PREVIOUSLY ASKED IN:
WBPSC Miscellaneous Preliminary 2023
Answer
12 days
Explanation
A's 1-day work = \\( \\frac{1}{12} \\), B's 1-day work = \\( \\frac{1}{6} \\). A, B, and C together finish in 3 days, so their 1-day work = \\( \\frac{1}{3} \\). Therefore, C's 1-day work = \\( \\frac{1}{3} - (\\frac{1}{12} + \\frac{1}{6}) \\) = \\( \\frac{1}{3} - \\frac{3}{12} \\) = \\( \\frac{1}{3} - \\frac{1}{4} \\) = \\( \\frac{1}{12} \\). Since C does \\( \\frac{1}{12} \\) of the work in 1 day, C alone will take 12 days to complete the work.
Key Points
- > Total work is considered as 1 unit in the fractional method.
- > Work done by A and B in 1 day = \\( \\frac{1}{12} + \\frac{1}{6} = \\frac{1}{4} \\).
- > Work done by all three in 1 day = \\( \\frac{1}{3} \\).
- > C's daily work = Total - (A+B) = \\( \\frac{1}{3} - \\frac{1}{4} = \\frac{1}{12} \\).
- > LCM method is faster: LCM of 12, 6, 3 is 12 (Total Work).
- > Efficiencies: A=1, B=2, (A+B+C)=4. Thus C=1 unit/day.
- > Time taken by C = 12/1 = 12 days.
Additional Information
LCM Method for Time & Work
| Person | Days | Total Work (LCM) | Efficiency (Units/Day) |
|---|---|---|---|
| A | 12 | 12 | 12/12 = 1 |
| B | 6 | 12 | 12/6 = 2 |
| A+B+C | 3 | 12 | 12/3 = 4 |
| C (Alone) | 12 | 12 | 4 - 3 = 1 |
Memory Tips
- Efficiency Rule: Always convert days into per-day efficiency. Subtraction gives the exact efficiency of the missing person.