Question

Ram takes six days less than bhagat to finish a piece of work if both of them together can finish the work in 4days in how many days bhagat alone can finish the work

Answer 1

hope you understand......…..

Answer 2

Answer:

12 days

Step-by-step explanation:

Let Ram takes x days to complete work

We are given that Ram takes six days less than bhagat to finish a piece of work

So, Bhagat takes x+6 days to complete work

Ram can do a part of work in 1 day = $\frac{1}{x}$

Bhagat can do a part of work in 1 day = $\frac{1}{x+6}$

Together they can do a part of work together =  $\frac{1}{x}+\frac{1}{x+6}$

We are given that together can finish the work in 4days

So, Together they can do a part of work together = $\frac{1}{4}$

So,  $\frac{1}{x}+\frac{1}{x+6}=\frac{1}{4}$

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

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

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

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

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

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

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

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

$x=-4,6$

Ram takes 6 days to complete work

Bhagat takes x+6 = 6+6 =12 days to complete work

Hence Bhagat alone can finish the work in 12 days