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Question

A,B and C complete a piece of work in 25,20 and 24 days respectively. All work together for 2 days and then A and B leave the work . C works for next 835 days and then A along with D join C and they all finish the work in next three days. In how many days D alone can complete the whole work ?
  1. 22 days
  2. 2112days
  3. 2212days
  4. 23 days

A
22 days
B
2212days
C
23 days
D
2112days
Solution
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Let the amount of work be x.

Now A does the work in 25 days.
In 1 day A does x25 work,

B does the work in 20 days.
In 1 day B does x20 work,

C does the work in 24 days.
In 1 day C does x24 work.

A works for (2+3) days =5 days.
In 5 days A does 5×x25 work = x5 work,

B works for 2 days.
In 5 days B does 2×x20 work=x10 and

C works for (2+835+3)days=685days.
In 685 days C does 685×x24 work=17x15 work.
The total work done by A,B and C, so far = x5+x10+17x13 work = 13x15 work.
The work left = x13x15 work

This work is done by D in 3 days.
D will finish the whole i.e x work in 3×152days =2212 days.

Ans- Option D.

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