Question

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

Answer 1

Answer:

30 days

Explanation:

Total no of days = 12 days

Let time taken by A to complete the work = x days

Let time taken by B to complete the work = (x+10) days

∴ In 1 day, A completes = 1 / (x) th work

∴ In 1 day , B completes = 1/ (x+10) th work

ATQ

1 / x   + 1 / x+10 = 1/12

x+ x+10 / x2 + 10x = 1/12

12 (2x+ 10) = x2 +10x

24x + 120 = x2 + 10x

∴ x2 - 14x - 120 = 0

x2 - 20x + 6x -120 = 0

x( x-20) +6(x-20) = 0

∴ x= -6  or x= 20

But since x is no of days, x ≠ -6..

Hence, x = 20

⇒ A will take 20 days to finish the work while B will take (20 + 10)= 30 days to finish the work..

Hope this helps you..!!