Shortcut Trick
Time Ratio (Vijay : Ramesh) = 140 : 100 = 7 : 5
Efficiency Ratio (Vijay : Ramesh) = 5 : 7 (Inversely proportional to time)
Combined Efficiency = 5 + 7 = 12 units/day
Total Work = Combined Efficiency × Together Time = 12 × 25 = 300 units
Vijay's alone time = Total Work ÷ Vijay's Efficiency = 300 ÷ 5 = 60 days
∴ The correct answer is 60 days.
Alternate Method
Given:
Time taken by Vijay and Ramesh together = 25 days
Vijay's time = Ramesh's time + 40% of Ramesh's time
Formula Used:
Efficiency = Total Work ÷ Time
Total Work = Combined Efficiency × Combined Time
| Person | Time | Total Work | Efficiency |
|---|
| Vijay | 60 | 300 | 5 |
| Ramesh | 300/7 | 7 | |
Combined efficiency of Vijay + Ramesh = 5 + 7 = 12 units/day
⇒ Let Ramesh's time be TR and Vijay's time be TV
⇒ TV = 1.4 × TR ⇒ TV/TR = 14/10 = 7/5
⇒ 1/TV + 1/TR = 1/25
⇒ 1/TV + 1.4/TV = 1/25
⇒ 2.4 / TV = 1/25
⇒ TV = 25 × 2.4 = 60 days
∴ The correct answer is 60 days.
Additional Information
Efficiency and Time Relationship
Efficiency is inversely proportional to the time taken to complete a work. If the ratio of time is a:b, then the ratio of efficiency is b:a.
Total Work Formula
Total Work = Individual Efficiency × Individual Time or Combined Efficiency × Combined Time.
Work and Wages
Wages are distributed in the ratio of the work done, which is equivalent to the ratio of efficiencies when everyone works for the same duration.