If P can do a work in 6 days and Q can do the same work in 8 days. If R who…
2023
If P can do a work in 6 days and Q can do the same work in 8 days. If R who can do the same work in 12 days, joins them, then the work will be completed in how many days?
- A.
7/3 days
- B.
8/3 days
- C.
10/3 days
- D.
11/3 days
Attempted by 61 students.
Show answer & explanation
Correct answer: B
Solution:
P's rate = 1/6 work per day, Q's rate = 1/8 work per day, R's rate = 1/12 work per day. Combined rate = 1/6 + 1/8 + 1/12.
Compute using LCM 24: 1/6 = 4/24, 1/8 = 3/24, 1/12 = 2/24. So combined rate = (4 + 3 + 2)/24 = 9/24 = 3/8 work per day.
Time to finish the work = reciprocal of rate = 1 ÷ (3/8) = 8/3 days.
Final answer: 8/3 days (about 2 2/3 days).