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` 

⇒ x² – 10x = 12(2x – 10) 

⇒ x² – 10x = 24x – 120 

⇒ x² – 34x + 120 = 0 

⇒ x² – (30 + 4)x + 120 = 0 

⇒ x² – 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.