P, Q and R alone can do a work in 12, 18 and 24 days respectively. They worked…
2021
P, Q and R alone can do a work in 12, 18 and 24 days respectively. They worked for 5 days, 4 days and 6 days respectively. They received Rs. 32000. What is the share of Q?
- A.
15000
- B.
8000
- C.
12000
- D.
6000
Attempted by 24 students.
Show answer & explanation
Correct answer: B
Step-by-Step Solution
Determine individual daily efficiency:
P can do the work in 12 days → Efficiency = 1/12 of the work per day.
Q can do the work in 18 days → Efficiency = 1/18 of the work per day.
R can do the work in 24 days → Efficiency = 1/24 of the work per day.
Calculate work done by each person:
P worked 5 days: Work done = 5 * (1/12) = 5/12
Q worked 4 days: Work done = 4 * (1/18) = 4/18 = 2/9
R worked 6 days: Work done = 6 * (1/24) = 6/24 = 1/4
Find a common denominator to compare the work:
The LCM of 12, 9, and 4 is 36.
Work done by P = (5/12) * (3/3) = 15/36
Work done by Q = (2/9) * (4/4) = 8/36
Work done by R = (1/4) * (9/9) = 9/36
Total work ratio (P:Q:R) = 15 : 8 : 9.
Calculate Q's share:
Total parts = 15 + 8 + 9 = 32 parts.
Q's share = (Q's parts / Total parts) * Total Payment
Q's share = (8 / 32) * 32,000 = (1/4) * 32,000 = Rs. 8,000.