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A can do work in 20 days. Then, he is assisted by B to complete the remaining work in 12 days. In how much time can B alone do the work?

Question

A can do work in 20 days. Then, he is assisted by B to complete the remaining work in 12 days. In how much time can B alone do the work?

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Solution

Let's solve the problem step by step:

  1. Let's assume that the total work to be done is represented by the variable "W".

  2. We are given that A can complete the work in 20 days. Therefore, A's work rate can be calculated as 1/20 of the total work per day.

  3. A and B together complete the remaining work in 12 days. This means that in 12 days, they complete 1 - 1/20 = 19/20 of the total work.

  4. Let's represent B's work rate as "x" (in terms of the total work per day). Since A and B together complete 19/20 of the work in 12 days, we can set up the equation: (1/20 + x) * 12 = 19/20.

  5. Simplifying the equation, we get: 12/20 + 12x = 19/20.

  6. Multiplying both sides of the equation by 20 to eliminate the fractions, we get: 12 + 240x = 19.

  7. Rearranging the equation, we get: 240x = 19 - 12.

  8. Simplifying further, we get: 240x = 7.

  9. Dividing both sides of the equation by 240, we get: x = 7/240.

  10. Therefore, B's work rate is 7/240 of the total work per day.

  11. To find out how much time B alone can do the work, we need to calculate the reciprocal of B's work rate. So, B can complete the work in 240/7 days.

  12. Simplifying the fraction, we get: B can complete the work in approximately 34.29 days.

Therefore, B alone can do the work in approximately 34.29 days.

This problem has been solved

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