Question

A and B can build a wall in `6(2)/(3)` days. If A's one day work is `1(1)/(4)` of one day work of B, find in 4 how many days A and B alone can build the wall.

Answer 1

Let A alone will do the work in x days
and B alone will do the same work in y days.
Then, A's 1 day work = `(1)/x` and B's 1 day work = `(1)/y`
According to given information, we have
`(1)/x + (1)/y = (1)/(6(2)/(3)`

⇒ `(1)/x + (1)/y = (3)/(20)`    ....(i)

And, 
`(1)/x = 1(1)/(4) xx (1)/y`

⇒ `(1)/x - (5)/(4y)` = 0        ....(ii)
Subtracting eqn. (ii) from eqn. (i), we get
`(1)/y + (5)/(4y) = (3)/(20)`

⇒ `(9)/(4y) = (3)/(20)`

⇒ 4y = `(9 xx 20)/(3)` = 60
⇒ y = 15
⇒ `(1)/x - (5)/(4(15))` = 0

⇒ `(1)/x = (1)/(12)`
⇒ x = 12
Thus, A alone will do the work in 12 days and B alone will do the same work in 15 days.