Question

Yash takes 6 days more to complete a certain work than bhumika. Together they finish the work in 4 days. How many days would each take to complete that work if the work alone?

Answer 1

Answer:

bhumika takes 6 days and yash takes 12 days

Answer 2

Therefore Yash takes 14 days and Bhumika takes 8 days to complete that work if they work alone.

Step-by-step explanation:

Given, Yash takes 6 days more to complete a certain work than Bhumika. Together they finish the work in 4 days.

Let , Bhumika takes x day to complete the work.

So, Yash takes (x+6) days to complete the work.

Therefore  Bhumika  can do $\frac{1}{x}$ part of the work in one day.

and Yash can do $\frac{1}{x+6}$ part of the work in one day.

According to the problem,

$4(\frac{1}{x}+\frac{1}{x+6}) = 1$

$\Leftrightarrow \frac{x+6+x}{x(x+6)} =\frac{1}{4}$

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

$\Leftrightarrow 4({2x+6}) ={1}{(x^2+6x)$

$\Leftrightarrow 8(x+6) =x(x+6)$

$\Leftrightarrow x(x+6)- 8(x+6) =0$

$\Leftrightarrow (x+6)(x-8)=0$

Either x+6=0       or x-8=0

          x= -6               x=8

x=8 [ because day can't negative]

Therefore Yash takes (8+6) days = 14 days and Bhumika takes 8 days to complete that work if they work alone.