Abu does a work in 15 days whereas Basu and Cornel does the same work in 12…
2025
Abu does a work in 15 days whereas Basu and Cornel does the same work in 12 and 20 days respectively. All the three started work together. Cornel left the work after 2 days and Basu left 3 days before competition of work. Find the total number of days in which work will be completed?
- A.
7(1/2)
- B.
7(1/4)
- C.
7(1/3)
- D.
7(2/3)
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Correct answer: D
Solution:
Let the total time to complete the work be x days.
One-day work of Abu = 1/15, Basu = 1/12, and Cornel = 1/20.
Cornel works for 2 days → work done by Cornel = 2/20.
Basu leaves 3 days before completion → Basu works (x − 3) days → work done by Basu = (x − 3)/12.
Abu works x days → work done by Abu = x/15.
Total work equation: x/15 + (x − 3)/12 + 2/20 = 1.
Clear denominators by multiplying both sides by 60: 4x + 5(x − 3) + 6 = 60.
Simplify: 4x + 5x − 15 + 6 = 60 → 9x − 9 = 60 → 9x = 69 → x = 69/9 = 23/3 = 7 2/3 days.
Answer: The work is completed in 23/3 = 7 2/3 days.