P can do as much work as Q and R together can do. P and Q can together do a piece of work in 8 hours and 24 minutes and R can do it in 42 hours. Find the time (in hours) that Q needs to do the work alone.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 21 hours.
P and Q can together do a piece of work in 8 hours and 24 minutes = 8 + 24/60 = 8 + 2/5 = 42/5 hours
and R can do it in 42 hours
L.C.M(42/5 and 42) = 42
The efficiency of P and Q = 42/42/5 = 5 units
The efficiency of R = 42/42 = 1 units
P + Q + R = 5 + 1 = 6 units
P can do as much work as Q and R together can do
P = 3 units
Q + R = 3 units
R's efficiency = 1 units
So, the efficiency of Q = 3 - 1 = 2 units
Time taken by Q = 42/2 = 21 hours