M and R together can do a work in 8 days. R and P together can do the same work in 6 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: A
Explanation
Work done by (M + R) in 1 day = 1/8
Work done by (R + P) in 1 day = 1/6
Work done by (P + M) in 1 day = 1/12
Combined work of all three -
2(M + R + P) = 1/8 + 1/6 + 1/12
= 3/24 + 4/24 + 2/24
= 9/24
= 3/8
M + R + P = 3/16
Work done by P -
= (M + R + P) - (M + R)
= 3/16 - 1/8
= 3/16 - 2/16
= 1/16
Time taken by P to work alone = 16 days