Question

. a boy takes 15 more hours than a man to complete a work . the boy worked for 18

hours and then the man replaced him and worked for 6 hours. thus 3/5th of the work

was completed. in how much time , will the work be completed considering that the

man continues to work ?​

Answer 1

Given:

Boy takes 15 hours more than a man to complete a work

Boy worked for 18 hours and the man worked for 6 hours after replacing the boy

3/5th of the work was completed

To find:

The remaining time required to complete the work considering the man continues to work

Solution:

Let "x" hours is the time taken by the man to complete the work.

And since the boy takes 15 hours more than the man

∴ "(x+15)" hours is the time taken by the boy

So,

The work done by the man in 1 hour = $\frac{1}{x}$

and

The work done by the boy in 1 hour = $\frac{1}{x \:+\: 15}$

It is given that if the boy work for 18 hours and the man after replacing the boy work for 6 hours then 3/5th of the work is done.

So, we can form an equation as:

$[18 * \frac{1}{x+15}] \:+\:[ 6\: * \:\frac{1}{x}] = \frac{3}{5}$

on dividing by 3 throughout the equation

⇒  $[ \frac{6}{x+ 15}] + [\frac{2}{x}] = \frac{1}{5}$

⇒ $6x \:+\:2(x+15) = \frac{x*(x+15)}{5}$

⇒ $5 * [6x + 2x + 30] = x^2 + 15x$

⇒ $30x + 10x + 150 = x^2 + 15x$

⇒ $x^2 + 15x - 30x - 10x - 150 = 0$

⇒ $x^2 - 25x - 150 = 0$

⇒ $x^2 - 30x + 5x - 150 = 0$

⇒ $x(x-30) + 5(x-30) = 0$

⇒ $(x- 30)(x+5) = 0$

⇒ $x = 30\: or -5$

since hours cannot be negative

∴ $x =$ 30 hours

Since only 3/5th of the work is done

∴ Remaining work = $1 - \frac{3}{5} = \frac{5 - 3}{5} = \frac{2}{5}$

Therefore,

If the man does $\frac{1}{30}$ of the work in 1 hour

Then, the remaining $\frac{2}{5}$ of the work will be done by the man in = $30\: * \:\frac{2}{5} = 6 * 2 =$ 12 hours

Thus, in 12 hours the work will be completed considering that the man continues to work.

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