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A blanket is sold for ₹1,148, which results in a loss of 30%. For how much should it be sold to gain 5%?
₹1,423
₹1,734
₹1,543
₹1,722
₹1,722
Use the ratio of selling prices: SP2=SP1×100−Loss%100+Gain%=1148×70105=1148×1.5=1722.
Selling Price (SP1) = ₹1,148, Loss = 30%, Required Gain = 5%
CP=1−100Loss%SP1,SP2=CP×(1+100Gain%)
Use the ratio of selling prices: SP2=SP1×100−Loss%100+Gain%=1148×70105=1148×1.5=1722.
Students often calculate the 5% gain on the selling price (1148) instead of the cost price, or they forget that a 30% loss means the item was sold at 70% of its cost.
Calculate Cost Price (CP)
Given SP1=1148 and a 30% loss, the CP is derived from 1148=CP×(1−0.30)=CP×0.70.
CP=0.71148=1640
Calculate Required Selling Price (SP2)
To gain 5%, the new selling price should be 105% of the CP.
SP2=1640×1.05=1722
D is correct because the cost price of the blanket is ₹1,640, and selling it at a 5% gain results in a price of ₹1,722.
This concept is fundamental to all profit/loss problems; always find the cost price first to bridge the gap between two different selling scenarios.
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