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P alone can complete the work in 12 days and Q alone can complete the work in 24 days. If P works alone for the first day and Q alone works for second day, after second day P and Q works together for next 5 days. After 7 days, R who has same work efficiency as Q, joins P and Q. In how many days, work will be completed?

P alone can complete the work in 12 days and Q alone can complete the work in 24 days. If P works alone for the first day and Q alone works for second day, after second day P and Q works together for next 5 days. After 7 days, R who has same work efficiency as Q, joins P and Q. In how many days, work will be completed? Correct Answer 8.5 days

Given,

P's 1 day’s work = 1/12

Q's 1 day's work = 1/24

R's 1 day's work = 1/24

(P + Q)’s 1 day's work = 1/12 + 1/24 = 1/8

(P + Q + R)’s 1 day's work = 1/12 + 1/24 + 1/24 = 1/6

First two days’ work = 1/12 + 1/24 = 1/8

(P + Q)’s 5 days’ work = 5/8

Total work completed by P and Q in 7 days =

= 5/8 + 1/8

= 3/4

Remaining work = 1 – 3/4 = 1/4

Number of days taken by P, Q and R to complete the work =

= 1/4 × 6

= 3/2

Total number of days = 7 + 1.5 = 8.5 days

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