A can do a piece of work in 4 days, B can do it in 20 days. With the help of…
2023
A can do a piece of work in 4 days, B can do it in 20 days. With the help of C, they finish the work in 2 days. In how many days can C alone do the whole work?
- A.
4 days
- B.
5 days
- C.
6 days
- D.
7 days
Attempted by 55 students.
Show answer & explanation
Correct answer: B
Answer: 5 days
Work-rate method (step-by-step):
A's rate = 1/4 work per day.
B's rate = 1/20 work per day.
Combined rate for finishing in 2 days = 1/2 work per day.
C's rate = combined rate − A's rate − B's rate = 1/2 − 1/4 − 1/20 = 1/5 work per day.
Time for C alone = 1 ÷ (1/5) = 5 days.
Quick check: 1/4 + 1/20 + 1/5 = 5/20 + 1/20 + 4/20 = 10/20 = 1/2, so together they finish in 2 days.