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A shopkeeper lists the price of a fan at 25% above its cost price and offers a 10% discount on its list price. If he earns a profit of ₹117, then what is the list price (in ₹) of the fan?
1308
1170
1346
896
1170
Let CP = 100x. List Price (LP) = 125x. Selling Price (SP) = 125x * 0.9 = 112.5x. Profit = 112.5x - 100x = 12.5x. Since 12.5x = 117, then x = 9.36. LP = 125 * 9.36 = 1170.
Markup = 25%, Discount = 10%, Profit = ₹117
Profit=SP−CP=(LP×(1−Discount%))−CP
Let CP = 100x. List Price (LP) = 125x. Selling Price (SP) = 125x * 0.9 = 112.5x. Profit = 112.5x - 100x = 12.5x. Since 12.5x = 117, then x = 9.36. LP = 125 * 9.36 = 1170.
Students often apply the 10% discount directly to the cost price instead of the list price (marked-up price).
Define Cost Price
Assume the Cost Price (CP) of the fan is 100x.
CP=100x
Determine List Price
The list price is 25% above the cost price.
LP=100x+25%of100x=125x
Calculate Selling Price
The shopkeeper offers a 10% discount on the list price (125x).
SP=125x×(1−0.10)=125x×0.9=112.5x
Equate Profit
Profit is SP−CP. We are given that the profit is ₹117.
112.5x−100x=117⇒12.5x=117
Find List Price
Solve for x and multiply by 125 to find the list price.
x=12.5117=9.36⇒LP=125×9.36=1170
B is correct because the calculation yields a List Price of ₹1170.
This type of percentage-chain problem is frequent in Data Interpretation and Profit/Loss sections; always define the base cost as 100 units to simplify complex percentage changes.
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