Shortcut Trick
Total Work = LCM(30, 40) = 120 units.
Efficiency of A = 120 ÷ 30 = 4 units/day, Efficiency of B = 120 ÷ 40 = 3 units/day.
Work done by B alone in the last 5 days = 5 × 3 = 15 units.
Remaining work done by A and B together = 120 − 15 = 105 units.
Days A and B worked together = 105 ÷ (4 + 3) = 15 days.
∴ The correct answer is 15 days.
Alternate Method
Given:
Time taken by A to complete the work = 30 days
Time taken by B to complete the work = 40 days
B finishes the remaining work alone in 5 days.
Method Used:
LCM Method for Time & Work: Total Work is assumed as the LCM of the given days, and efficiency is calculated as Total Work ÷ Days.
| Person | Days | Total Work | Efficiency |
|---|
| A | 30 | 120 | 4 |
| B | 40 | 3 | |
Calculations:
⇒ Total work = 120 units
⇒ Efficiency of B = 3 units/day
⇒ Work done by B in the last 5 days = 5 × 3 = 15 units
⇒ Work done by A and B together before A left = Total Work − Work done by B alone
⇒ Work done together = 120 − 15 = 105 units
⇒ Combined efficiency of A and B = 4 + 3 = 7 units/day
⇒ Number of days A and B worked together = 105 ÷ 7 = 15 days
⇒ This implies A left after 15 days.
∴ The correct answer is 15 days.
Additional Information
Pipes & Cisterns
This concept is identical to Time and Work. An inlet pipe filling a tank represents positive work, while an outlet pipe emptying the tank represents negative work.
Work & Wages
Wages are distributed strictly in the ratio of the total work done by each individual. If all individuals work for the exact same number of days, their wages are distributed in the ratio of their efficiencies.
Alternate Days Work
When workers perform tasks on alternate days, find the total work completed in one full cycle (e.g., 2 days) and scale it up to reach close to the total work without exceeding it.