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A shopkeeper sells an item for ₹571.20 after giving two successive discounts of 20% and 15% on its marked price. What is the marked price (in ₹) of the item?
780
820
840
760
840
Use the multiplier method: MP×0.8×0.85=571.20. Since 0.8×0.85=0.68, simply divide 571.20 by 0.68 to get the MP.
Selling Price (SP) = ₹571.20, First discount = 20%, Second discount = 15%.
MP=SP×(100−D1100)×(100−D2100)
Use the multiplier method: MP×0.8×0.85=571.20. Since 0.8×0.85=0.68, simply divide 571.20 by 0.68 to get the MP.
Many students try to add the discounts (20% + 15% = 35%) instead of applying them successively, which leads to an incorrect result of ₹878.76.
Define the discounts
Successive discounts of 20% and 15% mean the item is sold at 80% and 85% of its preceding value respectively.
SP=MP×10080×10085
Set up the equation
Substitute the given selling price into the equation: 571.20=MP×0.8×0.85.
MP=0.8×0.85571.20
Perform the calculation
Calculate the denominator: 0.8×0.85=0.68. Then divide: 571.20/0.68=840.
MP=0.68571.20=840
C is correct because the calculated marked price is ₹840, which matches option C.
This ratio-based approach is essentially the same logic used in compound interest and depreciation problems where percentage changes are applied sequentially.
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