Question

A takes 10 days less than the time taken by B to finish a piece of work. If both A and B together can finish the work in 12 days, find the time taken by B to finish the work.

Answer 1

Let B takes x days to complete the work.
Therefore, A will take `(x-10)`days. 

∴`1/x+1/((x-10))=1/12` 

⇒`((x-10)+x)/(x(x-10))=1/12` 

⇒`(2x-10)/(x^2-10x)=1/12` 

⇒`x^2-10x=12(2x-10)` 

⇒`x^2-10x=24x-120` 

⇒`x^2-34x+120=0` 

⇒`x^2-(30+4)x+120=0` 

⇒`x^2-30x-4x+120=0` 

⇒`x(x-30)-4(x-30)=0` 

⇒`(x-30)(x-4)=0` 

⇒`x=30  or  x=4` 

Number of days to complete the work by
B cannot be less than that by A; therefore, we get: x = 30
Thus, B completes the work in 30 days.