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X 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 until the completion of the work. How long did the work last?

Question

X 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 until the completion of the work. How long did the work last?

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Solution

Sure, let's solve this step by step:

  1. First, we need to find out how much work X and Y can do in a day. We know that X can complete the work in 20 days, so X can do 1/20 of the work in a day. Similarly, Y can do 1/12 of the work in a day.

  2. X started the work alone and worked for 4 days. So, in 4 days, X can do 4 * (1/20) = 1/5 of the work.

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

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

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

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

This problem has been solved

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