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A can do a half of certain work in 35 days and B one third of the same in 70 days. They together will do the whole work in.

Question

A can do a half of certain work in 35 days and B one third of the same in 70 days. They together will do the whole work in.

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Solution

To solve this problem, we first need to find out how long it would take for A and B to complete the work individually.

  1. A can do half of the work in 35 days, so A would take 35 * 2 = 70 days to complete the whole work.

  2. B can do one third of the work in 70 days, so B would take 70 * 3 = 210 days to complete the whole work.

Next, we need to find out their combined rate of work. The rate of work is the reciprocal of the time taken to complete the work.

  1. A's rate of work is 1/70 of the work per day.
  2. B's rate of work is 1/210 of the work per day.

So, their combined rate of work is 1/70 + 1/210 = 1/70 + 1/210 = 4/210 = 2/105 of the work per day.

Finally, to find out how long they would take to complete the work together, we take the reciprocal of their combined rate of work.

  1. Therefore, A and B together will do the whole work in 1 / (2/105) = 105/2 = 52.5 days.

This problem has been solved

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