Shortcut Trick
A completes 80% work in 20 days → 100% work in 25 days.
A + B complete remaining 20% work in 3 days → 100% work in 15 days.
Total Work = LCM(25, 15) = 75 units.
Efficiency: A = 3 units/day, A + B = 5 units/day ∴ B = 5 − 3 = 2 units/day.
Time for B = 75 ÷ 2 = 37 1/2 days.
∴ The correct answer is 37 1/2 days.
Alternate Method
Given:
A completes 80% (4/5) of the work in 20 days.
Remaining work = 100% − 80% = 20% (1/5).
A + B complete this 20% work in 3 days.
Formula Used:
Total Days = (Days × 100) ÷ Percentage of work done
Efficiency = Total Work ÷ Total Days
Calculations:
⇒ Total days taken by A to complete work = (20 × 100) ÷ 80 = 25 days.
⇒ Total days taken by A + B to complete work = (3 × 100) ÷ 20 = 15 days.
| Person | Days | Total Work | Efficiency |
|---|
| A | 25 | 75 | 3 |
| A + B | 15 | 5 | |
⇒ Efficiency of B alone = Efficiency of (A + B) − Efficiency of A
⇒ Efficiency of B = 5 − 3 = 2
⇒ Time taken by B alone = Total Work ÷ Efficiency of B
⇒ Time = 75 ÷ 2 = 37.5 days
∴ The correct answer is 37 1/2 days.
Additional Information
Work and Efficiency Relationship
Work is directly proportional to efficiency and time. If work is constant, time is inversely proportional to efficiency (T1/T2 = E2/E1).
Combined Work Formula
If person X takes x days and person Y takes y days, the time taken together is T = (x × y) ÷ (x + y) days.
Percentage Work to Full Work
To find the time for 100% work when p% is done in d days, use: Total Time = (d ÷ p) × 100.