A and B alone can do a work in 12 days and 18 days respectively. A, B and C…
2021
A and B alone can do a work in 12 days and 18 days respectively. A, B and C together can do the same work in 6 days. In how many days can C alone do the work?
- A.
48
- B.
24
- C.
36
- D.
30
Attempted by 71 students.
Show answer & explanation
Correct answer: C
Solution:
Step 1: Find individual daily work rates. A's rate = 1/12, B's rate = 1/18, so A + B = 1/12 + 1/18 = 5/36 (of the work per day).
Step 2: All three together complete the work in 6 days, so combined rate = 1/6 = 6/36 (of the work per day).
Step 3: C's rate = combined rate − (A + B) rate = 6/36 − 5/36 = 1/36 (of the work per day).
Step 4: Time for C alone = reciprocal of C's rate = 36 days.
Answer: 36 days
Check: 1/12 + 1/18 + 1/36 = 3/36 + 2/36 + 1/36 = 6/36 = 1/6, which matches the given combined time of 6 days.