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A can complete a work in 11 more days than B, while A does the same work in 36 days more than C. A+ B can complete the whole work in same time in which C alone does the whole work. In how many days A alone could complete the same work?

Question

A can complete a work in 11 more days than B, while A does the same work in 36 days more than C. A+ B can complete the whole work in same time in which C alone does the whole work. In how many days A alone could complete the same work?

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Solution

Let's denote the time it takes for A, B, and C to complete the work as a, b, and c respectively.

From the problem, we know that:

  1. a = b + 11
  2. a = c + 36
  3. 1/a + 1/b = 1/c

We can substitute the first two equations into the third to get:

1/(b+11) + 1/b = 1/(b+11-36)

Solving this equation gives us b = 15.

Substituting b = 15 into the first equation gives us a = 15 + 11 = 26.

So, A alone could complete the work in 26 days.

This problem has been solved

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