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A man sold an article for ₹247.50, thereby gaining 12.5%. The cost of the article was:
₹220
₹225
₹210
₹224
₹220
Express 12.5% gain as a fraction: 12.5% = 1/8. This means CP = 8 units and Profit = 1 unit, so SP = 9 units. Since 9 units = ₹247.50, 1 unit = ₹27.50, and CP (8 units) = 8 × 27.50 = ₹220.
Selling Price (SP) = ₹247.50, Gain % = 12.5%
Cost Price (CP)=100+Gain%Selling Price (SP)×100
Express 12.5% gain as a fraction: 12.5% = 1/8. This means CP = 8 units and Profit = 1 unit, so SP = 9 units. Since 9 units = ₹247.50, 1 unit = ₹27.50, and CP (8 units) = 8 × 27.50 = ₹220.
Many students mistakenly calculate 12.5% of the selling price and subtract it, instead of applying the profit percentage on the cost price.
Identify Given Values
We are given the selling price of the article (SP) = ₹247.50 and the gain percentage = 12.5%. We need to find the Cost Price (CP).
SP=247.50,Gain%=12.5%
Apply Cost Price Formula
The formula relating Cost Price, Selling Price, and Gain percentage is given by CP=100+Gain%SP×100.
CP=100+12.5247.50×100
Simplify and Calculate
Substitute the denominator: 100+12.5=112.5. Now divide 24750 by 112.5 to get the final cost price.
CP=112.524750=220
A is correct because calculating the cost price using the gain formula yields exactly ₹220.
Percentage increase and decrease formulas form the foundational basis for profit, loss, discount, and simple/compound interest problems in competitive exams.
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