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Which of the following percentages is equivalent to 81тАЛ?
12.5%
10%
15%
20%
12.5%
Use the formula Successive Percentage Change: Net Effect = x - y - (x * y / 100), where x is the markup (25) and y is the discount (10). Result: 25 - 10 - (25 * 10 / 100) = 15 - 2.5 = 12.5%.
Marked price is 25% above cost price (MP = 1.25 CP), and a discount of 10% is allowed on the marked price.
Gain%=((1+100xтАЛ)(1тИТ100yтАЛ)тИТ1)├Ч100
Use the formula Successive Percentage Change: Net Effect = x - y - (x * y / 100), where x is the markup (25) and y is the discount (10). Result: 25 - 10 - (25 * 10 / 100) = 15 - 2.5 = 12.5%.
Students often wrongly subtract the percentages directly (25% - 10% = 15%) instead of accounting for the fact that the discount is applied to the already marked-up price.
Assume Cost Price
Let the Cost Price (CP) of the goods be 100.
CP=100
Calculate Marked Price
Since the trader marks goods 25% above CP, the Marked Price (MP) is 100+25%┬аof┬а100=125.
MP=125
Calculate Selling Price
The trader allows a discount of 10% on the MP. Selling Price (SP) = MPтИТ10%┬аof┬аMP=125тИТ12.5=112.5.
SP=112.5
Calculate Gain Percentage
Gain is SPтИТCP=112.5тИТ100=12.5. Gain percentage = 10012.5тАЛ├Ч100=12.5%.
Gain%=12.5%
A is correct because the effective gain calculated after a 25% markup and 10% discount is 12.5%.
This concept is identical to applying successive percentage changes in compound interest problems or tax calculations: Net% = (a + b + (a*b)/100).
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