M and R together can do a work in 16 days. R and P together can do the same work in 24 days. P and M together can do the same work in 12 days. In how many days can P alone do the same work?
Show answer & explanation
Correct answer: D
Explanation
M + R = 1/16 -------(1)
R + P = 1/24 --------(2)
P + M = 1/12 -------(3)
Adding the three equations -
2(M + R + P)
= 1/16 + 1/24 + 1/12
= 3/48 + 2/48 + 4/48
= 9/48
= 3/16
M + R + P = 3/32
Work done by P in one day -
P = (M + R + P) - (M + R)
= 3/32 - 1/16
= 3/32 - 2/32
= 1/32
P alone will complete the work = 32 days