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Ravi can complete a task in 30 days. Sumit is 50% more efficient than Ravi. How many days does Sumit take to complete the same task?
15 days
20 days
25 days
18 days
20 days
Given: Ravi completes a task in 30 days. Sumit is 50% more efficient than Ravi.
Ravi completes a task in 30 days. Sumit is 50% more efficient than Ravi.
EfficiencyтИЭTime1тАЛ
Use the inverse ratio of efficiency: If efficiency ratio of Ravi to Sumit is 2:3, then time ratio is 3:2. Since 3 units = 30 days, 2 units = 20 days.
A common mistake is calculating 50% less time than 30 (i.e., 15 days), forgetting that time and efficiency are inversely proportional.
Define Efficiency Ratio
If Ravi's efficiency is 100%, Sumit's efficiency is 100%+50%=150%. The ratio of efficiency (Ravi:Sumit) is 100:150=2:3.
Efficiency┬аRatio=2:3
Determine Time Ratio
Since time is inversely proportional to efficiency, the time ratio (Ravi:Sumit) is the reciprocal of the efficiency ratio, which is 3:2.
Time┬аRatio=3:2
Calculate Sumit's Time
Ravi takes 30 days, which represents 3 parts of the ratio. Thus, 1 part is 330тАЛ=10 days. Sumit takes 2 parts, so 2├Ч10=20 days.
Time=23тАЛ├ЧRaviтАЩs┬аTime┬а(Incorrect)тЖТTime=32тАЛ├Ч30=20
B is correct because Sumit is more efficient, so he must take less time than Ravi, specifically 32тАЛ of Ravi's time which equals 20 days.
This concept is identical to speed-time problems in kinematics where higher speed results in less time for a constant distance.