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Archana can eat 21 litchis in 60 minutes. She wants to know how many minutes it would take her to eat 35 litchis at the same pace.
120 minutes
80 minutes
90 minutes
100 minutes
100 minutes
Use the ratio of litchis: 35/21=5/3. Multiply the initial time by this ratio: 60├Ч(5/3)=100 minutes.
Archana eats 21 litchis in 60 minutes. We need to find the time taken for 35 litchis at the same pace.
L1тАЛT1тАЛтАЛ=L2тАЛT2тАЛтАЛ
Use the ratio of litchis: 35/21=5/3. Multiply the initial time by this ratio: 60├Ч(5/3)=100 minutes.
Students often accidentally invert the ratio, calculating 60├Ч(21/35) instead of 60├Ч(35/21), leading to the incorrect answer of 36 minutes.
Establish the proportionality
Since the rate of eating is constant, the time taken is directly proportional to the number of litchis.
TimeтИЭNumber
Set up the ratio equation
Let T1тАЛ=60 minutes for L1тАЛ=21 litchis. Let T2тАЛ be the time for L2тАЛ=35 litchis.
35T2тАЛтАЛ=2160тАЛ
Calculate the result
Solve for T2тАЛ: T2тАЛ=2160├Ч35тАЛ. Simplifying 35/21 gives 5/3. Thus, 60├Ч35тАЛ=20├Ч5=100.
T2тАЛ=100┬аminutes
D is correct because applying the ratio method, the time taken for 35 litchis is 100 minutes.
This concept of direct variation is fundamental for time-and-work problems, which frequently appear in competitive exams like RRB.
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