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A trader buys a watch for 2,400. He wants to gain a profit of 25% after allowing a discount of 20% on the marked price. What should be the marked price (in тВ╣) for this purpose?
3,500
3,750
4,000
4,250
3,750
Use the ratio of CP to MP: MPCPтАЛ=100+Profit%100тИТDiscount%тАЛ. Here, 12580тАЛ=MPCPтАЛ. Given CP = 2,400 (which is 80 units ├Ч 30), so MP = 125 units ├Ч 30 = 3,750.
Cost Price (CP) = 2,400. Profit percentage = 25%. Discount percentage = 20%.
MP=(1тИТ100Discount%тАЛ)CP├Ч(1+100Profit%тАЛ)тАЛ
Use the ratio of CP to MP: MPCPтАЛ=100+Profit%100тИТDiscount%тАЛ. Here, 12580тАЛ=MPCPтАЛ. Given CP = 2,400 (which is 80 units ├Ч 30), so MP = 125 units ├Ч 30 = 3,750.
Students often calculate the discount on the Cost Price instead of the Marked Price or try to add percentages linearly, i.e., 25%тИТ20%=5%.
Calculate Selling Price (SP)
To get a profit of 25% on a cost of 2,400, the selling price must be calculated using the profit formula: SP=CP├Ч(1+10025тАЛ).
SP=2400├Ч1.25=3000
Relate SP to Marked Price (MP)
The selling price is the marked price after a 20% discount, represented as SP=MP├Ч(1тИТ10020тАЛ).
3000=MP├Ч0.8
Calculate Marked Price
Solve for MP by dividing the selling price by 0.8: MP=0.83000тАЛ.
MP=830000тАЛ=3750
B is correct because the calculated marked price is 3,750.
This concept of relating cost and marked price is identical to calculating the effective rate in successive percentage changes, frequently tested in compound interest and tax-inclusive pricing problems.
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