Shortcut Trick
Total work = LCM(8, 4, 16) = 16 units.
Efficiency: A = 2, B = 4, C = 1.
Work done in 2 days (cycle): Day 1 (A alone) = 2 units, Day 2 (A+B+C) = 7 units ⇒ Total 9 units in 2 days.
Remaining work = 16 − 9 = 7 units. Day 3 (A alone) completes 2 units. Remaining = 5 units.
Time for Day 4 (A+B+C) = 5/7 days. Total time = 3 + 5/7 = 26/7 days.
∴ The correct answer is 26/7 days.
Alternate Method
Given:
Time taken by A = 8 days
Time taken by B = 4 days
Time taken by C = 16 days
Concept Used:
Total work is the LCM of the days taken by each person.
Efficiency = Total Work ÷ Days
| Person | Days | Total Work | Efficiency |
|---|
| A | 8 | 16 | 2 |
| B | 4 | 4 | |
| C | 16 | 1 | |
Calculations:
⇒ Work done by A on 1st day = 2 units
⇒ Work done by A, B, and C together on 2nd day = 2 + 4 + 1 = 7 units
⇒ Total work done in 1 cycle of 2 days = 2 + 7 = 9 units
⇒ Remaining work after 2 days = 16 − 9 = 7 units
⇒ Work done by A on the 3rd day = 2 units
⇒ Remaining work after 3 days = 7 − 2 = 5 units
⇒ On the 4th day, A, B, and C work together. Time taken to do 5 units = 5 ÷ 7 days
⇒ Total time taken = 3 days + 5/7 days = (21 + 5)/7 = 26/7 days
∴ The correct answer is 26/7 days.
Additional Information
Alternate Day Work Concept
When individuals work on alternate days or in a specific cyclic pattern, calculate the total work done in one complete cycle (e.g., 2 or 3 days). Multiply the cycle to get as close to the total work as possible without exceeding it, then calculate the remaining work day by day.
Work and Wages
Wages are always distributed in proportion to the total work done by each individual. If workers work together for the exact same duration, their wages are directly proportional to their individual efficiencies.
Pipes and Cisterns
Works exactly like Time & Work problems, but an outlet pipe or a leak is considered to do negative work, which is subtracted from the total filling efficiency to find the net work rate.