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P and Q can do a piece of work in 12 days and 15 days respectively. P started the work alone and then after 3 days, Q joined him till the work was completed. How long did the work last?

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#### Solution

P can do a piece of work in 12 days.

∴ P’s 1 day work = `1/12`

P’s 3 day’s work = `3 xx 1/12 = 3/12`

Q can do a piece of work in 15 days.

∴ Q’s 1 day work = `1/15`

Remaining work after 3 days = `1 - 3/12 = 9/12`

(P + Q)'s 1 day work = `1/2 + 1/15`

= `5/60 + 4/60`

= `9/60`

∴ Number of days required to finish the remaining work 9

= `"Remaining work"/(("P" + "Q")"'s" 1 "day work")`

= `(9/12)/(9/60)`

= `9/12 xx 60/9`

= 5

Remaining work lasts for 5 days

Total work lasts for 3 + 5 = 8 days.

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