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P can complete a work in 15 days and Q in 24 days. They began the work together but Q left the work 2 days before its completion. In how many days was the work completed?

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P can complete a work in 15 days and Q in 24 days. They began the work together but Q left the work 2 days before its completion. In how many days was the work completed?


1). 12
2). 10
3). 9
4). 11


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1 answers

2 vote
Answered by on | Votes 2 |

Time taken by P = 15 days

Time taken by Q = 24 days

Let Total work = LCM of 15 and 24 = 120 units

Efficiency of P = 120/15 = 8 units/day

Efficiency of Q = 120/24 = 5 units/day

Total Efficiency of P and Q = 8 + 5 = 13 units/day

Total work done by Q in 2 days = 5 × 2 = 10 units

Now New Total work = 120 + 10 = 130 units

∴ Total time taken to complete the work = 130/13 = 10 days

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