Shortcut Trick
Combined work of Ravi and Raghav for 10 days (25 − 15) is done by Raghav alone in 20 days.
Efficiency Ratio (Ravi + Raghav) : Raghav = 20 : 10 = 2 : 1.
Total Work = Combined Efficiency × Total Days = 2 × 25 = 50 units.
Time taken by Raghav alone = Total Work ÷ Raghav efficiency = 50 ÷ 1 = 50 days.
∴ The correct answer is 50 days.
Alternate Method
Given:
Time taken by (Ravi + Raghav) = 25 days.
Work done together = 15 days.
Remaining work done by Raghav = 20 days.
Formula Used:
Work = Efficiency × Time
Calculations:
⇒ Let the efficiency of Ravi be 'a' and Raghav be 'b'.
⇒ Total Work = 25 × (a + b)
⇒ Work done in 15 days = 15 × (a + b)
⇒ Remaining Work = 25(a + b) − 15(a + b) = 10(a + b)
⇒ According to the question, 10(a + b) = 20 × b
⇒ 10a + 10b = 20b
⇒ 10a = 10b ⇒ a = b (Efficiencies are equal)
⇒ Total Work = 25 × (b + b) = 50b
⇒ Time taken by Raghav alone = 50b ÷ b = 50 days.
∴ The correct answer is 50 days.
Additional Information
Efficiency and Time Relationship
Efficiency is inversely proportional to the time taken to complete a work. If the ratio of efficiencies of A and B is x : y, then the ratio of time taken is y : x.
Work and Wages
Wages are always distributed in the ratio of the actual work done by each individual, which is equivalent to the ratio of their efficiencies if they work for the same duration.
Combined Work Formula
If A takes 'x' days and B takes 'y' days, together they take (x × y) ÷ (x + y) days to complete the work.