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Select the correct answerX and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?Options6 days15 days20 days10 days

Question

Select the correct answerX and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?Options6 days15 days20 days10 days

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Solution

To solve this problem, we need to first find out the work done by X and Y in one day.

  1. X can complete the work in 20 days. So, the work done by X in one day is 1/20.
  2. Y can complete the work in 12 days. So, the work done by Y in one day is 1/12.

Now, let's calculate the work done by X in the first 4 days. Since X can do 1/20 of the work in one day, in 4 days he will do 4*(1/20) = 1/5 of the work.

The remaining work is 1 - 1/5 = 4/5.

Now, X and Y work together to complete the remaining work. In one day, X and Y together can do (1/20 + 1/12) = 8/120 = 1/15 of the work.

So, to complete the remaining 4/5 of the work, X and Y will take (4/5) / (1/15) = 12 days.

Therefore, the total time taken to complete the work is 4 days (X alone) + 12 days (X and Y together) = 16 days.

So, none of the options given are correct. The work lasted for 16 days.

This problem has been solved

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