A alone can do 2/3rd of the work in 12 days . B alone can do the 1/4th of the…
2025
A alone can do 2/3rd of the work in 12 days . B alone can do the 1/4th of the work in 6 days . Working together A , B and C complete it in 8 days . What part of the work will be completed by C in 4 days ?
- A.
1/9
- B.
2/7
- C.
1/6
- D.
3/7
Attempted by 3 students.
Show answer & explanation
Correct answer: A
Concept: If a person completes a fraction f of a task in d days, their work rate is f/d per day, and their alone-time to finish the whole task is d/f days. When several people work together, their daily rates simply add: combined rate = rate(A) + rate(B) + rate(C). So one person's individual rate can be found by subtracting the known rates from the combined rate.
Applying it here:
A completes 2/3 of the work in 12 days, so A's rate = (2/3) ÷ 12 = 1/18 work per day (A alone would take 18 days).
B completes 1/4 of the work in 6 days, so B's rate = (1/4) ÷ 6 = 1/24 work per day (B alone would take 24 days).
A, B and C together finish the work in 8 days, so their combined rate = 1/8 work per day.
C's rate = 1/8 − 1/18 − 1/24. Using LCM 72: 9/72 − 4/72 − 3/72 = 2/72 = 1/36 work per day.
In 4 days, C completes 4 × 1/36 = 4/36 = 1/9 of the work.
Cross-check: Adding the three individual rates back — 1/18 + 1/24 + 1/36 = 4/72 + 3/72 + 2/72 = 9/72 = 1/8 — reproduces the given combined rate exactly, confirming C's 4-day share of 1/9.