Question

A and B together can complete a piece of work in 4 days, but A alone can do it a in 12 days. How many days would B alone take to do the same work.

Answer 1

Number of days A takes alone to complete the work = 12 Days.

∴ Amount of work done by A in 1 day = `(1)/(12)`

Let the number of Days B working alone = x

∴ Amount of work done by B in 1 day = `(1)/x`

No of Days they take working together = 4 days

∴ Amount of work done by both in 1 day = `(1)/(4)`

⇒ `(1)/(12) + (1)/x = (1)/(4)`

⇒ `(1)/x = (1)/(4) - (1)/(12)`

= `(3 - 1)/(12)`

= `(2)/(12)`

= `(1)/(6)`
⇒ x = 6 days.
Thus, the number of Days B working alone = 6 days.