Work rates, combined work and efficiency.
45 solved questions · 15 easy · 20 medium · 10 hard
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A can complete a piece of work in 12 days and B can complete it in 24 days. In how many days can they finish it working together?
Answer: C. 8 days
Solution
A's 1-day work = 1/12, B's 1-day work = 1/24 Together = 1/12 + 1/24 = 3/24 = 1/8 Time = 8 days Answer: 8 days
Shortcut: Two workers: (12 x 24) / (12 + 24) = 288 / 36 = 8 days.
A can do a work in 10 days. What fraction of the work will A finish in 4 days?
Answer: A. 2/5
Solution
A's 1-day work = 1/10 In 4 days = 4/10 = 2/5 Answer: 2/5
A and B together can do a job in 6 days. A alone can do it in 10 days. How many days will B alone take?
Answer: D. 15 days
Solution
Together 1-day work = 1/6; A's 1-day work = 1/10 B's 1-day work = 1/6 - 1/10 = 5/30 - 3/30 = 2/30 = 1/15 B alone takes 15 days Answer: 15 days
8 men can complete a work in 15 days. In how many days can 12 men complete the same work?
Answer: B. 10 days
Solution
Total work = 8 x 15 = 120 man-days Days for 12 men = 120 / 12 = 10 days Answer: 10 days
Shortcut: More men, fewer days: 15 x 8/12 = 10.
A is twice as efficient as B. Together they finish a work in 12 days. How many days will A alone take?
Answer: C. 18 days
Solution
Let B take 2x days, then A takes x days 1/x + 1/(2x) = 1/12 3/(2x) = 1/12, so x = 18 A alone takes 18 days Answer: 18 days
Shortcut: Together time = 12 means A alone = 12 x 3/2 = 18 days (A does 2/3 of the work).
A can do a work in 20 days. He works for 5 days and then leaves. How many more days would A need to finish the rest?
Answer: A. 15 days
Solution
A's 1-day work = 1/20; in 5 days = 5/20 = 1/4 Remaining = 3/4 Time = (3/4) / (1/20) = 15 days Answer: 15 days
5 workers can finish a job in 6 days. How many days will 10 workers take?
Answer: D. 3 days
Solution
Total = 5 x 6 = 30 worker-days For 10 workers: 30 / 10 = 3 days Answer: 3 days
The efficiencies of A and B are in the ratio 3 : 2. If A can complete a job in 12 days, how many days will B take?
Answer: B. 18 days
Solution
Time is inversely proportional to efficiency A : B days = 2 : 3 A takes 12 days, so B takes 12 x 3/2 = 18 days Answer: 18 days
A can do a work in 18 days and B can do it in 9 days. How many days will they take together?
Answer: C. 6 days
Solution
1/18 + 1/9 = 1/18 + 2/18 = 3/18 = 1/6 Time = 6 days Answer: 6 days
6 women can complete a work in 10 days. How many women are needed to complete it in 4 days?
Answer: A. 15 women
Solution
Total = 6 x 10 = 60 woman-days Women needed = 60 / 4 = 15 Answer: 15 women
A does 3/5 of a work in 9 days. How many days will A take to complete the whole work?
Answer: D. 15 days
Solution
3/5 of the work takes 9 days Whole work = 9 x 5/3 = 15 days Answer: 15 days
A can finish a work in 10 days and B in 15 days. Working together, how many days will they take?
Answer: B. 6 days
Solution
1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6 Time = 6 days Answer: 6 days
A can build a wall in 24 days. B is three times as efficient as A. How many days will B take to build it?
Answer: C. 8 days
Solution
B is 3 times as efficient, so he takes 1/3 of the time 24 / 3 = 8 days Answer: 8 days
A, B and C can do a work alone in 10, 15 and 30 days respectively. How long will they take if they work together?
Answer: A. 5 days
Solution
1/10 + 1/15 + 1/30 = 3/30 + 2/30 + 1/30 = 6/30 = 1/5 Time = 5 days Answer: 5 days
A can make 5 units of a product per day and B can make 4 units per day. How many days will they take together to make 180 units?
Answer: D. 20 days
Solution
Together = 5 + 4 = 9 units per day Time = 180 / 9 = 20 days Answer: 20 days
A can do a work in 20 days and B in 30 days. They work together for 6 days and then A leaves. In how many more days will B finish the rest?
Answer: B. 15 days
Solution
Together 1-day work = 1/20 + 1/30 = 1/12 In 6 days = 6/12 = 1/2 Remaining = 1/2, B's rate = 1/30 Time = (1/2) x 30 = 15 days Answer: 15 days
A can do a work in 10 days and B in 15 days. They work on alternate days, A starting first. In how many days will the work be completed?
Answer: C. 12 days
Solution
A's 1-day work = 1/10, B's = 1/15 In a 2-day cycle: 1/10 + 1/15 = 1/6 Six cycles complete the work: 6 x 2 = 12 days Answer: 12 days
A and B together can do a work in 12 days, B and C in 15 days, and A and C in 20 days. How many days will all three take together?
Answer: A. 10 days
Solution
(A+B) + (B+C) + (A+C) = 1/12 + 1/15 + 1/20 = (5 + 4 + 3)/60 = 12/60 = 1/5 This equals 2(A+B+C), so A+B+C = 1/10 All three together take 10 days Answer: 10 days
Shortcut: Add the three pair rates and halve the result.
A can do a work in 10 days and B in 15 days. They are paid ₹3,000 for completing it together. What is A's share?
Answer: D. ₹1,800
Solution
Work rates A : B = 1/10 : 1/15 = 3 : 2 They work the same number of days, so wages are in the ratio 3 : 2 A's share = 3/5 of 3,000 = ₹1,800 Answer: ₹1,800
12 men can finish a work in 20 days. After 8 days, 6 men leave. In how many more days will the remaining men finish the work?
Answer: B. 24 days
Solution
Total work = 12 x 20 = 240 man-days Done in 8 days = 12 x 8 = 96 Left = 144 man-days Men now = 6 Time = 144 / 6 = 24 days Answer: 24 days
A is 3 times as efficient as B and takes 60 days less than B to do a work. How many days will they take working together?
Answer: C. 22 1/2 days
Solution
Let A take x days, then B takes 3x days 3x - x = 60, so x = 30 A = 30 days, B = 90 days Together: 1/30 + 1/90 = 4/90 = 2/45 Time = 45/2 = 22 1/2 days Answer: 22 1/2 days
A is 25% more efficient than B. If B alone can finish a job in 45 days, in how many days will A and B together finish it?
Answer: A. 20 days
Solution
Efficiency A : B = 125 : 100 = 5 : 4 Time A : B = 4 : 5. B = 45 days, so A = 36 days Together: 1/36 + 1/45 = 5/180 + 4/180 = 9/180 = 1/20 Time = 20 days Answer: 20 days
10 men working 8 hours a day can complete a work in 12 days. In how many days can 15 men working 4 hours a day complete it?
Answer: D. 16 days
Solution
Total work = 10 x 8 x 12 = 960 man-hours New rate = 15 x 4 = 60 man-hours per day Days = 960 / 60 = 16 Answer: 16 days
A can do a work in 12 days and B in 18 days. They start together, but A leaves 3 days before the work is finished. In how many days is the work completed?
Answer: B. 9 days
Solution
Let the work last x days. B works x days, A works (x - 3) days x/18 + (x - 3)/12 = 1 Multiply by 36: 2x + 3(x - 3) = 36 5x = 45, so x = 9 days Answer: 9 days
A can build a wall in 15 days and B in 10 days. They start together, and after 4 days A leaves. How many more days will B need to finish it?
Answer: C. 3 1/3 days
Solution
Together 1-day work = 1/15 + 1/10 = 1/6 In 4 days = 4/6 = 2/3 Remaining = 1/3, B's rate = 1/10 Time = (1/3) x 10 = 3 1/3 days Answer: 3 1/3 days
20 men can complete a work in 24 days. After 6 days, 5 men leave. In how many more days will the remaining men finish the work?
Answer: A. 24 days
Solution
Total = 20 x 24 = 480 man-days Done in 6 days = 120 Left = 360 man-days Men now = 15 Time = 360 / 15 = 24 days Answer: 24 days
A, B and C can do a piece of work in 10, 15 and 30 days respectively. They work together and are paid ₹4,200. How much does A get?
Answer: D. ₹2,100
Solution
Rates 1/10 : 1/15 : 1/30 = 3 : 2 : 1 (total 6 parts) All work for the same time, so wages follow the same ratio A's share = 3/6 of 4,200 = ₹2,100 Answer: ₹2,100
A can do a work in 9 days and B in 18 days. A starts the work and B joins him after 3 days. In how many days from the start is the work finished?
Answer: B. 7 days
Solution
A's work in 3 days = 3/9 = 1/3 Remaining = 2/3 A + B together = 1/9 + 1/18 = 1/6 per day Time for the rest = (2/3) / (1/6) = 4 days Total = 3 + 4 = 7 days Answer: 7 days
One man does the work of two women. 6 men and 8 women can finish a job in 12 days. How many days will 3 men and 6 women take?
Answer: C. 20 days
Solution
Convert to men: 8 women = 4 men, so first group = 6 + 4 = 10 men Total work = 10 x 12 = 120 man-days Second group: 6 women = 3 men, so 3 + 3 = 6 men Days = 120 / 6 = 20 Answer: 20 days
A can finish a work in 40 days and B in 60 days. A works alone for 10 days and then B joins him. In how many more days will they finish the work together?
Answer: A. 18 days
Solution
A's work in 10 days = 10/40 = 1/4 Remaining = 3/4 Together = 1/40 + 1/60 = 5/120 = 1/24 per day Time = (3/4) x 24 = 18 days Answer: 18 days
A and B together can do a work in 6 days; B and C together in 10 days; A and C together in 7 1/2 days. In how many days can C alone do it?
Answer: D. 30 days
Solution
A+B = 1/6, B+C = 1/10, A+C = 2/15 Sum = 5/30 + 3/30 + 4/30 = 12/30, so 2(A+B+C) = 2/5 A+B+C = 1/5 C = 1/5 - 1/6 = 1/30 C alone takes 30 days Answer: 30 days
A can do 1/4 of a work in 5 days and B can do 2/5 of it in 8 days. How many days will they take together to finish the work?
Answer: B. 10 days
Solution
A: 1/4 of the work in 5 days, so whole work in 20 days B: 2/5 of the work in 8 days, so whole work in 20 days Together: 1/20 + 1/20 = 1/10 Time = 10 days Answer: 10 days
A, B and C can do a work in 10, 15 and 30 days respectively. They work one day each in turn: A on day 1, B on day 2, C on day 3, and so on. In how many days is the work finished?
Answer: C. 15 days
Solution
1-day work: A = 1/10, B = 1/15, C = 1/30 In a 3-day cycle: 1/10 + 1/15 + 1/30 = 6/30 = 1/5 Five cycles finish the work: 5 x 3 = 15 days Answer: 15 days
A and B can do a job in 10 days. With C's help they finish it in 6 days. How many days will C alone need?
Answer: A. 15 days
Solution
A+B = 1/10, A+B+C = 1/6 C = 1/6 - 1/10 = 5/30 - 3/30 = 2/30 = 1/15 C alone takes 15 days Answer: 15 days
A contractor employs 30 men to finish a road in 40 days. After 25 days only one-third of the road is finished. How many extra men must he employ to finish the rest in the remaining time?
Answer: D. 70 men
Solution
30 men in 25 days did 1/3 of the work, so the full work = 30 x 25 x 3 = 2,250 man-days Left = 2,250 - 750 = 1,500 man-days in the remaining 15 days Men needed = 1,500 / 15 = 100 Extra men = 100 - 30 = 70 Answer: 70 men
A, B and C can do a piece of work in 10, 12 and 20 days respectively. They start together, but A leaves 2 days and C leaves 4 days before the work is finished, while B works till the end. In how many days is the work completed?
Answer: B. 6 days
Solution
Let the work last x days: B works x days, A works (x - 2), C works (x - 4) x/12 + (x - 2)/10 + (x - 4)/20 = 1 Solving, x = 6 Check: 6/12 + 4/10 + 2/20 = 1 Answer: 6 days
A alone can do a job in 6 days and B alone in 8 days. With C's help they finish it in 3 days, and they are paid ₹9,000 in all. What should C get?
Answer: C. ₹1,125
Solution
A = 1/6, B = 1/8, A+B+C = 1/3 C = 1/3 - 1/6 - 1/8 = (8 - 4 - 3)/24 = 1/24 Shares of work in 3 days = 1/2 : 3/8 : 1/8 = 4 : 3 : 1 C's share = 1/8 of 9,000 = ₹1,125 Answer: ₹1,125
A can do a work in 12 days and B in 16 days. They work on alternate days, B starting first. In how many days will the work be finished?
Answer: A. 13 3/4 days
Solution
Take total work = 48 units: A = 4 units/day, B = 3 units/day B, A, B, A, ... gives 7 units per 2 days After 12 days (6 cycles): 42 units. Left = 6 Day 13 is B's: 3 units, total 45, left 3 Day 14 is A's: A needs 3/4 of a day Total = 13 3/4 days Answer: 13 3/4 days
A can do a work in 15 days and B in 30 days. They work together for 3 days, then C joins them and the work is finished in 2 more days. In how many days can C alone do the whole work?
Answer: D. 4 days
Solution
A + B = 1/15 + 1/30 = 1/10 per day In 3 days = 3/10, remaining = 7/10 The remaining work is done in 2 days, so A+B+C = 7/20 per day C = 7/20 - 1/10 = 5/20 = 1/4 C alone takes 4 days Answer: 4 days
A and B start a work together. After 4 days A leaves and B finishes the remaining work in 9 more days. If B alone can do the whole work in 15 days, in how many days can A alone do it?
Answer: B. 30 days
Solution
B alone in 9 days does 9/15 = 3/5 So A and B together did 2/5 in 4 days: 1/10 per day A = 1/10 - 1/15 = 1/30 A alone takes 30 days Answer: 30 days
A can complete a job in 22 days. B is 50% more efficient than A, and C is twice as efficient as B. In how many days will A, B and C together complete the job?
Answer: C. 4 days
Solution
Efficiency A : B : C = 2 : 3 : 6 (B = 1.5 times A, C = 2 times B) Total efficiency = 11 units. A alone does 2 units/day, so total work = 2 x 22 = 44 units Time together = 44 / 11 = 4 days Answer: 4 days
A, B and C can finish a work in 12, 15 and 20 days respectively. They start together, but C leaves after 2 days. In how many days from the start is the work finished?
Answer: A. 6 days
Solution
Rates: 5/60, 4/60, 3/60; together 12/60 per day In 2 days = 24/60, left = 36/60 A + B = 9/60 per day Time for the rest = 36/9 = 4 days Total = 2 + 4 = 6 days Answer: 6 days
30 men can finish a work in 60 days. After 15 days, 20 more men join them. By how many days is the work finished earlier than the original schedule?
Answer: D. 18 days
Solution
Total = 30 x 60 = 1,800 man-days; done in 15 days = 450 Left = 1,350 man-days with 50 men: 1,350 / 50 = 27 days Original remaining time = 45 days Earlier by 45 - 27 = 18 days Answer: 18 days
B takes 6 days more than A to do a work alone. Together they finish it in 4 days. In how many days can B alone do the work?
Answer: B. 12 days
Solution
Let A take x days, B takes (x + 6) 1/x + 1/(x + 6) = 1/4 4(2x + 6) = x(x + 6) x^2 - 2x - 24 = 0, so (x - 6)(x + 4) = 0, x = 6 A = 6 days, B = 12 days Answer: 12 days
A alone can do a job in 20 days and B alone in 30 days. With C's help the three complete it in 8 days and are paid ₹1,200. What is C's share?
Answer: C. ₹400
Solution
A + B = 1/20 + 1/30 = 1/12; all three = 1/8 C = 1/8 - 1/12 = 1/24 Work done in 8 days: A = 2/5, B = 4/15, C = 1/3 = 6/15 : 4/15 : 5/15 C's share = 5/15 of 1,200 = ₹400 Answer: ₹400
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