Shortcut Trick
Efficiency ratio of Amit : Vinit = 3 : 1
Time ratio (inverse of efficiency) = 1 : 3
Difference in time units = 3 − 1 = 2 units → 32 days
1 unit = 16 days (Amit's time) | 3 units = 48 days (Vinit's time)
Together time = (16 × 48) ÷ (16 + 48) = 768 ÷ 64 = 12 days
∴ The correct answer is 12 days.
Alternate Method
Given:
Efficiency of Amit = 3 × Efficiency of Vinit
Time taken by Amit = TA | Time taken by Vinit = TV
Formula Used:
Work = Efficiency × Time | Together Time = (TA × TV) ÷ (TA + TV)
Calculations:
⇒ Since Efficiency is inversely proportional to Time:
⇒ TV / TA = 3 / 1
⇒ TV − TA = 32 days
⇒ 3x − 1x = 32 ⇒ 2x = 32 ⇒ x = 16
⇒ TA = 16 days and TV = 48 days
⇒ Combined Time = (16 × 48) ÷ (16 + 48)
⇒ Combined Time = 768 ÷ 64 = 12 days
∴ The correct answer is 12 days.
Additional Information
Efficiency and Time Relationship
Efficiency is inversely proportional to the time taken to complete a work. If the ratio of efficiency is a:b, the ratio of time taken is b:a.
Work and Wages
Wages are always distributed in the ratio of the work done or the ratio of efficiencies if the time period for all workers is the same.
Combined Work Formula
If A takes 'x' days and B takes 'y' days, then together they take (xy) ÷ (x + y) days to complete the work.