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If P, Q and R can complete a job in 24, 16 and 12 days respectively, how long will they take to complete the job working together?
Question

If P, Q and R can complete a job in 24, 16 and 12 days respectively, how long will they take to complete the job working together?

A.

6 days

B.

5 days 8 hours

C.

5 days 12 hours

D.

5 days

Correct option is B

Given:
P does the work in 24 days
Q does the work in 16 days
R does the work in 12 days
Solution:
Total work = LCM of 24, 16, 12 = 48 unit
Work done by A in 1 day = 48/24 = 2 unit
Work done by B in 1 day = 48/16 = 3 unit
Work done by C in 1 day = 48/12 = 4 unit
They together will compete the work = 48/(2+3+4) = 48/9= 5135 \frac{1}{3}​ days
= 5 days+ 13×24\frac13 \times 24​​
= 5 days 8 hours

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