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A shopkeeper sells an item for ₹770.7 after giving two successive discounts of 58% and 80% on its marked price. Had he not given any discount, he would have earned a profit of 25%. What is the cost price (in ₹) of the item?
7322
7353
7315
7340
7340
Calculate MP first: 770.7/(0.42×0.2)=770.7/0.084=9175. Then CP = 9175/1.25=7340.
Selling Price (SP) = ₹770.7, Successive Discounts = 58% and 80%, Profit if no discount = 25%.
MP=(1−d1)(1−d2)SP, CP=1+profit%MP
Calculate MP first: 770.7/(0.42×0.2)=770.7/0.084=9175. Then CP = 9175/1.25=7340.
Students often apply the 25% profit directly to the discounted selling price (770.7) instead of the marked price.
Calculate Marked Price (MP)
Since two successive discounts of 58% and 80% are given, the multiplier is (1−0.58)×(1−0.80)=0.42×0.2=0.084. Dividing SP by this gives the MP.
MP=0.42×0.2770.7=0.084770.7=9175
Calculate Cost Price (CP)
The problem states that if no discount were given (i.e., at MP), the profit would be 25%. Thus, MP=CP×1.25.
CP=1.259175=7340
D is correct because the calculated cost price is ₹7340.
This concept is fundamentally identical to 'Effective Percentage Change' problems in compound interest or population growth scenarios.
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