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A shopkeeper lists the price of a fan at 22% above its cost price and offers a 15% discount on its list price. What is the cost price (in ₹) of the fan if he sells it at ₹5,185?
4,800
5,000
4,500
5,680
5,000
Use the multiplier method: CP×1.22×0.85=5185. Simplifying 1.22×0.85=1.037. Since 5185/1.037=5000, we immediately find the answer.
Marked price is 22% above cost price, discount is 15% on marked price, and selling price is ₹5,185.
SP=CP×(1+100Profit%)×(1−100Discount%)
Use the multiplier method: CP×1.22×0.85=5185. Simplifying 1.22×0.85=1.037. Since 5185/1.037=5000, we immediately find the answer.
Students often incorrectly calculate the effective percentage change by adding or subtracting the percentages directly (22% - 15% = 7%) instead of applying them sequentially.
Define the relationship
Let the cost price be CP. The marked price MP is 1.22×CP. The selling price SP after a 15% discount is 0.85×MP.
SP=(CP×1.22)×0.85
Equate and Solve
Substitute the known selling price SP=5185 into the equation and solve for CP.
5185=CP×1.22×0.85
Calculate the result
Calculate the product 1.22×0.85=1.037. Then divide 5185 by 1.037.
CP=1.0375185=5000
B is correct because the cost price calculates to exactly ₹5,000 using the sequential percentage application.
This is equivalent to finding the net percentage increase, which is a standard technique in compound interest and population growth problems.
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