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A merchant marks his goods 25% above the cost price. He then allows two successive discounts of 20% and 10% on the marked price. What is the final profit or loss percentage?
10% profit
10% loss
2% loss
2% profit
10% loss
Assume Cost Price is 100. Then Marked Price is 125. First discount of 20% makes it 125├Ч0.8=100. Second discount of 10% on 100 makes it 90. Final result is 100тЖТ90, which is a 10% loss.
Marked price is 25% above cost price, followed by two successive discounts of 20% and 10%.
Effective┬аChange=(1+100aтАЛ)├Ч(1тИТ100d1тАЛтАЛ)├Ч(1тИТ100d2тАЛтАЛ)тИТ1
Assume Cost Price is 100. Then Marked Price is 125. First discount of 20% makes it 125├Ч0.8=100. Second discount of 10% on 100 makes it 90. Final result is 100тЖТ90, which is a 10% loss.
Students often add the percentages: 25тИТ20тИТ10=тИТ5%, or incorrectly calculate the second discount on the original marked price instead of the reduced price.
Set the base values
Assume the Cost Price (CP) is 100. Given the markup of 25%, the Marked Price (MP) becomes:
MP=100├Ч(1+0.25)=125
Apply the first discount
The first discount is 20%. Applying this to the MP, we get:
Price┬аafter┬а20%┬аdiscount=125├Ч(1тИТ0.20)=125├Ч0.8=100
Apply the second discount
The second discount is 10%. Applying this to the price after the first discount, we get:
Selling┬аPrice┬а(SP)=100├Ч(1тИТ0.10)=100├Ч0.9=90
Calculate the final percentage
Comparing the final Selling Price (90) to the original Cost Price (100), the loss is:
Loss=100тИТ90=10,Loss┬аpercentage=10010тАЛ├Ч100=10%
B is correct because the final selling price of 90 against a cost price of 100 results in a 10% loss.
This concept of chain multipliers is identical to the method used for calculating compound interest or successive population growth/decline problems.