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A and B working together can do work in 6 days. If A takes 5 days less than B to finish the work, in how many days B alone can do the work:

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5, 7

15, 08

10, 15

7, 90

answer is C.

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Detailed Solution

Concept- Generatethe equations and substitute them on one another. After that we have to solve the quadratic equation
Given, A and B working together in 6 days, A takes 5 days less than B to finish the work
Suppose,

B = x

A = x - 5

…….(1),

\frac{1}{x} - \frac{1}{x - 5} = \frac{1}{6}

(\frac{x - 5 + x}{x^{2} - 5 x}) = \frac{1}{6}

Cross multiplication,

12 x - 30 = x^{2} - 5 x

x^{2} - 17 x + 30 = 0

x^{2} - 15 x - 2 x + 30 = 0

(x - 2) (x - 15) = 0

x = 2, 15

Put the value in equation (1),

A = x - 5

A = 15 - 5 = 10

B = 15

Hence, the correct option is 3.

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