Question

A and B together can do a piece of work in 6 days. Whereas A alone can do the same work in 9 days. Then B alone will do same work in ______.

पर्याय

• 15 days

• 6 days

• 18 days

• 54 days

Answer 1

A and B together can do a piece of work in 6 days. Whereas A alone can do the same work in 9 days. Then B alone will do same work in 18 days.

Explanation:

Given,

A alone can do the same work in 9 days.

So, one day work of A = `1/9`

Let B alone can do the same work in y days.

So, one day work of B = `1/y`

As together they can do work in 6 days.

∴ In one day, both of them do `1/6​`th part of work.

∴ `9/1​+y/1​=6/1​`

⇒ `(1 × y)/(9 × y) ​+ (1 × 9)/(y xx9) ​= 6/1​`

⇒ `y/(9y​) + 9/(9y) ​= 6/1​`

⇒ `(y + 9)/(9y) = 1/6`

⇒ 6(y + 9) = 9y

⇒ 6y + 54 = 9y

⇒ 9y − 6y = 54

⇒ 3y = 54

⇒ y = `54/3`

⇒ y =18

∴ B alone can complete the work in 18 days.