Question

A and B together can complete a piece of work in 6 days. A can do it alone in 10 days. Find the number of days in which B alone can do the work.

Answer 1

Let the number of days in which B alone can do the work be x days.

So, B can do `(1)/x` part of the work in a day.
Given that the number of days in which A alone can do the work is 10 days.

So. A can do `(1)/(10)` part of the work in a day.

Together they can complete the work in 6 days.

So, together they can do `(1)/(10)` part of the work in a day.

As per the given condition,

`(1)/x + (1)/(10) = (1)/(6)`

⇒ `(10 + x)/(10x) = (1)/(6)`

⇒ 6(10 + x) = 10x
⇒ 60 + 6x = 10x
⇒ 4x = 60
⇒ x = 15
Hence, B can complete the work in 15days.