Chapter 23 Work and Wages Activity involving physical efforts, done in order to achieve a result is known as work. Money received by a person for a certain work is called the wages of the person for that particular work, In other words, we can find the entire wages of any person by the following formula For example If Arjun's monthly wages ? 4200 and he worked for all 30 days, then his daily wages will be calculated as Total wages = Number of days x Daily wages 4200 = 30 x Daily wages Important Points Wages is directly proportional to the work done. It means, more money will be received for more work and less money will be received for less work. ♦ Wages is indirectly proportional to the time taken by the individual.
♦ Wages is directly proportional to 1 day work of each individual, For example If Karan can do a piece of work in 10 days and Arun can do the same piece of work in 15 days. Then, ratio of Karan and Arun's wages will be 15 :10 i.e., 3 :2. ♦ If X, Y and Z can do a piece of work in d\, a\ and d3 days respectively, then ratio of their shares is d2 d3 -.djdi-. dj d2 Fast Track Formulae to solve the QUESTIONS Formula 1 If A and e can do a piece of work in x and y days respectively, the ratio of their wages will be y: x. Then, the wages earned by A and e will be Ex. 1 Akansha can do a piece of work in 6 days, while Vasudha can do the same work in 5 days. If the total amount to be given for this work is ? 660, then what will be the share of Vasudha, if both work together. Formula 2
if A, B and C can do a piece of work in x, y and z days respectively, the ratio of their wages will be yz: xz: xy. Then, wages earned by A, B and C respectively will be Ex. 2 A, B and C take ? 535 for doing a piece of work together. If working alone, each takes 5 days, 6 days and 7 days respectively, then find the share of each. : Formula 3 Total wages earned by certain persons in doing certain work. Total wages = (1 person's 1 day's wages) x (Number of persons) x (Number of days) ∴ Required number of persons Ex. 3 Wages of 45 women for 48 days amount to ? 31050. How many men must work for 16 days to receive ? 11500, if the daily wages of a man being double those of a woman?
Formula 4 A can do a piece of work in x days. With the help of B, A can do the same work in y days. If they get ? a for that work, then Ex. 4 Suresh can do a work in 20 days. Suresh and Surendra together do the same work in 15 days. If they got ? 400 for that work, then find the share of Suresh and Surendra? Formula 5 X, Y and Z undertake to do a work for ? R. If together they do only m/n of the work and rest is done by C alone, then the share of C is given by Ex. 5 A, B and C undertake to do a work for ? 480. A and B together do 1/4 of the work and rest is done by the C alone. How much should C get?
Ex. 6 X and Y contracted a piece of work for ? 1600. X alone can do it in 6 days, while Y alone can do that work in 8 days. They completed the work in 3 days taking help of A. Find the share of A. Ex. 7 A can do a piece of work in 10 days, while B alone can do it in 15 days. They work together for 5 days and rest of the work is done by M in 2 days. If they get ? 9000 for the whole work, then how should they divide the money?
Fast Track Practice Exercise © Base Level Questions 1. Shantanu can do a piece of work in 12 days and Manu can do the same work in 10 days. If they work together, in what ratio Shantanu and Manu will receive their wages? (a) 5 : 6 (b) 3 : 2 (c) 1 : 6 (d) 5 : 7 (e) None of the above 2. A can do a piece of work in 9 days and B can do the same work in 15 days. If they work together, in what ratio A and B will receive their wages? [Bank Clerks 2008] (a) 3 : 5 (b) 5 : 3 (c) 2 : 5 fdj 5 : 2 (ej None of the above
3. A man and a hoy received X 1400 as wages for 10 days for the work they did together. The man's efficiency in the work was six times that of the boy. What is the daily wages of the boy? (a) no (b) X 15 (c) ?20 (d) X 30 4. A alone can do a piece of work in 8 days while B alone can do it in 10 days. If they together complete this work and get X 900 as their remuneration, then find the shares of both the persons. (a) A = ?800ande=? 100 (b) A = X 500 and B = X 400 (c) A = X 600 and B = X 300 (d) A = X 300 and S = X 600 (e) None of the above 5. A can do a piece of work in 3 days while B can do the same work in 4 days. If they work together for a total wages of X 2800, how much does A get? [Bank Clerks 2009] (a) X 1200 (b) X 1900 (c) X 1300 (d) X 1600 (e) None of the above 6. A alone can do a piece of work in 3 days, while B alone can do the same work in 2 days. If they work together to complete the work, their total wages is fixed X 225. Find the share of A. [RRB 2008] (a) X 90 (b) X 75 (c) X 95 (d) X 65 (e) None of the above 7. A can finish a work in 15 days, B in 20 days and C in 25 days. All these three worked together and earned X 4700. The share of C is [CDS 2012] (a) ?1200 (b) ?1500
(c) ?1800 (d) ?2000 8. A person can do a piece of work in 26 days and an another person can do the same work in 39 days. If they work together, then by what per cent the wages of 1st person is more than that of 2nd person? [UP Police 2007] (a) 25% (b) 35% (c) 15% (d) 50% 9. A alone can finish a work in 2 days, while B alone can finish it in 3 days. If they work together to finish it, then out of total wages of X 6000, what will be the 20% of A's share? [Hotel Mgmt. 2009] (a) X 720 (b) X 350 (c) X 820 (d) X 420 (e) None of the above 10. Vandana can do a piece of work in 10 days. With the help of Ruchi, she can do the same work in 6 days. If they get X 200 for that work, then what will be the share of Ruchi in the received remuneration? (a) X 120 (b) X 100 (c) X 60 (d) X 80 (e) None of the above 11. A sum of money is sufficient to pay A's wages for 21 days and B's wages for 28 days. The same money is sufficient to pay the wages of both for [SSC CCL 2013] 12. Amit, Vipul and Kapil can do a piece of work in 12, 16 and 24 days, respectively. If they complete the work together and get an amount of X 2700, then what is the share of Vipul in that amount? (a) X 450 (b) X 1000 (c) X 225 (d) X 900 (e) None of the above 13. P, Q and R enter into a contract for a piece of work for X 1100. P and Q together are supposed to do 7/22 of the work. How much does R get?
(a) X 750 (b) X 350 (c) X 4751 (d) X 900 (e) None of the above 14. Ramesh and Suresh undertaken to do a piece of work for X 800. Ramesh alone can do it in 12 days, while Suresh alone can do it in 16 days. With the assistance of a boy, they finish it in 6 days. How should the money be divided? (a) Ramesh = X 100, Suresh = X 300 and boy = X 400 (b) Ramesh = X 200, Suresh = X 200 and boy = X 400 (c) Ramesh = X 400, Suresh = X 300 and boy = X 100 (d) Ramesh = X 300, Suresh = X 400 and boy = X 100 (e) None of the above 15. A, B and C completed a work costing X 1800. A worked for 6 days, B worked for 4 days and C worked for 9 days. If their daily wages are in the ratio of 5:6:4, how much amount will be received by A"> [SSC CPO 2007] (a) X 600 (b) X 500 (c) X 900(d) X 450 16. A and B undertaken to do a piece of work for ? 1200. A alone can do it in 8 days, while B can do it in 6 days. With the help of C, they complete it in 3 days. Find Cs share. [SSC CGL (Main) 2012] (a) ? 450 (b) X 300 (c) X 150 (d) X 100 17. A, B and C can do a piece of work in 20, 24 and 30 days, respectively. They undertook to do the piece of work for X 5400. They begin the work together but B left 2 days before the completion of work and C left 5 days before the completion of work. The share of A from the assured money is [SSC CPO 2013] (a) ? 2700 (b) X 540 (c) X 1800 (d) X 600 Exercise © Higher Skill Level Questions
1. A, B and C get X 5400 for doing a work in 36 days. A and C get X 1880 for doing the same work in 20 days, while B and C get X 3040 for doing the same work in 40 days. Find the amount received by C per day. (a) X 50 (b) X 25 (c) X 30 (d) X 20 (e) None of the above 2. Total wages of 3 men, 2 women and 4 boys is X 26. If the wages of 3 men is equal to that of 4 women and the wages of 2 women is equal to that of 3 boys, then find out the total wages of 4 men, 3 women and 2 boys. (a) X 29 (b) X 35 (c) X 65 (d) X 20 (e) None of the above 3. A person was appointed for a 50 days job on a condition that he will be paid X 12 for every working day but he will be fined X 6 for every day he remains absent. After the completion of the work, he got X 420. For how many days, he did not work? (a) 15 days (b) 5 days (c) 10 days (d) 20 days (e) None of the above 4. Total wages for a work is X 1280. A alone can do a piece of work in 8 days, while B alone can do it in 12 days. If A and B work on alternate days, then find the share of A. (a) X 800 (b) X 500 (c) X 600(d) X 700 (e) None of the above 5. 4 men and 6 women get X 1600 by doing a piece of work in 5 days. 3 men and 7 women get X 1740 by doing the same work in 6 days. In how many days, 7 men and 6 women can complete the same work getting X 3760? [SSC CGL 2009] (a) 6 days (b) 8 days (c) 10 days (d) 12 days 6. Men, women and children are employed to do a work in the proportion of 3 : 2 : 1 and their wages as 5:3:2. When 90 men are employed, total daily wages of all amounts to ? 10350. Find the daily wages of a man.
[SSC CGL (Main) 2012] (a) ? 45 (b) ? 57:50 (c) ? 115 (d) ? 75 7. 2 men and 1 woman can do a piece of work in 14 days, while 4 women and 2 men can do the same work in 8 days. If a man gets X 90 per day, what should be the wages per day of a women? [CDS 2013] (a)? 48 (b)? 60 (c) ? 72 fdj?135 Answer with Solutions Exercise © Base Level Questions
Exercise © Higher Skill Level Questions
2. (a) Let the wages of 1 man, 1 woman and 1 boy are ? x, ? y and ? z, respectively. According to the question, 3x+2y+4z = 26 ...(i) 3x = 4v ...(ii) and 2y = 3z ... (iii) From Eqs. (i) and (ii), we get 4y + 2y + 4z = 26 => 6/+4z = 26 ...(iv) From Eqs. (iii) and (iv), we get 9z + 4z = 26 => 13z = 26 z = 2 From Eqs. (ii) and (iii), we get y = 3 and x = 4 .•. Wages of 4 men, 3 women and 2 boys =4X4+3X3+2X2 = 16 + 9 + 4=?29 3. (c) Let the person did not work for x days. It means that he worked for (50 — x) days. .'. Fine for being absent = ? 6x Wages for working days = 12 (50 - x) According to the question, Received wages = 12(50-x)-6x = 420 => 600-12x-6x = 420
=> 18x = 600-420 = 180
6. (d) Let the numbers of men, women and children are 3y, 2y and y, respectively. Given, 3y = 90 => y = 30 Number of women = 60 and number of children = 30 Let the men's, women's and children's wages be ? 5x, ? 3xand ? 2x, respectively. According to the question, Total daily wages = ? 10350 => 90 x5x + 60 x3x+ 30 x2x= 10350 => x(450 + 180 + 60) = 10350