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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.
Solution
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.
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