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P and Q together can complete some work in 30 days. Q and R together can do the same in 24 days. R and P together will take 20 days to complete it. If
Question

P and Q together can complete some work in 30 days. Q and R together can do the same in 24 days. R and P together will take 20 days to complete it. If they all work together, in how many days will the job get done?

A.

25

B.

8

C.

15

D.

16

Correct option is D


Solution:
One day work of P and Q = 1/30
One day work of Q and R = 1/24
One day work of R and P = 1/20
One day work of P, Q and R = 1/2 (1/30+ 1/24+ 1/20)
= 1/2 ((4+5+6)/120)
= 1/2 (15/120)
= 1/2 (1/8)
=1/16
Therefore, P, Q and R can complete the work together in 16 days.

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