Question

A

takes

10

days less than the time taken by

B

to finish a piece of work. If both

A

and

B

together can finish the work in

12

days, find the time taken by

B

to finish the work.

Accepted Answer

Let $10$ alone take $x$ days to finish the work.
Then, $A$ one day's work $12$

$A$ alone can finish it in $(x - 10)$ days.
Then, $A' s$ one day's work $= \frac{1}{x - 10}$

It is given that $A$ and $B$ together can finish the work in $12$ days.

$A' s$ one day's work $+ B' s$ one day's work $= (A + B)' s$ one day's work.

$\frac{1}{x} + \frac{1}{x - 10} = \frac{1}{12}$

$\frac{x - 10 + x}{x (x - 10)} = \frac{1}{12}$

$\frac{2 x - 10}{x (x - 10)} = \frac{1}{12}$

$x^{2} - 10 x = 24 x - 120$

$x^{2} - 10 x - 24 x + 120 = 0$

$x^{2} - 34 x + 120 = 0$

Factorising quadratic equation by splitting the middle term, we get:

$x^{2} - 30 x - 4 x + 120 = 0$

$x (x - 30) - 4 (x - 30) = 0$

$(x - 30) (x - 4) = 0$

$(x - 30) = 0$ or $(x - 4) = 0$

$x = 30$ or $x = 4$

But $x = 4$ is not correct as we substitute the value of $x$ as $4$ , $A$ 's work will be negative which is not correct.

Therefore, $x = 30$ is correct.

Hence, the time taken by $B$ to finish the work is $x = 30$ days.

R. D. Sharma Solutions for Chapter: Quadratic Equations, Exercise 12: EXERCISE 4.12

R. D. Sharma Mathematics Solutions for Exercise - R. D. Sharma Solutions for Chapter: Quadratic Equations, Exercise 12: EXERCISE 4.12

Questions from R. D. Sharma Solutions for Chapter: Quadratic Equations, Exercise 12: EXERCISE 4.12 with Hints & Solutions

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