Shortcut Trick
Total work = LCM(20, 60) = 60 units.
Efficiency: A = 60 ÷ 20 = 3 units/day, B = 60 ÷ 60 = 1 unit/day.
Work done by B alone in the last 12 days = 12 × 1 = 12 units.
Remaining work done by A and B together from the beginning = 60 − 12 = 48 units.
Days A and B worked together = 48 ÷ (3 + 1) = 12 days.
∴ The correct answer is 12 days.
Alternate Method
Given:
Time taken by A alone to complete the work = 20 days
Time taken by B alone to complete the work = 60 days
Time taken by B to complete the remaining work = 12 days
Formula Used:
Total Work = Efficiency × Time Taken
| Person | Days | Total Work | Efficiency |
|---|
| A | 20 | 60 | 3 |
| B | 60 | 1 | |
Calculations:
⇒ Work completed by B alone in the last 12 days = Efficiency of B × Days = 1 × 12 = 12 units
⇒ Remaining work to be completed by A and B together = Total Work − Work done by B
⇒ Remaining work = 60 − 12 = 48 units
⇒ Combined efficiency of A and B = 3 + 1 = 4 units/day
⇒ Number of days A and B worked together initially = Remaining work ÷ Combined efficiency
⇒ Days A and B worked together = 48 ÷ 4 = 12 days
This means A worked for 12 days from the beginning before leaving the work.
∴ The correct answer is 12 days.
Additional Information
Total Work & Efficiency Trick
Total work is universally taken as the Lowest Common Multiple (LCM) of individual completion times. Efficiency is inversely proportional to the time taken.
Alternate Days Working
When individuals work on alternate days, calculate the work done in a complete cycle (e.g., 2 days for 2 persons) and scale it up to reach the closest multiple near the total work.
Work & Wages Distribution
Wages are always distributed in proportion to the total units of work completed by each individual. If they work for the same duration, wages are directly distributed based on their efficiencies.