Question

A and B together can do a piece of work in 4 days, but A alone can do it in 12 days. How many days would B alone take to do the same piece of 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)/(12)` part of the work in a day.

Together they can complete the work in 6 days.

So, together they can do `(1)/(4)` part of the work in a day.

As per the given condition,

`(1)/x + (1)/(12) = (1)/(4)`

⇒ `(12 + x)/(12x) = (1)/(4)`

⇒ 4(12 + x) = 12x
⇒ 48 + 4x = 12x
⇒ 8x = 48
⇒ x = 6
Hence, B can complete the work in 6days.