Practice Questions: Time and Work

Q1: A can do a piece of work in 10 days, and B can do the same work in 30 days. In how many days can the work be completed if A and B work together?
(a) 4 5 / 2
(b) 7 1 / 2
(c) 6 9 / 5
(d) 2 3 / 5
(e) None of these
Ans: (b)
Sol: A's 1 day's work = 1 / 10.
B's 1 day's work = 1 / 30.
Combined 1 day's work = 1 / 10 + 1 / 30 = 2 / 15.
Required time = 1 ÷ (2 / 15) = 15 / 2 = 7 1 / 2 days.

Q2: A and B together can do a piece of work in 9 days. 'A' Alone can complete the work in 12 days. How long will B alone take to complete the job?
(a) 30 days
(b) 50 days
(c) 60 days
(d) 36 days
(e) 20 days
Ans: (d)
Sol: (A + B)'s 1 day's work = 1 / 9.
A's 1 day's work = 1 / 12.
Therefore B's 1 day's work = 1 / 9 - 1 / 12 = 4 / 36 - 3 / 36 = 1 / 36.
So B alone takes 36 days.

Q3: A can do work in 25 days. When he had worked for 15 days, B replaced him. If he completes the remaining work in 10 days, in how many days can B alone finish the work?
(a) 20 days
(b) 10 days
(c) 30 days
(d) 40 days
(e) None of these
Ans: (e)
Sol: A's 1 day's work = 1 / 25.
A's work in 15 days = 15 × (1 / 25) = 3 / 5.
Remaining work = 1 - 3 / 5 = 2 / 5, done by B in 10 days.
B's 1 day's work = (2 / 5) ÷ 10 = 1 / 25.
Thus B alone will finish the whole work in 25 days.

Q4: A is thrice as good a workman as B and is therefore able to finish a piece of work in 30 days less than B. Find the time in which they can do it working together.
(a) 11 1 / 4
(b) 5 2 / 3
(c) 6 2 / 3
(d) 20 4 / 2
(e) None of these.
Ans: (a)
Sol: Let B take x days, then A takes x - 30 days.
Since A is thrice as good as B, time ratio A : B = 1 : 3, so (x - 30) : x = 1 : 3.
Therefore 3(x - 30) = x ⇒ 3x - 90 = x ⇒ 2x = 90 ⇒ x = 45 days (B).
So A = 45 - 30 = 15 days.
Combined 1 day's work = 1 / 15 + 1 / 45 = 4 / 45.
Time together = 1 ÷ (4 / 45) = 45 / 4 = 11 1 / 4 days.

Q5: 1 woman or 2 men or 3 boys can do a piece of work in 55 days, then the same piece of work will be done by 1 man, 1 woman and 1 boy in how many days?
(a) 18 days
(b) 30 days
(c) 32 days
(d) 16 days
(e) None of these
Ans: (b)
Sol: From the data: 1 woman = 2 men = 3 boys (in terms of ability to do the whole work in same time).
So 1 boy = (1 woman) / 3 = (2 men) / 3 = 2 / 3 man.
Now 1 man + 1 woman + 1 boy = 1m + 2m + (2 / 3)m = 11 / 3 men equivalent.
If 2 men take 55 days, total work = 2 men × 55 days.
Time for 11 / 3 men = (2 × 55) ÷ (11 / 3) = 110 × 3 / 11 = 30 days.

Q6: If 5 men and 2 boys are working together, can do three times as much work per hour as a man and a boy together. The ratio of the work done by a man and that of a boy for a given time is
(a) 1 : 2
(b) 2 : 1
(c) 1 : 3
(d) 3 : 1
(e) None of these
Ans: (a)
Sol: Given 5 men + 2 boys = 3 × (1 man + 1 boy).
So 5m + 2b = 3m + 3b ⇒ 2m = b ⇒ 1 boy = 2 men.
Hence the ratio man : boy = 1 : 2.

Q7: If 2 men and 3 boys can do a piece of work in 16 days and 3 men and 2 boys can do it in 14 days, how long will 5 men and 4 boys take to do it?
(a) 6 days
(b) 8 days
(c) 9 days
(d) 10 days
(e) None of these
Ans: (b)
Sol: Let m and b be daily work of one man and one boy respectively.
2m + 3b = 1 / 16 and 3m + 2b = 1 / 14.
Multiply first by 3: 6m + 9b = 3 / 16.
Multiply second by 2: 6m + 4b = 1 / 7.
Subtract: 5b = 3 / 16 - 1 / 7 = (21 - 16) / 112 = 5 / 112 ⇒ b = 1 / 112.
Then 2m = 1 / 16 - 3b = 1 / 16 - 3 / 112 = 7 / 112 - 3 / 112 = 4 / 112 ⇒ m = 1 / 56.
Now 5 men + 4 boys = 5 × (1 / 56) + 4 × (1 / 112) = 5 / 56 + 4 / 112 = 10 / 112 + 4 / 112 = 14 / 112 = 1 / 8.
Time = 1 ÷ (1 / 8) = 8 days.

Q8: A and B complete a piece of work in 5 days working together. If A had worked twice, the work would have been completed in 4 days. In how many days can A alone complete the work?
(a) 20 days
(b) 18 days
(c) 24 days
(d) 15 days
(e) None of these
Ans: (a)
Sol: Let A take a days and B take b days.
1 / a + 1 / b = 1 / 5 ..........(1)
If A's rate were doubled: 2 / a + 1 / b = 1 / 4 ..........(2)
Subtract (1) from (2): (2 / a + 1 / b) - (1 / a + 1 / b) = 1 / 4 - 1 / 5 ⇒ 1 / a = 1 / 20 ⇒ a = 20 days.

Q9: If I must hire 6 men and 8 boys for 6 days to do the same piece of work as 8 men and 15 boys could do in 4 days, compare the efficiency ratio of the men and the boys.
(a) 1 : 2
(b) 1 : 3
(c) 1 : 4
(d) 1 : 5
(e) None of these
Ans: (e)
Sol: Total work = (6m + 8b) × 6 = (8m + 15b) × 4.
So 36m + 48b = 32m + 60b ⇒ 4m = 12b ⇒ m = 3b.
Therefore the efficiency ratio man : boy = 3 : 1.

Q10: 3 men or 5 women can do work in 6 days. How long will 6 men and 5 women take to finish the work?
(a) 2.5 days
(b) 2 days
(c) 3 days
(d) 3.5 days
(e) None of these
Ans: (b)
Sol: 3 men = 5 women ⇒ 1 man = 5 / 3 women.
So 6 men + 5 women = 6 × (5 / 3) women + 5 women = 10 + 5 = 15 women equivalent.
If 5 women do the work in 6 days, then 15 women will do it in (5 × 6) / 15 = 2 days.

Q11: 4 men can do a piece of work in 10 days, 2 women can do it in 15 days and 5 children can do it in 12 days. In how many days can 8 men, 5 women and 15 children together complete the piece of work?
(a) 2 days
(b) 3 days
(c) 4 days
(d) 5 days
(e) None of these
Ans: (e)
Sol: 4 men's 1 day's work = 1 / 10 ⇒ 1 man = 1 / 40 per day.
2 women's 1 day's work = 1 / 15 ⇒ 1 woman = 1 / 30 per day.
5 children's 1 day's work = 1 / 12 ⇒ 1 child = 1 / 60 per day.
Combined 1 day's work = 8 × (1 / 40) + 5 × (1 / 30) + 15 × (1 / 60) = 1 / 5 + 1 / 6 + 1 / 4 = 37 / 60.
Time = 1 ÷ (37 / 60) = 60 / 37 days.

Q12: 3 men can do a piece of work in 12 days, 5 women in 8 days and 20 children in 3 days. In how many days can a man, a woman, and a child work together to complete the piece of work?
(a) 12 days
(b) 13 days
(c) 14 days
(d) 15 days
(e) None of these
Ans: (e)
Sol: 3 men in 12 days ⇒ 1 man = 1 / 36 per day.
5 women in 8 days ⇒ 1 woman = 1 / 40 per day.
20 children in 3 days ⇒ 1 child = 1 / 60 per day.
Combined 1 day's work = 1 / 36 + 1 / 40 + 1 / 60 = (10 + 9 + 6) / 360 = 25 / 360 = 5 / 72.
Time = 1 ÷ (5 / 72) = 72 / 5 = 14 2 / 5 days.

Q13: A certain number of men can complete a piece of work in 40 days. If there were 8 men more the work could be finished in 10 days less. How many men were there afterwards?
(a) 32 men
(b) 28 men
(c) 24 men
(d) 15 men
(e) None of these
Ans: (a)
Sol: Let initial number of men = x.
x men take 40 days ⇒ total work = 40x man-days.
(x + 8) men take 30 days ⇒ total work = 30(x + 8) man-days.
Equate: 40x = 30(x + 8) ⇒ 40x = 30x + 240 ⇒ 10x = 240 ⇒ x = 24.
Afterwards there are x + 8 = 24 + 8 = 32 men.

Q14: If A can d0 ¼ of the work in 4 days and B can do ⅛ of the work in 3 days, how much will A get if both work together and are paid Rs. 4,500 in all?
(a) Rs. 1,800
(b) Rs. 2,400
(c) Rs. 2,700
(d) Rs. 2,900
(e) None of these
Ans: (c)
Sol: A does 1/4 in 4 days ⇒ A's full time = 16 days ⇒ A's 1-day work = 1 / 16.
B does 1/8 in 3 days ⇒ B's full time = 24 days ⇒ B's 1-day work = 1 / 24.
Ratio of daily work A : B = 1 / 16 : 1 / 24 = 3 : 2.
So A's share = 3 / (3 + 2) × 4,500 = 3 / 5 × 4,500 = Rs. 2,700.

Q15: 6 men can complete a piece of work in 12 days. 8 women can do the same piece of work in 18 days whereas 18 children can complete it in 10 days. 4 men, 12 women and 20 children work together for 2 days. If only men were to complete the remaining work in 1 day, how many men would be required totally?
(a) 36 men
(b) 24 men
(c) 18 men
(d) Cannot be determined
(e) None of these
Ans: (a)
Sol: Let daily rates be m, w and c for man, woman and child respectively.
From 6 men in 12 days: 6m × 12 = 1 ⇒ m = 1 / 72.
From 8 women in 18 days: 8w × 18 = 1 ⇒ w = 1 / 144 ⇒ 1 woman = 1 / 2 man (since 1 / 144 = (1 / 72) / 2).
From 18 children in 10 days: 18c × 10 = 1 ⇒ c = 1 / 180 ⇒ 1 child = 2 / 5 man (since (1 / 180) ÷ (1 / 72) = 72 / 180 = 2 / 5).
Thus 2 men = 4 women = 5 children (men-equivalent statement).
Now 4 men + 12 women + 20 children = 4m + 12(1 / 2 m) + 20(2 / 5 m) = 4m + 6m + 8m = 18m.
Daily work of 18 men-equivalents = 18 × (1 / 72) = 1 / 4.
Work done in 2 days = 2 × 1 / 4 = 1 / 2. Remaining work = 1 / 2.
To finish remaining 1 / 2 in 1 day at rate m per man: required men = (1 / 2) ÷ (1 / 72) = 36 men in total.