A alone can do a piece of work in 10 days, B alone in 12 days ,C alone in 15…
2024
A alone can do a piece of work in 10 days, B alone in 12 days ,C alone in 15 days .If all start work at same day . A works for 2 days and C leaves before 3 days of remaining work. In how many days work will finish ?
- A.
19/3
- B.
20/3
- C.
7
- D.
22/3
Attempted by 750 students.
Show answer & explanation
Correct answer: B
Key idea: let x be the total number of days to finish the work. A works for 2 days, B works for x days, and C leaves 3 days before completion, so C works (x - 3) days.
A's rate = 1/10 work per day
B's rate = 1/12 work per day
C's rate = 1/15 work per day
Write the total-work equation:
2*(1/10) + x*(1/12) + (x - 3)*(1/15) = 1
Multiply both sides by 60 (LCM of 10, 12, 15):
12 + 5x + 4(x - 3) = 60
Simplify: 12 + 5x + 4x - 12 = 60 → 9x = 60 → x = 20/3
Therefore, the work finishes in 20/3 days (approximately 6.67 days).
