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If 12 boxes of sweets cost 840 rupees, how many boxes can be purchased for 2100 rupees?
25
30
35
40
30
Use the ratio of the total budget to the cost: 2100/840=210/84=2.5. Multiply the original quantity by this factor: 12├Ч2.5=30.
Cost of 12 boxes = 840 rupees. Total budget available = 2100 rupees.
Cost1тАЛQuantity1тАЛтАЛ=Cost2тАЛQuantity2тАЛтАЛ
Use the ratio of the total budget to the cost: 2100/840=210/84=2.5. Multiply the original quantity by this factor: 12├Ч2.5=30.
Students often calculate the cost of a single box (840/12=70) and then divide 2100 by 70, but errors occur if division of 2100/70 is performed incorrectly under time pressure.
Define the relationship
Since the number of boxes is directly proportional to the total cost, we set up the proportionality constant.
C1тАЛn1тАЛтАЛ=C2тАЛn2тАЛтАЛ
Substitute the given values
Substitute n1тАЛ=12, C1тАЛ=840, and C2тАЛ=2100 into the formula to solve for n2тАЛ.
84012тАЛ=2100n2тАЛтАЛ
Solve for n2тАЛ
Isolate n2тАЛ by multiplying both sides by 2100. Calculating 12├Ч(2100/840) simplifies to 12├Ч2.5.
n2тАЛ=84012├Ч2100тАЛ=12├Ч2.5=30
B is correct because the ratio calculation shows that for 2100 rupees, exactly 30 boxes can be purchased.
This concept of direct variation is fundamental in solving problems related to work-time efficiency, mixtures, and currency conversions in data interpretation sets.