
Shortcut Trick
Remaining work after 20 days = (30 − 20) ÷ 30 = 1/3.
A finishes this 1/3 work in 20 days.
Time taken by A alone to finish full work = 20 × 3 = 60 days.
∴ The correct answer is 60 days.

Alternate Method
Given:
Time taken by (A + B) = 30 days.
Work done by (A + B) in 20 days.
Remaining work done by A in 20 days.
Formula Used:
Total Work = Efficiency × Time
Remaining Work = Total Work − Work Done
| Persons | Time | Work | Efficiency |
|---|
| A + B | 30 | 60 | 2 |
| A alone | 60 | 1 | |
Calculations:
⇒ Let Total Work = LCM(30, 20) × something or just 60 units.
⇒ Efficiency of (A + B) = 60 ÷ 30 = 2 units/day.
⇒ Work done by (A + B) in 20 days = 2 × 20 = 40 units.
⇒ Remaining work = 60 − 40 = 20 units.
⇒ This 20 units is done by A in 20 days.
⇒ Efficiency of A = 20 ÷ 20 = 1 unit/day.
⇒ Time for A alone = Total Work ÷ Efficiency of A = 60 ÷ 1 = 60 days.
∴ The correct answer is 60 days.

Additional Information
Efficiency and Time Relation
Efficiency is inversely proportional to time taken. If the ratio of efficiency of A and B is x:y, then the ratio of time taken is y:x.
Combined Work Formula
If A can do work in x days and B in y days, then together they take (x × y) ÷ (x + y) days to complete the work.
Pipes and Cisterns
The same principle applies where filling pipes have positive efficiency and outlet pipes (leaks) have negative efficiency.