P and Q together can complete a work in 30 days. Q and R together can complete the same work in 37.5 days. R and P together can complete the same work in 150 days. In how many days can all three complete the same work while working together?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 30 days.
P and Q together can complete a work in 30 days,
Q and R together can complete the same work in 37.5 days, and
R and P together can complete the same work in 150 days
Total work (L.C.M of 30, 75/2, and 150) = 150 units
The efficiency of P and Q = 150/30 = 5
The efficiency of Q and R = 150/75/2 = 4
The efficiency of R and P = 150/150 = 1
Now,
⇒ 2(P + Q + R) = (5 + 4 + 1)
⇒ (P + Q + R) = 10/2
Efficiency of P, Q, and R = 5
Hence, the time taken by P, Q, and R together to complete the work = 150/5 = 30 days