Question

Pintu Takes $6$ days more than those of Nishu to Complete Certain Work. If They Work Together They Finish it in $4$ Days. How Many Days Would it Take to Complete the Work if they Work Alone.

Answer 1

Let the number of days taken by Nishu be $x$

So,Number of days taken by Pintu will be $x+6$

Nishu's $1$ day work$=\frac{1}{x}$

Pintu's $1$ day work$=\frac{1}{x+6}$

Work done together in $4$ days$=\frac{1}{4}$

$\Rightarrow \frac{1}{x}+\frac{1}{x+6}=\frac{1}{4}$

$\Rightarrow \frac{x+6+x}{x^2+6x}=\frac{1}{4}$

$\Rightarrow 8x+24=x^2+6x$

$\Rightarrow x^2+6x-8x-24=0$

$\Rightarrow x^2-2x-24=0$

$\Rightarrow x^2-6x+4x-24=0$

$\Rightarrow x(x-6)+4(x-6)=0$

$\therefore x=-4,6$

Number of days cannot be negative.So,$x=6$

Thus, number of days taken by Nishu$=6$ and that of Pintu$=6+6=12$