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A shopkeeper sold an item at a 10% loss. If he sold it for 150 more, he would have gained 5%. What was the cost price?
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1000
Calculate the total percentage gap (10%+5%=15%) and equate it to the absolute value 150. Since 15%=150, then 1%=10, and 100%=1000.
Initial loss is 10%, final gain is 5%, and the price difference for this change is 150.
CP=Difference┬аin┬аPercentageDifference┬аin┬аSPтАЛ
Calculate the total percentage gap (10%+5%=15%) and equate it to the absolute value 150. Since 15%=150, then 1%=10, and 100%=1000.
Many students subtract the percentages (5%тИТ10%=тИТ5%) instead of adding the absolute shift from loss to gain, leading to incorrect calculations.
Define the percentage gap
To move from a 10% loss to a 5% gain, the selling price must increase by the sum of the loss and the gain percentages.
10%+5%=15%
Equate percentage to absolute value
The problem states this shift corresponds to an increase of 150 in the selling price. Thus, 15% of the Cost Price (CP) is 150.
15%┬аof┬аCP=150
Solve for CP
Solve the equation for CP by dividing 150 by 0.15.
CP=0.15150тАЛ=1000
A is correct because the 15% total change in margin equals 150, making the base cost price 1000.
This 'Difference Method' is identical to solving problems involving time and speed (e.g., reaching a destination earlier vs later) where you sum the time offsets.
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