A, B and C can do a piece of work in 20, 15 and 30 days respectively. They…
2023
A, B and C can do a piece of work in 20, 15 and 30 days respectively. They start the work together, but C leaves 6 days before the completion of the work. In how many days is the work done?
- A.
9 days
- B.
6 days
- C.
8 days
- D.
10 days
Attempted by 2 students.
Show answer & explanation
Correct answer: C
Concept: When several people work together on a task, their combined work over the time each one actually works must add up to 1 complete job. If a person can finish the whole work alone in n days, their work rate is 1/n of the job per day, and the amount of work they contribute equals (work rate) × (number of days they actually work).
Application: Let the total time to complete the work be x days. A and B work for the entire x days, since only C leaves early. C leaves 6 days before completion, so C works for (x − 6) days.
A's work rate is 1/20 per day, B's is 1/15 per day, and C's is 1/30 per day.
Total work done: x/20 + x/15 + (x − 6)/30 = 1.
Multiply throughout by 60 (LCM of 20, 15, 30): 3x + 4x + 2(x − 6) = 60.
Simplify: 3x + 4x + 2x − 12 = 60, so 9x = 72.
Solve: x = 8.
Cross-check: With x = 8, A contributes 8/20, B contributes 8/15, and C works for (8 − 6) = 2 days, contributing 2/30. Adding these: 8/20 + 8/15 + 2/30 = 1, confirming the total work equals one complete job.
