Question

A takes 6 days less than the time taken by B to finish a piece of work.If both together can finish it by 4 days.Find the time taken by B to finish the work​

Answer 1

Suppose B alone takes x days to finish the work. Then A alone can finish it in (x−6) days

Now A's one day's work + B's one day's work =  

x

1

​  

+  

x−6

1

​  

 

and (A+B)'s one day's work =  

4

1

​  

 

∴  

x

1

​  

+  

x−6

1

​  

=  

4

1

​  

 

⇒  

x(x−6)

x−6+x

​  

=  

4

1

​  

⇒  

x  

2

−6x

2x−6

​  

=  

4

1

​  

 

⇒8x−24=x  

2

−6x

⇒x  

2

−14x+24=0

⇒x  

2

−12x−2x+24=0

⇒(x−12)(x−2)=0

⇒x=12orx=2

But x cannot be less than 6.

So x=12

Hence, B also can finish the work in 12 days.