Shortcut Trick
Total work = LCM(8, 12) = 24 units.
Efficiency of (A + B) = 3 units/day, and (B + C) = 2 units/day.
Total work done: 4A + 6B + 11C = 4(A + B) + 2(B + C) + 9C = 24
⇒ 4(3) + 2(2) + 9C = 24 ⇒ 16 + 9C = 24 ⇒ C = 8/9 units/day.
Time for C alone = 24 ÷ (8/9) = 27 days.
∴ The correct answer is 27 days.
Alternate Method
Given:
Time taken by (A + B) together = 8 days
Time taken by (B + C) together = 12 days
A worked for 4 days, B worked for 6 days, and C finishes the remaining work in 11 days.
Formula Used:
Total Work = LCM of given days
Efficiency = Total Work ÷ Time
| Person | Days | Total Work | Efficiency |
|---|
| A + B | 8 | 24 | 3 |
| B + C | 12 | 2 | |
Calculations:
Let the daily efficiency of A, B, and C be A, B, and C units respectively.
⇒ Total work done = 4A + 6B + 11C = 24
We can rewrite the equation by splitting the terms to match the known combined efficiencies:
⇒ 4A + 4B + 2B + 2C + 9C = 24
⇒ 4(A + B) + 2(B + C) + 9C = 24
Substitute the efficiencies of (A + B) and (B + C) from the table:
⇒ 4 × 3 + 2 × 2 + 9C = 24
⇒ 12 + 4 + 9C = 24
⇒ 16 + 9C = 24
⇒ 9C = 24 − 16
⇒ 9C = 8
⇒ C = 8/9 units/day
Now, calculate the total time C alone will take to complete the total work:
⇒ Time taken by C = Total Work ÷ Efficiency of C
⇒ Time taken by C = 24 ÷ (8/9)
⇒ Time taken by C = (24 × 9) ÷ 8
⇒ Time taken by C = 3 × 9 = 27 days
∴ The correct answer is 27 days.
Additional Information
Pipes & Cisterns
Conceptually identical to Time & Work. Inlet pipes have positive efficiency (filling work) while outlet pipes have negative efficiency (emptying work).
Work & Wages
Wages are strictly distributed in the ratio of the actual total work done by each individual, not merely based on their time spent or efficiency alone.
Alternate Days Work
Calculate the combined work done in one complete rotation cycle (e.g., 2 days for 2 people) and multiply by an integer to reach closest to the total work.