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Question
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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