A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in:
- (a) 4 days
- (b) 6 days
- (c) 8 days
- (d) 12 days
- (b) 6 days
A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B had to leave and A alone completed the remaining work. The whole work was completed in:
- (a) 8 days
- (b) 10 days
- (c) 12 days
- (d) 15 days
- (c) 12 days
A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work?
- (a) 18 days
- (b) 24 days
- (c) 30 days
- (d) 36 days
- (a) 18 days
1. Calculate the individual work rates of A, B, and C:
- For A and B:
- A and B together can complete the work in 30 days.
- Combined work rate of A and B:
Work rate of A + B =1/30of the work per day
- For B and C:
- B and C together can complete the work in 24 days.
- Combined work rate of B and C:
Work rate of B + C =1/24of the work per day
- For C and A:
- C and A together can complete the work in 20 days.
- Combined work rate of C and A:
Work rate of C + A =1/20of the work per day
2. Determine the individual work rates of A, B, and C:
- Adding all three equations to find A + B + C:
- (A + B) + (B + C) + (C + A) =
1/30+1/24+1/20 - 2A + 2B + 2C =
1/30+1/24+1/20 - 2(A + B + C) =
1/30+1/24+1/20 - Find a common denominator (120):
1/30 = 4/120,1/24 = 5/120,1/20 = 6/120 - 2(A + B + C) =
4/120+5/120+6/120=15/120=1/8 - A + B + C =
1/16
- (A + B) + (B + C) + (C + A) =
- Therefore:
- Work rate of A + B =
1/30 - Work rate of B + C =
1/24 - Work rate of C + A =
1/20 - A + B + C =
1/16 - A = (A + B + C) – (B + C) =
1/16–1/24=1/48 - B = (A + B + C) – (C + A) =
1/16–1/20=1/80 - C = (A + B + C) – (A + B) =
1/16–1/30=7/240
- Work rate of A + B =
3. Calculate the total work done by A, B, and C together in 10 days:
- Combined work rate:
1/16 - Work done in 10 days = 10 ×
1/16=10/16=5/8
4. Determine the remaining work and the time A will take to finish it:
- Remaining work:
- Remaining work = 1 –
5/8=3/8
- Remaining work = 1 –
- Time taken by A alone:
- Work rate of A =
1/48 - Time required =
3/8/1/48=3/8× 48 = 18 days
- Work rate of A =
Therefore, A will take:
- (a) 18 days more to finish the work.
A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work is:
- (a) 4 days
- (b) 6 days
- (c) 8 days
- (d) 18 days
- (a) 4 days
Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?
- (a) 3:4
- (b) 4:3
- (c) 5:3
- (d) Data inadequate
- (b) 4:3
A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in:
- (a) 4 days
- (b) 6 days
- (c) 8 days
- (d) 12 days
- (c) 8 days
A can finish a work in 24 days, B in 9 days and C in 12 days. B and C start the work but are forced to leave after 3 days. The remaining work was done by A in:
- (a) 5 days
- (b) 5/6 days
- (c) 10 days
- (d) 10 × 1/2 days
- (c) 10 days
X can do a piece of work in 40 days. He works at it for 8 days and then Y finished it in 16 days. How long will they together take to complete the work?
- (a) 13 ⅓ days
- (b) 20 days
- (c) 15 days
- (d) 26 days
- (a) 13 ⅓ days
A and B can do a job together in 7 days. A is 1 3/4 times as efficient as B. The same job can be done by A alone in:
- (a) 9 × ⅓ days
- (b) 11 days
- (c) 12 × 1/4 days
- (d) 16 × ⅓ days
- (b) 11 days
A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?
- (a) 30 days
- (b) 40 days
- (c) 60 days
- (d) 70 days
- (c) 60 days