Shortcut Trick
Work done by A in 20 days = 20 ÷ 55 = 4/11.
Remaining work = 1 − 4/11 = 7/11.
Time taken by B for total work = 49 × (11/7) = 77 days.
Time taken by both together = (A × B) ÷ (A + B) = (55 × 77) ÷ (55 + 77) = 4235 ÷ 132 = 385/12 days.
∴ The correct answer is 385/12 days.
Alternate Method
Given:
Time taken by A to complete the work = 55 days
Days worked by A = 20 days
Time taken by B to finish remaining work = 49 days
Formula Used:
Work Done = Efficiency × Time
Calculation:
⇒ Work done by A in 20 days = 20/55 = 4/11 of the total work
⇒ Remaining work = 1 − 4/11 = 7/11 of the total work
⇒ Time taken by B alone to complete the whole work = 49 × (11/7) = 77 days
Now, finding the total work by taking LCM of days taken by A and B.
| Person | Days | Total Work | Efficiency |
|---|
| A | 55 | 385 | 7 |
| B | 77 | 5 | |
⇒ Total efficiency of A and B = 7 + 5 = 12 units/day
⇒ Time taken by A and B together = Total Work ÷ Total Efficiency = 385/12 days
∴ The correct answer is 385/12 days.
Additional Information
Total Work Concept
Total Work is universally assumed as the Lowest Common Multiple (LCM) of the individual times. This makes the calculation of daily efficiency an integer value, which significantly simplifies further calculations.
Work & Wages
Wages are always distributed in the ratio of the actual work done by each person. If multiple individuals work for the same number of days, their wages are simply distributed in the ratio of their efficiencies.
Pipes & Cisterns Connection
Pipes and Cisterns work on the exact same logic as Time & Work. The only difference is that a filling pipe has a positive efficiency, while an emptying pipe (or a leak) has a negative efficiency.
Combined Time Formula
If two individuals A and B can complete a task individually in 'x' and 'y' days respectively, their combined time to finish the same work together is directly given by (x × y) ÷ (x + y) days.