Shortcut Trick
Let Total Work = LCM(10, 15) = 30 units.
Efficiency of A = 30 ÷ 10 = 3 units/day, and B = 30 ÷ 15 = 2 units/day.
Work done by B in the first 5 days = 5 × 2 = 10 units.
Remaining work (30 − 10 = 20 units) is done by A and B together (combined efficiency = 5).
Total time = 5 days + (20 ÷ 5) days = 5 + 4 = 9 days.
∴ The correct answer is 9 days.
Alternate Method
Given:
Time taken by A = 10 days
Time taken by B = 15 days
B starts the work and A joins him after 5 days.
Formula Used:
Total Work = Efficiency × Time
Calculation:
| Person | Days | Total Work | Efficiency |
|---|
| A | 10 | 30 | 3 |
| B | 15 | 2 | |
⇒ Work done by B in the initial 5 days = Efficiency of B × 5 = 2 × 5 = 10 units
⇒ Remaining work = 30 − 10 = 20 units
⇒ When A joins B, their combined efficiency = 3 + 2 = 5 units/day
⇒ Time taken by A and B to finish the remaining work = 20 ÷ 5 = 4 days
⇒ Total days required to complete the total work = Initial 5 days + 4 days = 9 days
∴ The correct answer is 9 days.
Additional Information
LCM Method for Total Work
Assuming total work as the least common multiple (LCM) of the given times ensures individual efficiencies are whole numbers, avoiding complex fraction calculations.
Efficiency and Time Relationship
Efficiency is inversely proportional to the time taken to complete a specific task. If a person takes less time, their daily work efficiency is proportionally higher.
Combined Working
When individuals work together simultaneously, their total efficiency is the sum of their individual efficiencies (Combined Efficiency = EA + EB).