A can do a piece of work in 10 days, and B can do the same work in 15 days. In how many days can they complete the work if they work together?
Answer:
6 days
A's 1 day's work = 1/10. B's 1 day's work = 1/15. Together, their 1 day's work = (1/10) + (1/15) = (3+2)/30 = 5/30 = 1/6. Therefore, working together, they will complete the work in 6 days.
2
If X can finish a job in 20 days and Y can finish the same job in 30 days, how long will they take to finish it together?
Answer:
12 days
X's rate = 1/20, Y's rate = 1/30. Combined rate = 1/20 + 1/30 = 3/60 + 2/60 = 5/60 = 1/12. Thus, they will finish the job in 12 days.
3
A and B working together can complete a work in 12 days. If A alone can complete it in 20 days, in how many days can B alone complete the work?
Answer:
30 days
Combined rate (A+B) = 1/12. A's rate = 1/20. B's rate = (1/12) - (1/20) = (5-3)/60 = 2/60 = 1/30. So, B alone can complete it in 30 days.
4
P and Q together can do a piece of work in 8 days. If P alone takes 12 days to do it, how many days will Q take to do it alone?
Answer:
24 days
Combined rate = 1/8. P's rate = 1/12. Q's rate = (1/8) - (1/12) = (3-2)/24 = 1/24. Q will take 24 days to complete it alone.
5
A can build a wall in 8 days, and B can build it in 12 days. Working together, how many days will it take them to build the wall?
A, B, and C can complete a piece of work in 10, 12, and 15 days respectively. If they work together, in how many days will the work be finished?
Answer:
4 days
Combined 1 day's work = 1/10 + 1/12 + 1/15 = (6 + 5 + 4)/60 = 15/60 = 1/4. They will finish the work together in 4 days.
7
X, Y, and Z can independently finish a project in 20, 30, and 60 days respectively. How long will it take for them to finish the project if they all work together?
Answer:
10 days
Combined rate = 1/20 + 1/30 + 1/60 = (3 + 2 + 1)/60 = 6/60 = 1/10. Together, they will take 10 days to finish.
8
A and B together can do a work in 12 days, B and C in 15 days, and C and A in 20 days. In how many days can they complete the work if they all work together?
Answer:
10 days
2(A + B + C) = 1/12 + 1/15 + 1/20 = (5 + 4 + 3)/60 = 12/60 = 1/5. So, A + B + C = 1/10. They will take 10 days to complete the work.
9
A and B can do a work in 8 days, B and C in 12 days, and A, B, and C together in 6 days. How long would A and C take to complete the work together?
Answer:
8 days
A+B+C = 1/6. A = (A+B+C) - (B+C) = 1/6 - 1/12 = 1/12. C = (A+B+C) - (A+B) = 1/6 - 1/8 = 1/24. A+C = 1/12 + 1/24 = 3/24 = 1/8. They take 8 days.
10
A can do a piece of work in 24 days, B in 6 days, and C in 12 days. Working together, they will complete the same work in:
A can do a piece of work in 10 days and B in 15 days. They work together for 2 days, and then A leaves. How many days will B take to finish the remaining work?
Answer:
10 days
Combined rate = 1/10 + 1/15 = 1/6. In 2 days, they complete 2*(1/6) = 1/3 of the work. Remaining work = 2/3. B's rate is 1/15. Time taken by B = (2/3) / (1/15) = 10 days.
12
X can do a job in 20 days and Y in 30 days. They work together for 4 days, after which X leaves. In how many days will Y finish the remaining work?
Answer:
20 days
Combined rate = 1/20 + 1/30 = 1/12. In 4 days, they do 4*(1/12) = 1/3. Remaining work = 2/3. Y's rate is 1/30. Time for Y = (2/3) / (1/30) = 20 days.
13
A and B can do a work in 12 and 15 days respectively. They began the work together, but B left 3 days before the completion of the work. In how many days was the total work completed?
Answer:
8 days
Let total days be T. A works for T days, B works for T-3 days. (T/12) + ((T-3)/15) = 1. Multiply by 60: 5T + 4(T-3) = 60 => 9T - 12 = 60 => 9T = 72 => T = 8 days.
14
A can finish a work in 10 days and B in 15 days. They start together, but A leaves 5 days before the completion of the work. How many days did the work take to complete?
Answer:
9 days
Let total days be T. A works for T-5 days, B works for T days. ((T-5)/10) + (T/15) = 1. Multiply by 30: 3(T-5) + 2T = 30 => 5T - 15 = 30 => 5T = 45 => T = 9 days.
15
A, B, and C can do a piece of work in 10, 12, and 15 days respectively. They started the work together, but A left after 2 days. In how many days will B and C finish the remaining work?
Answer:
3 1/3 days
All three's 1 day work = 1/10+1/12+1/15 = 1/4. In 2 days, they did 2/4 = 1/2 work. Remaining = 1/2. B+C rate = 1/12+1/15 = 9/60 = 3/20. Time = (1/2) / (3/20) = 10/3 = 3 1/3 days.
16
P can do a task in 15 days and Q in 20 days. They work together for 4 days and then Q leaves. P finishes the remaining work. How many days in total did P work?
Answer:
12 days
P and Q's combined rate = 1/15 + 1/20 = 7/60. In 4 days, they do 28/60 = 7/15. Remaining = 8/15. P takes (8/15)/(1/15) = 8 days to finish. Total days P worked = 4 + 8 = 12 days.
17
A can do a work in 30 days and B in 45 days. They work together, but B leaves 5 days before the work is finished. What is the total number of days taken to finish the work?
Answer:
20 days
Let total days be T. A works for T days, B works for T-5 days. (T/30) + ((T-5)/45) = 1. Multiply by 90: 3T + 2(T-5) = 90 => 5T - 10 = 90 => 5T = 100 => T = 20 days.
18
A takes twice as much time as B to finish a piece of work. If they can finish the work together in 14 days, how many days will A alone take to finish it?
Answer:
42 days
If A takes twice the time of B, A's rate is half of B's. Let A's rate be 1/2x, B's rate be 1/x. Together: 1/2x + 1/x = 3/2x = 1/14. 2x = 42. So A takes 2x = 42 days.
19
A is thrice as fast as B. If they finish a job together in 15 days, how many days will B alone take to finish the job?
Answer:
60 days
A = 3B in efficiency. Let B's rate be 1/x, A's rate is 3/x. Combined rate = 4/x = 1/15. So x = 60. B alone takes 60 days.
20
A is 50% more efficient than B. If A can do a work in 20 days, how many days will B take to do the same work?
Answer:
30 days
A is 150% of B in efficiency. So, Rate of A = 1.5 * Rate of B. Time taken by B = 1.5 * Time taken by A = 1.5 * 20 = 30 days.
