work in 1 day. or, Ram and Shyam can do 8 60 work in 1 day. or, Ram and Shyam can do 1 work in 60 8 days = 71 2 days. Hence, they will finish the work in 71 2 days. Example 8: Hari can do a piece of work in 20 days. If Hari and Gopal can do it in 12 days working together, in how many days will Gopal finish it alone? Solution: Here, In 20 days, Hari can do 1 work. or, In 1 day, Hari can do 1 20 work. or, In 12 days, Hari and Gopal can do 1 work. or, In 1 day, Hari and Gopal can do 1 12 work. Now, Gopal alone will do 1 12 – 1 20 work in 1 day. or, Gopal alone will do 5 – 3 60 work in 1 day. or, Gopal alone will do 2 60 work in 1 day. or, Gopal alone will do 1 work in 60 2 days = 30 days. Hence, Gopal alone will finish the work in 30 days.
86 Perfect Mathematics Class 8 Exercise 2.6 1. a) If the cost of 10 bags is Rs.9500, find the cost of 13 bags. b) If the cost of 4 calculators is Rs.2240, find the cost of 3 calculators. c) If a water pipe can fill a tank of 3000 litres in 1 hour, how many litres of water does the pipe fill in 25 minutes? 2. a) If the cost of 7 pens is Rs.490, how many pens can be bought for Rs.770? b) 7 men can pack 840 packets of goods. How many men can pack 240 packets of goods? c) The cost of 9 bags is Rs.8550. How many bags can be bought for Rs.15200? 3. a) If the ratios 2 : 3 and x : 6 are in indirect proportion, find the value of x. b) If the ratios 3 : 5 and 10 : (x + 3) are in inverse proportion, find the value of x. c) If the ratios 6 : (x + 2) and (3x – 1) : 4 are in inverse proportion, find the value of x. 4. a) If 20 workers can build a wall in 10 days, in how many days will 8 workers build the wall? b) If 15 men can do a piece of work in 24 days, in how many days can 20 men do the work? 5. a) If 18 men can dig a plot of land in 20 days, how many men can dig the land in 24 days? b) 20 workers can do a piece of work in 10 days. How many workers should be added to complete the work in 8 days? 6. a) 30 workmen are required to dig a canal in 40 days. How many workmen should be added to dig it in 30 days? b) If 15 men can complete a piece of work in 40 days, how many men should be added to complete the work in 30 days? 7. a) Rita can do a piece of work in 6 days and Sita can do the same in 12 days. If they work together, in how many days will they finish the work? b) A can build a well in 9 hours and B can build it in 15 hours. If both of them work together, in how many hours will they complete it? 8. a) Dina can do a piece of work in 10 days. If Dina and Rabina can do it in 6 days working together, in how many days will Rabina finish it alone? b) A can build a well in 28 hours. If A and B can build it in 12 hours working together, in how many hours will B complete it alone? c) A, B and C can do a piece of work in 10 days, 15 days and 30 days respectively. In how many days will they finish the work, if they work together? 9. a) The bus fare of 2 students for traveling 5 km is Rs.100. (i) Find the bus fare for 1 km distance per student. (ii) Find the bus fare of 3 students for traveling 10 km.
Discount 87 b) The speed of a car is 60 km per hour. (i) What distance does the car travel in 5 hours? (ii) How long will it take to drive the same distance if his speed is 40 km per hour? 10. a) 2 men can do 3 pieces of work in 9 days. (i) Find in how many days 1 man will do 1 piece of work. (ii) Find in how many days 3 men will do 2 pieces of work. b) A man runs at the rate of 8 km per hour. (i) What distance does he cover in 3 hours? (ii) He changes his speed to 6 km per hour. Find how long he will take to cover the same distance. 11. a) In a camp, there are provisions for 400 persons for 23 days. (i) If it is used for 1 person, how long does it take to complete? (ii) If 60 more persons join the camp, find the number of days the provision will last. b) 10 workers complete a piece work in 12 days working 4 hours daily. (i) In how many days will 1 worker complete it working 1 hour daily? (ii) In how many days will 8 workers complete the same work working for 6 hours daily? You can go to a shop neighboring your home and buy five goods you want. If you certain quantities of such types of goods next week, estimate the cost for them. Prepare a report and present it in your classroom. SN Particulars Quantity Cost in Rs. Calculating process 1. Biscuits buying 12 pkts 200 Biscuits needed 15 pkts x 2. ........... buying ....... pcs ........ .......... needed ....... pcs y Project Work Exercise 2.6 Unitary Method 1. a) Rs.12350 1. b) Rs.1680 1. c) 1250 litres 2. a) 11 2. b) 2 men 2. c) 16 3. a) 9 3. b) 3 3. c) 1 4. a) 25 days 4. b) 18 days 5. a) 15 men 5. b) 5 workers 6. a) 10 workmen 6. b) 5 men 7. a) 4 days 7. b) 5 5 8 days 8. a) 15 days 8. b) 21 days 8. c) 5 days 9. a) (i) Rs. 10 9. a) (ii) Rs.300 9. b) (i) 300km 9. b) (ii) 7.5hrs 0. a) (i) 6 days 10. a) (ii) 4 days 10. b) (i) 24 km 10. b) (ii) 4 hrs 11. a) (i) 9200 days 11. a) (ii) 20 days 11. b) (i) 480days 11. b) (ii) 10 days
88 Perfect Mathematics Class 8 Mixed Exercise Unitary Method 1. The cost of 10 kg apples is Rs. 3200. a) What is the cost of 1kg apple? b) How much more is the cost of 3 kg of apple than the cost of 1kg apple? 2. 10 men earns Rs. 160000 in 20 days. a) How much does 1 man earn in a day? b) How much do 15 men earn in 10 days at the same rate? c) How many days do 10 men have to work to earn Rs.96000? 3. If 32 people take 24 days to paint 6 houses ,then a) How long will it take to paint 6 houses by 1 man? b) If the work is to be completed in 8 days, how many peoples should be added? 4. If 25 men earn Rs.5,00,000 in 30 days, then a) How much does a man earn in a day? b) How many men will earn 5,00,000 in 10 days? c) How many days are required for 25 men to earn 1,00,000? d) What is the earning of 5 men in 40 days? 5. 10 people of a community constructed a shelter with bamboo in 14 days. Likewise, 7 people of a community take a task to complete the construction of the shelter with the same measurement. a) If the people work 8 hours per day to construct the first shelter, how long will it take for 7 men to complete the construction of the second shelter in 16 days? b) How long does it take to construct a second shelter if 7 people work for 8 hours per day? 6. If 10 men earn Rs. 1,60,000 in 20 days then a) How much does a man earn in a day? b) How much will 15 men earn in 10 days at the same rate? c) How many days will it takes for 10 men to earn Rs.96,000 at the same rate? Mixed Exercise A Unitary Method 1. a) Rs. 320 1. b) Rs.640 more 2. a) Rs.800 2. b) Rs.120000 2. c) 12 days 3. a) 768 days 3. b) 64 people 4. a) Rs.666.67 4. b) 75 men 4. c) 6 day 4. d) Rs.1,33,333.33 5. a) 10 hrs. per day 5. b) 20 days 6. a) Rs.800 6. b) Rs.1,20,000 6 c) 12 days
Discount 89 2.7 Simple Interest 2.7.1 Interest Introduction Sometimes, we deposit money into our bank account for a certain period of time. At the end of that period, the bank pays back the money which we have deposited with some additional money for using our money. The additional money paid by the bank is called interest. If you deposit Rs.10000 in a bank, after a year, the bank provides you Rs. 650 more money, then a) Principal (P) = Rs.10000 b) Simple Interest (I) = Rs.650 c) Time period (T) = 1 year d) Amount (A ) = Rs. 10000 + Rs. 650 = Rs.10650 e) Rate of interest (R) = 650 10000 × 100% = 6.5% The following table indicates the sum deposited by different people and the interest received from the bank. Complete the table given below. People Principal Interest Amount Rohini Rs.2000 Rs.40 Rs.2040 Kedar Rs.4000 Rs.500 ? Sushma Rs. 8500 ? Rs. 9000 Gokul ? Rs.200 Rs.5000 Activity - 1 Some Definitions Principal : The money borrowed, lent out or deposited is called the principal or the sum. Interest : The additional money paid by the borrower or bank is called the interest. Amount : The total money paid by the borrower or the lender is called the amount. Rate : The interest on Rs.100 for 1 year is known as the rate of interest per year. Simple interest : If the interest is calculated uniformly on the original sum throughout the whole period, it is called simple interest.
90 Perfect Mathematics Class 8 Example 1: Find the simple interest on Rs.15000 at the rate of 8% per year for 3 years. Solution: Here, Principal (P) = Rs. 15000 Rate of interest (R) = 8% Time (T) = 3 years Now, The simple interest for Rs.100 for 1 year (I) = Rs. 8 or, The simple interest for Re.1 for 1 year (I) = Rs. 8 100 or, The simple interest for Rs. 15000 for 1 year (I) = Rs. 8 100 × 15000 or, The simple interest for Rs. 15000 for 3 year (I) = Rs. 8 100 × 15000 × 3 = Rs. 3600 Hence, the required simple interest is Rs.3600. Formula for Simple Interest Let P be the principal, R be the rate of interest, T be the time (in years) and I be the interest produced in time T. The simple interest for Rs. 100 for 1 year (I) = R or, The simple interest for Re.1 for 1 year (I) = R 100 or, The simple interest for Rs.P for 1 year (I) = R × P 100 or, The simple interest for Rs.P for T years (I) = P × T × R 100 . Thus, we have, I = P × T × R 100 , where R must be in percent per year and T must be in years. The other forms of this formula are as follows : 1. I = P×T×R 100 2. P = 100×I T×R 3. T = 100×I P× R 4. R = 100×I P×T Example 2: Find the simple interest on Rs.24000 at the rate of 12% per annum for 1 year and 6 months. Solution: Here, Principal (P) = Rs.24000 Rate of interest (R) = 12%
Discount 91 Time (T) = 1 year and 6 months = 11 2 yrs. = 3 2 yrs. We have, Simple interest for Rs. 100 for 1 year (I) = Rs.12 or, The simple interest for Re.1 for 1 year (I) = Rs. 12 100 or, The simple interest for Rs. 24000 for 1 year (I) = Rs.24000 × 12 100 or, The simple interest for Rs. 24000 for 3 2 years (I) = Rs. 2400 × 12 × 3 2 100 = Rs. 24000×12×3 100×2 = Rs. 4320 Hence, the required simple interest is Rs.4320. Example 3: If the simple interest on Rs.12500 for 3 years is Rs.3000, find the rate of interest. Solution: Here, Principal (P) = Rs.12500, Time (T) = 3 years, Interest (I) = Rs.3000 By formula R = 100×I P×T = 100×3000 12500×3 = 8 Hence, the rate of interest is 8% per annum. Example 4: If the interest of certain sum of money at 12% rate for 2 years is Rs.1440, find the sum. Solution: Here, Interest (I) = Rs. 1440 Time (T) = 2 years Rate of interest (R) = 12% By formula, Principal (P) = 100×I T × R = 100 × 1440 2 × 12 = 144000 24 = 6000 Hence, the sum is Rs. 6000.
92 Perfect Mathematics Class 8 Exercise 2.7.1 1. a) Define principal and give a suitable example. b) What is interest? Give an example. c) What do you understand by rate of interest? Explain. d) Write the formula to calculate interest? e) Express 3 years and 8 months in terms of year. 2. Find the simple interest for each of the following. S.N Principal Time Rate of interest a) Rs.10000 6 years 10% p.a. b) Rs.12000 21 months 12% p.a. c) Rs.54000 73 days 8% p.a. d) Rs.225000 2 years and 6 months 6.25% p.a. 3. Find the rate of simple interest in each of the following cases. S.N Principal Time Simple interest a) Rs.80000 2 years Rs.20800 b) Rs.40000 4 years Rs.43200 c) Rs.70000 2 years and 6 months Rs.14000 4. Find the time period in the following cases. S.N Principal Interest Rate of interest a) Rs.60000 Rs.19500 13% p.a. b) Rs.30000 Rs.4500 5% p.a. c) Rs.20500 Rs.7380 12% p.a. 5. Find the principal in each of the following cases. S.N Interest Time Rate of interest a) Rs.15750 5 years 7% p.a. b) Rs.5625 3 years 12.5% p.a. c) Rs.3720 2 years and 6 months 8% p.a. 6. a) Find the simple interest and amount on Rs.8000 for 3 years at 5% per year. b) Calculate the rate of interest if Rs.7800 is paid as interest on Rs. 40000 for 1 1 2 years.
Amount 93 c) How long will a sum of Rs. 75000 take to earn Rs. 22500 at the rate of 5% per year? d) Find the principal that earns an interest of Rs.22400 at the rare of 10% per year in 3 years and 6 months? 7. a) Radhika took a loan of Rs. 70000 at the rate of 12% p.a. If she paid the loan after 5 years, then how much interest did she pay? b) Pawan took a loan from Pasang at the rate of 8% p.a. for 30 months. If he paid Rs.9000 as interest after 30 months, then what was the sum borrowed? c) Sonam took a loan of Rs.32000 from a finance company. If the amount of interest in 4 years was Rs.19200, then what was the rate of interest? Exercise 2.7.1 Interest 1. d) I = P × T × R 100 1. e) 11 3 years 2. a) Rs.6000 2. b) Rs. 2520 2. c) Rs. 864 2. d) Rs.35156.25 3. a) 13% 3. b) 27% 3. c) 8% 4. a) 2.5 years 4. b) 3 years 4. c) 3 years 5. a) Rs. 45000 5. b) Rs.15000 5. c) Rs.18600 6. a) Rs. 1200, Rs. 9200 6. b) 13% 6. c) 6 years 6. d) Rs.64000 7. a) Rs. 42000 7. b) Rs. 45000 7. c) 15% 2.7.2 Amount The total of the principal and the simple interest is called the amount. It is denoted by A. Therefore, Amount = Principal + Interest or, A = P + I If amount (A), time (T) and rate of interest (R) are given, we can find principal as : P = A ×100 100 + TR Example 1: Mr. Jha borrowed a sum from a development bank at 12% per year interest. a) If the borrowed sum is Rs.100, how much interest should he pay in 1 year? b) If the borrowed sum is Rs. 27,000, how much interest should he pay in 3 years? c) Find the amount required to clear the loan at the end of 3 years.
94 Perfect Mathematics Class 8 Solution: a) He should pay the interest of Rs.12 in 1 year. b) Here, Principal (P) = Rs. 27,000 Time (T) = 3 years Rate (R) = 12% per year Now, Interest (I) = P×T × R 100 = Rs. 27,000 × 3 × 12 100 = Rs. 9,720 Hence, the required interest is Rs.9,720 c) Again, amount (A) = P + I = Rs. 27,000 + Rs.9,720 = Rs. 36,720 Hence, the required amount is Rs.36,720. Example 2: Rohan has deposited the amount of his money in two banks, A and B in the ratio of 3: 2. The amount of money deposited in bank A is Rs.60,000. a) What is the amount that he deposited in bank B? b) How much interest and amount that Rohan will receive from bank A after 2 years , if the rate of interest is 5% per annum? c) How long should he deposit the sum in bank B at the same rate of interest in order to earn the interest same as that from bank A? Solution: a) Let Rohan deposited his money in Bank A be 3x and in Bank B be 2x. Now, 3x + 2x = Rs.60,000 or, 5x = Rs. 60,000 or, x = Rs. 60,000 5 or, x = Rs. 12,000 ⸫ He deposited 2x = 2 × Rs.12,000 = Rs. 24,000 in Bank B. b) From Bank A Principal (P) = 3x = 3 × Rs. 12,000 = Rs. 36,000 Time (T) = 2 years, Rate (R) = 5%
Amount 95 Interest (I) = ? Amount (A) = ? We know that, Interest (I) = P×T × R 100 = 36,000 × 2 × 5 100 = Rs. 3,600 Again, We know that, Amount (A) = P + I = Rs.36,000 + Rs. 3,600 = Rs.39,600 ⸫ He got 3,600 as interest and 39,000 as amount from Bank A c) Principal (P) = Rs. 24,000 Rate (R) = 5% Interest (I) = Rs.3,600 Time (T) = ? We Know that, Time (T) = 100 × I P × R = 100×3,600 24,000 × 5 = 3,60,000 1,20,000 = 3 ⸫ It takes 3 years. Example 3: At what rate will Rs.15000 become Rs. 19800 in 4 years? Find the simple interest of Rs. 30000 for 3 years at the same rate. Solution: Here, in the first case, Principal (P) = Rs.15000, Amount (A) = Rs. 19800, Time (T) = 4 years Rate of interest (R) = ? We know that, A = P + I or, Rs. 19800 = Rs.15000 + I or, I = Rs.19800 – Rs.15000 \ I = Rs.4800 By formula, Rate of interest (R) = 100×I P×T = 100×4800 15000×4 = 8
96 Perfect Mathematics Class 8 The rate of interest is 8% per annum. Again, in the second case, Principal (P1) = Rs. 30000, Time (T1) = 3 years, Rate of interest (R1) = 8% per year Then, by formula, Interest (I1) = P1×T1×R1 100 = Rs.30000×3×8 100 = Rs. 7200 The interest on Rs.30000 for 3 years is Rs.7200. Exercise 2.7.2 1. a) Define amount and give an example. b) If P is the principal and I is the interest, then what is the formula to calculate amount (A)? c) If Rs. 12000 earns Rs. 2880 as interest in 3 years, then find the amount. d) Sanjaya borrowed a loan of Rs.25000. After 3years, while clearing the debt, if he paid Rs. 30000. Find the interest paid. 2. Find the simple interest and amount on each of the following cases: S.N Principal Time Rate of interest a) Rs.2000 5 years 6 months 8% p.a. b) Rs.2250 6 years 12% p.a. c) Rs.68000 2 years and 6 months 7% p.a. 3. Find the rate of simple interest in each of the following cases : S.N Principal Amount Time a) Rs.30000 Rs.49500 6 years 6 months b) Rs.85000 Rs.127500 5 years c) Rs.12500 Rs.17820 4 years 4. Find the principal in each of the following cases : S.N Amount Time Rate of interest a) Rs.18500 6 years 8% p.a. b) Rs.35500 7 years 6% p.a. c) Rs.21000 8 years 5% p.a.
Amount 97 5. a) At what rate will Rs.13000 earn Rs.5200 in 4 years? Find the simple interest of Rs.40000 for 3 years at the same rate. b) If the interest for 3 years on Rs.12500 be Rs.3000, find the amount of Rs.30000 after 2 years at the same rate of interest. c) If Rs.45000 will be Rs.54000 in 4 years, what sum becomes Rs. 63750 in 5 years at the same rate of interest? 6. Alisha took a loan of Rs. 38000 from a bank at the rate of 12% p.a. If she cleared the loan in 3 years, then find the amount of money paid. 7. Dilliram deposited a sum of money in a bank at the rate of 8% p.a. After 5 years, if he got a total amount Rs.210000, find the sum deposited. 8. Neelam deposited Rs. 500000 in a bank for 5 years at the rate of 10% p.a. simple interest. If she needs to pay 5% income tax on the interest received, find the actual amount of money Neelam received. 9. Harka deposited Rs. 800000 in a bank for 4 year 6 months at the rate of 10% p.a. simple interest. If the bank charges 5% income tax on the interest, then a) Find the interest in 4 years. b) Find the amount of income tax. c) Find the amount of money receive after 4 years. 10. Rama took a loan of Rs. 1200000 from a bank to go for abroad study at the rate of 12% p.a. simple interest. If she cleared the loan after 10 years, then a) What is the interest paid by her? b) How much money does she need to pay to clear the loan? Visit a local credit and co-operative limited. Inquire the process of providing loan to its members and rate of interest decided at recent time. Consider the loan for two persons with the amount Rs.20000 and Rs.25000 respectively for 3 years. Calculate the simple interest of these two sums after 3 years. Find the difference of these interests. Present the information of the document required for the loan and the interest of these two persons in the class. Project Work Exercise 2.7.2 Amount 1. b) A = P + I 1. c) Rs. 14880 1. d) Rs.5000 2. a) Rs. 880, Rs. 2880 2. b) Rs.1620, Rs.3870 2. c) Rs.11900, Rs.79900 3. a) 10% 3. b) 10% 3. c) 10.64% 4. a) Rs.12500 4. b) Rs. 25000 4. c) Rs.15000 5. a) 10%, Rs.12000 5. b) Rs. 4800 5. c) Rs.51000 6. Rs.51680 7. Rs.150000 8. Rs.737500 9. a) Rs. 360000 9. b) Rs.18000 9. c) Rs. 1142000 10. a) Rs.1440000 10. b) Rs.2640000
98 Perfect Mathematics Class 8 Mixed Exercise A Simple Interest 1. Sangita has deposited Rs. 1,00,000 in a commercial bank for 2 years at the rate of Rs. 5 interest per annum for Rs.100. a) At what percent of interest rate per annum had Sangita deposited the amount of money? b) How much simple interest will Sangita get in 2 years at the same rate of interest? c) The ages of elder and younger daughter of Sangita are 12 years and 8–years respectively. 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? 2. Rajan deposited some amount of money he has in bank P and bank Q in the ratio of 5 : 4. If he deposited Rs. 80,000 in bank P, a) How much money did Rajan deposit in bank Q? b) How much simple interest will Rajan obtain in 2 years at the rate of 10% per annum from bank P? c) How much amount did Rajan obtain from bank P after 2 years? d) For how many years will Rajan have to deposit the amount in bank Q with same rate to obtain the same amount of interest as from bank P? 3. Sujan deposited some amount of money he has in bank M and bank N in the ratio of 5 : 3. If he deposited Rs. 50,000 in bank M. a) How much money did Sajan deposit in bank N? b) How much interest will Sujan obtain in 2 years at the rate of 12% per annum from bank M? c) How much amount did Sujan obtain from bank M after 2 years? d) For how many years will Sujan have to deposit the amount in Bank N with same rate to obtain the same amount of interest as from Bank M? 4. Krishna deposited Rs. 60000 at rate 8% p.a. in saving account. After 5 years he withdraw Rs. 40000 and total interest of 5 years. a) If Amount (A), Rate (R) and Time (T) are given write the formula to calculate the principal (P). b) Find the interest of five years. c) How long should he keep the remaining amount in the bank to get total interest Rs. 28800 from the beginning? 5. Tulashi had borrowed a loan of Rs.6000 from a bank 4 years ago. If she had paid total amount of Rs.9000 and got rid of the loan,
Amount 99 a) Write R in terms of I, P and T, where the symbols have their usual meanings. b) Find the simple interest. c) What was the rate of interest. d) In how many years the principal and interest are to be equal? 6. Nepal Bank gives a loan at 18% simple interest p.a. Ram Sahu pays Rs.91000 in repayment of a loan from the bank at the end of 8 months, a) If Amount (x), Rate (y) & Time (z) are given, write the formula to calculate the principal (P). b) What was the sum borrowed? c) Find the interest paid in 8 months. d) Compare the principal and interest. 7. A bank takes 5% tax on the interest when Rs.75000 is deposited by Sanumaya in the bank at the rate of 8% p.a. for 6 months. a) Write the meaning of 8% interest. b) What is the total interest of six months? c) Find the tax amount. d) Sanumaya distributed the post-tax interest to her two sons in the ratio of 12 : 7. How much does the son receiving the smaller amount receive? 8. Pemba deposits Rs. 15000 in a bank at the rate of 12% p.a. If he has to pay 8% of the interest yield as an income tax, a) What is the 8% tax on Rs. 100? b) What is the total interest in 6 years? c) Find the tax amount. d) Pemba distributed the post-tax interest to her two sons in the ratio of 4 : 5. How much does the son receiving the larger amount receive? 9. Dipika borrowed Rs. 80,000 from her friend Dipak at the rate of 12% per annum for 21 2 years. a) Find the interest to be paid after 22 years. b) Find the amount to be paid after 2 1 2 years. c) If Dipak calculates the interest at the rate of 10% how much will be the profit for Dipika? 10. Reema took a loan of Rs.80,000 from a money lender, who charged interest at the rate of 10% per annum. After 5 years she paid him Rs.50,000 and a laptop to clear the debt. a) Find the interest for 5 years.
100 Perfect Mathematics Class 8 b) What is the amount after 5 years? c) By how much is the price of the laptop more or less than Rs.80000? 11. Ram borrows a loan of Rs.2,40,000 for upgrading his poultry farm from Agricultural Development Bank at the rate of 10% p.a. for 2 years 6 months. Answer the following questions. a) Write the formula to find simple interest. b) How much simple interest does he pay after 2 years 6 months? c) How much amount will he have to pay to clear the debt? Mixed Exercise A Simple Interest 1. a) 5% 1. b) Rs.10,000 1. c) Rs.20,000 2. a) Rs.64,000 2. b) Rs.16,000 2. c) Rs.96,000 2. d) 2.5 yrs 3. a) Rs.30,000 3. b) Rs.12,000 3. c) Rs.62,000 3. d) 3.33 yrs. 4. a) P = A × 100 100 + TR, 4. b) Rs.24,000 4. c) 3 years 5. a) R = I × 100 P × T 5. b) Rs.3000 5. c) 12.5% p.a. 5. d) 8 years 6. a) x × 100 100 × yz 6. b) Rs.81,250 6. c) Rs.9750 6. d) 25 : 3 7. b) Rs. 3000 7. c) Rs.150 7. d) Rs.1,050 8. a) Rs.8 8. b) Rs. 10,800 8. c) Rs.864 8. d) Rs.5,520 9. a) Rs.24,000 9. b) Rs. 1,04,000 9. c) Rs.4,000 10. a) Rs.40,000 10. b) Rs.1,20,000 10. c) Rs.10,000 less 11. a) I = P × T × R 100 11. b) Rs.60,000 11. c) Rs.3,00,000 Mixed Exercise B Sets and Arithmetic 1. If U = {x : 2 ≤ x ≤ 15, x∈N} and B = {multiple of 3} is a subset of U, a) List the elements of U and B. b) Also find n(U) and n(B). c) Prove that n(U) = n(B) + n(B). 2. A and B are two subsets of universal set U. If n(U) = 50, n(A) = 35, n(B) = 25 and n(A∩B) = 15. a) Illustrate the given information in a Venn-diagram. b) Find n(A∪B) and n(A – B). c) Also find n(B – A) and n(A∪B). 3. a) Simplify : 1 2 + 2 – 1 2 + 1 4
Amount 101 b) Simplify : 241235 + 424015 – 14445 c) Simplify : (1.2 × 109 ) × (6.2 × 10–3 ) 6 × 10–2 d) The distance between the moon and the earth is 384,400 km. Express it into scientific notation. 4. Rajani earns Rs.25000 per month. She spends 10% on rent and 20% on cloth. The ratio of her expenditure on food and education is 3 : 4 and finally she saves Rs.3500. a) Find the sum that she spends on rent and cloth per month. b) Find the sum of expenditures on food and education per month. c) Find the sum of expenditures on food and cloth. 5. The marked price of an article is Rs. 15000. If the shopkeeper allows 10% discount and adds 13% VAT, a) Find the discount amount. b) Calculate the amount of VAT. c) How much will the customer pay for the article? 6. If 15 men can complete a piece of work in 40 days, a) How many men can complete the work in 20 days? b) In how many days will 20 men complete the work? c) How many men should be added to complete the work in 30 days? 7. If the interest for 3 years on Rs.12500 be Rs.3000. a) Find the rate of interest. b) Find the interest of Rs.50000 after 2 years at the same rate of interest. c) Find the amount of Rs.30000 after 2 years at the same rate of interest. Mixed Exercise B Sets and Arithmetic 1. a) U = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}, B = {3, 6, 9, 12, 15} 1. b) 14, 5 2. b) 45, 25 2. c) 10, 5 3. a) 7 4 3. b) 1210305 3. c) 1.24 × 108 3. d) 3.844 × 10 5 km 4. a) Rs. 2500, Rs.5000 4. b) Rs.6000, Rs.8000 4. c) Rs. 11000 5. a) Rs.1500 5. b) Rs.1755 5. c) Rs. 11745 6. a) 30 6. b) 30 6. c) 5 7. a) 8% 7. b) Rs.8000 7. c) Rs.34800