Question

Pintu takes 6 more days than the Nissu to complete same work.if they work together they finish the same work in 4 days. how many days required to complete to work if they do alone

Answer 1

Answer:

Nishu takes 6 days to complete the work.

And Pintu takes 12 days to complete the work.

Step-by-step-explanation:

Let Nishu takes x days to complete the work.

And Pintu takes ( x + 6 ) days to complete the same work.

In one day, Nishu does

$\sf\:\dfrac{1}{x}$ part of the work.

And Pintu does

$\sf\:\dfrac{1}{x\:+\:6}$ part of the work.

In one day, they together do

$\sf\:(\:\dfrac{1}{x}\:+\:\dfrac{1}{x\:+\:6}\:)$ part of the work.

$\therefore\sf\:\frac{1}{x}\:+\:\dfrac{1}{x\:+\:6}\\\\\implies\sf\:\dfrac{x\:+\:6\:+\:x}{x\:(\:x\:+\:6\:)}\\\\\implies\sf\:\dfrac{2x\:+\:6}{x^{2}\:+\:6x}$

Now,

Total number of days they both take to complete the work is $\sf\:\dfrac{x^{2}\:+\:6x}{2x\:+\:6}$

From the given condition,

$\sf\:\dfrac{x^{2}\:+\:6x}{2x\:+\:6}\:=\:4\\\\\implies\sf\:x^{2}\:+\:6x\:=\:4\:(\:2x\:+\:6\:)\\\\\implies\sf\:x^{2}\:+\:6x\:=\:8x\:+\:24\\\\\implies\sf\:x^{2}\:+\:6x\:-\:8x\:-\:24\:=\:0\\\\\implies\sf\:x^{2}\:-\:2x\:-\:24\:=\:0\\\\\implies\sf\:x^{2}\:-\:6x\:+\:4x\:-\:24\:=\:0\\\\\implies\sf\:x\:(\:x\:-\:6\:)\:+\:4\:(\:x\:-\:6\:)\:=\:0\\\\\implies\sf\:(\:x\:-\:6\:)\:(\:x\:+\:4\:)\:=\:0\\\\\implies\sf\:x\:-\:6\:=\:0\:\:\:or\:\:\:x\:+\:4\:=\:0\\\\\implies\boxed{\red{\sf\:x\:=\:6}}\:\sf\:\:or\:\:\:\boxed{\red{\sf\:x\:=\:-\:4}}$

But, the number of days cannot be negative.

$\therefore\sf\:x\:=\:-\:4\:is\:unacceptable.\\\\\sf\:x\:=\:6\\\\\sf\:(\:x\:+\:6\:)\:=\:(\:6\:+\:6\:)\:=\:12$

Nishu takes 6 days to complete the work.

And Pintu takes 12 days to complete the work.