Question

A take 27 hours more to complete work a and b together and b takes 3 hours more to complete work a and b then in how many hours a alone can do the work​

Answer 1

Answer:

9 hrs

Step-by-step explanation:

Let, A and B while working alone would have completed the job in a hours and b hours respectively.

So, efficiency of A = (1 / a) and efficiency of B = (1 / b).

Combined efficiency of A and B = (1 / a) + (1 / b) = {(a + b) / ab}

So, on working together, A and B would have completed the job in {ab / (a + b)} hours.

So, a - {ab / (a + b)} = 27

Or, a^2 = 27 * (a + b)……………………(1)

And, b - {ab / (a + b)} = 3

Or, b^2 = 3 * (a + b)………………………..(2)

(1) / (2) gives: (a^2) / (b^2) = 27 / 3

Or, a = 3b………………………………………..(3)

Thus, from (1) and (3):-

a^2 = 27a + 27b = 27a + 9a = 36a

Or, a = 36……………….since, a ≠ 0.

So, b = (a / 3) = 12.

So, {ab / (a + b)} = 9.

Thus, A and B working together would have completed the job in 9 hours.

hope it helps you