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A can do a piece of work in 5 days and B in 20 days. They work together for 2 days and then both leave the work. Then C alone can finish the remaining work in 6 days. In how many days will C finish the full work?

Question

A can do a piece of work in 5 days and B in 20 days. They work together for 2 days and then both leave the work. Then C alone can finish the remaining work in 6 days. In how many days will C finish the full work?

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Solution

Sure, let's solve this step by step:

  1. First, we need to find the work done by A and B in one day. A can finish the work in 5 days, so A can do 1/5 of the work in one day. Similarly, B can do 1/20 of the work in one day.

  2. When A and B work together, they can do (1/5 + 1/20) = 1/4 of the work in one day.

  3. They work together for 2 days, so in 2 days, they can do 2*(1/4) = 1/2 of the work.

  4. This means that after A and B leave, 1/2 of the work is still remaining.

  5. C can finish this remaining work in 6 days, so C can do 1/2 of the work in 6 days, which means C can do 1/12 of the work in one day.

  6. Therefore, to finish the full work, C will take 1 / (1/12) = 12 days.

This problem has been solved

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