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P alone can do `1/2` of a work in 6 days and Q alone can do `2/3` of the same work in 4 days. in how many days will they finish `3/4` of the work, working together?

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#### Solution

`1/2` of the work is done by P in 6 days

∴ Full work is done by P in `6/(1/2)` = 6 × 2 = 12 days

`2/3` of work done by Q in 4 days.

∴ Full work is done by Q in `4/(2/3) = 4 xx 3/2` = 6 days

(P + Q) will finish the whole work in `"ab"/("a" + "b")` days

= `(12 xx 6)/(12 + 6)`

= `(12 xx 6)/18`

= 4 days

(P + Q) will finish `(-3)/4` of the work in `4 xx 3/4` = 3 days.

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