Question 1

A, B and C get ₹ 5400 for doing a work in 36 days. A and C get ₹ 1880 for doing the same work in 20 days, while B and C get ₹ 3040 for doing the same work in 40 days. Find the amount received by C per day.

Accepted Answer

Amount received by ( A + B + C) per day = 5400/36 = ₹ 150 ∴ A + B + C = ∴ 150.................(i) Similarly, amount received by (A + C) per day = 1880/20 = ₹ 94 ∴ A + C = ₹ 94 ........................(ii) Amount received by (B + C) per day = 3040/40 = ₹ 76 ∴ B + C = ₹ 76 ........................(iii) From Eqs. (i) and (iii), we get A + 76 = ₹ 150 A = 150 - 76 = ₹ 74 By putting the value of A in Eq. (ii), we get 74 + C = ₹ 94 ∴ C = 94 - 74 = ₹ 20 Hence, amount received by C per day = ₹ 20

Question 2

Total wages of 3 men, 2 women and 4 boys is ₹ 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.

Accepted Answer

Let the wages of 1 man, 1 woman and 1 boy are ₹ P, ₹ Q and ₹ R, respectively. According to the question, 3P + 2Q + 4R = 26 ....(i) 3P = 4Q ....(ii) and 2Q = 3R ....(iii) From Eqs. (i) and (ii), we get 4Q + 2Q + 4R = 26 ⇒ 6Q + 4R = 26.........................(iv) From Eqs. (iii) and (iv), we get 9R + 4R = 26 ⇒ 13R = 26 ∴ R = 2 From Eqs. (ii) and (iii), we get Q = 3 and P = 4 ∴ Wages of 4 men, 3 women and 2 boys = (4 x 4) + (3 x 3) + (2 x 2) = 16 + 9 + 4 = ₹ 29

Question 3

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.

Accepted Answer

Let the numbers of men, women and children are 3k, 2k and k, respectively. Given, 3k = 90 ⇒ k = 30 Number of women = 60 and number of children = 30 Let the men's, women's and children's wages be ₹ 5p, ₹ 3p and ₹ 2p, respectively. According to the question, Total daily wages = ₹ 10350 ⇒ 90 x 5p + 60 x 3p + 30 x 2p = 10350 ⇒ p x (450 + 180 + 60) = 10350 ∴ p = 10350/690 = 15 ∴ Daily wages of a man = 15 x 5 = ₹ 75

Question 4

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 men gets ₹ 90 per day, what should be the wages per day of a women?

Accepted Answer

Let man be represented by m and woman be represented by w. ∵ 2m + 1w = 1/14 ⇒ 14 x (2m + 1w ) = 1 ...(i) and 4w + 2m = 1/8 8 x (4w + 2m) = 1 ...(ii) On equating Eqs. (i) and (ii), we get 14 (2m + 1w) = 8 (4w + 2m) ⇒ 28m + 14w = 32w + 16m ⇒ 28m - 16m = 32w - 14w ⇒ 12m = 18w ∴ m/w = 18/12 = 3/2 So, efficiency of 1 man and 1 woman is 3 : 2. So, their wages must be in the same ratio 90/x = 3/2 [here, x = wages of a woman ] ∴ x = 90 x 2 / 3 = ₹ 60

Question 5

Total wages for a work is ₹ 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.

Accepted Answer

Work for 1 st 2 days = (1/8) + (1/12) = 5/24 ∴ Work for 8 days = (5/24) x (8/2) = 5/6 ∴ Remaining work = 1- (5/6) = (6 - 5) / 6 = 1/6 On 9th day, A's work = 1/8 Remaining work after 9 days = (1/6) - (1/8) = (4 - 3) / 24 = 1/24 B will finish this work in (12 x 1)/24 = 1/2 day Clearly, A worked for 5 days from starting. ∴ Work done by A in 5 days = (1/8) x 5 = 5/8 ∴ A's share = (5/8) x 1280 = 5 x 160 = ₹ 800

Question 6

4 men and 6 woman get ₹ 1600 by doing a piece of work in 5 days. 3 men and 7 women get ₹ 1740 by doing the same work in 6 days. In how many days, 7 men and 6 women can complete the same work getting ₹ 3760?

Accepted Answer

∵ In 5 days , (4 men + 6 women ) get ₹ 1600. ∴ In 1 day, (4 men + 6 women) get ₹ 1600/5 = ₹ 320 ....(i) In 1 day number of person to get ₹ 1 = 320 / 4 men + 6 women ....(ii) Similarly, in second condition, In 1 day, number of person to get ₹ 1 = (1740 / 6) x (3 men + 7 women) = 290 / (3 men + 7 women) ....(iii) From Eqs. (ii) and (iii), we get 320 / (4 men + 6 women) = 290 / (3 men + 7 women) 96 men + 224 women = 116 men + 174 women ⇒ 20 men = 50 women ⇒ Man / Women = 5/2 ∴ 1 women = 2/5 man From Eq. (i), 1 day, (4 men + 6 women) = (4 men + 6 x 2/5 men) = 32/5 men get ₹ 320 ∴ In 1 day, 1 man get = 320 x 5 /32 = ₹ 50 ∴ In 1 day, 1 woman get = 50 x 2/5 = ₹ 20 ∴ In 1 day, (7 men + 6 women) get 7 x 50 + 6 x 20 = ₹ 470 ∴ Required number of days = 3760 / 470 = 8 days

Question 7

The first man alone can complete this work in 7 days. The second man alone can do this work in 8 days. If they are working together to complete this work in 3 days and also taking help of a boy, then how should the money be divided?

Accepted Answer

Question 8

Two men undertake a piece of work for $600. Individually, they can complete the work in 6 days and 8 days, respectively. With the assistance of a boy they completed the work in 3 days. The boy's share should be:

Accepted Answer

Question 9

A man and a boy received $800 as wages for 5 days for the work they did together. The man's efficiency in the work was three times that of the boy. What are the daily wages of the boy?

Accepted Answer

Question 10

A, B and C are employed to do a piece of work for $575. A and C are supposed to finish 19 / 23 of the work together. Amount shall be paid to B is:

Accepted Answer

Question 11

A and B undertook to do a piece of work for $4500. A alone could do it in 8 days and B alone in 12 days. With the assistance of C they finished the work in 4 days. Then C's share of the money is:

Accepted Answer

Question 12

A, B and C undertake to complete a piece of work for ₹ 1440. A alone can complete the work in 8 days, B in 12 days and C in 16 days. They complete the work with the help of D in 3 days. What does D get?

Accepted Answer

Work and Wages Questions