Question

A takes 10days 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 alone to finish the work.​

Answer 1

Answer:-

• the time taken by B to finish the work is 30 days.

Explaination:-

Let B will take x days to complete the work.

Work done by B in 1 day = 1/x

And A will complete the work = x - 10

Work done by A in 1 day= 1/(x - 10)

According to the Question,

⇒ 1/x +  1/(x - 10) = 1/12

⇒ 2x - 10/x² - 10x = 1/12

⇒ 12(2x - 10) = x² - 10x

⇒ 24x - 120 = x² - 10x

⇒ x² - 10x - 24x + 120 = 0

⇒ x² - 34x + 120 = 0

⇒ x² 30x - 4x + 120 = 0

⇒ x( x - 30) - 4(x - 30) = 0

⇒ (x - 30) (x - 4) = 0

⇒ x - 30 = 0  or  x - 4 = 0

⇒ x = 30, 4 (Neglecting 4 )

⇒ x = 30

Hence,  the time taken by B to finish the work is 30 days.