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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
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.
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.
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