P and Q can do a work together in 30 days. Q and R can do the same work together in 24 days and R and P can do it together in 20 days. They started the work together, but Q and R left after 10 days. How many more days will P take to finish the remaining work?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 18.
Concept used:
Total work = Efficiency × time
Calculations:
Let the total work done by P and Q, Q and R, and R and S (LCM of 30, 24, and 20) = 120 units
Efficiency of P + Q = 120/30 = 4
Efficiency of Q + R = 120/24 = 5
Efficiency of R + P = 120/20 = 6
Efficiency of (P + Q + R) = 15/2 = 7.5
Now,
Efficiency of P = 7.5 - 5 = 2.5
Work done by P, Q, and R for the starting 10 days = 7.5 × 10 = 75 units
Remaining work = 120 - 75 = 45 units
Days taken by P to finish the remaining work = 45/2.5 = 18 days