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A merchant marks his goods at 40% above the cost price and allows a discount of 15%. If he sells the item for ₹714, what is the cost price of the item?
₹600
₹650
₹580
₹700
₹600
Use the decimal multiplier method directly: 1.40×0.85=1.19, so 1.19×CP=714⟹CP=600.
Marked price is 40% above cost price, discount is 15%, selling price is ₹714.
SP=CP×(1+100Markup%)×(1−100Discount%)
Use the decimal multiplier method directly: 1.40×0.85=1.19, so 1.19×CP=714⟹CP=600.
Students often net out the percentages as 40%−15%=25%, forgetting that the discount applies to the marked price, not the cost price.
Identify Given Data
We are given the markup percentage, discount percentage, and the final selling price SP=714.
SP=714,Markup=40%,Discount=15%
Establish the Relation
The marked price is 1.40 times the cost price, and the selling price is 0.85 times the marked price.
SP=CP×1.40×0.85
Calculate Effective Multiplier
Multiplying the factors gives the overall multiplier relating cost price to selling price: 1.40×0.85=1.19.
1.19×CP=714
Solve for Cost Price
Divide the selling price by 1.19 to get the cost price CP=600.
CP=1.19714=600
A is correct because the cost price of the item is ₹600.
Understanding successive percentage changes is crucial for tackling problems involving multi-stage discounts and financial mathematics.
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