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A shopkeeper sells an item at a profit of 15%. If he had sold it for Rs. 40 more, he would have gained 20%. What is the cost price of the item?
Rs. 600
Rs. 700
Rs. 800
Rs. 900
Rs. 800
Calculate the difference in profit percentages (20% - 15% = 5%) and equate this to the given price difference (Rs. 40). Then, find 100% using unitary method.
Initial profit = 15%, Increased profit = 20%, Increased selling price = Rs. 40.
CP=Difference┬аin┬аProfit┬аPercentageDifference┬аin┬аSPтАЛ├Ч100
Calculate the difference in profit percentages (20% - 15% = 5%) and equate this to the given price difference (Rs. 40). Then, find 100% using unitary method.
Students often calculate the difference of 15% and 20% but erroneously apply it to the selling price instead of the cost price, or confuse profit percentage with profit value.
Define the profit difference
The difference between the two profit percentages is 20%тИТ15%=5%. This 5% of the Cost Price (CP) represents the extra amount obtained by increasing the price.
20%тИТ15%=5%
Set up the equation
Since 5% of the CP is equal to Rs. 40, we can write the equation as 0.05├ЧCP=40.
0.05├ЧCP=40
Calculate the Cost Price
Solving for CP: CP=0.0540тАЛ=800. Thus, the cost price is Rs. 800.
CP=540├Ч100тАЛ=800
C is correct because the cost price of the item is Rs. 800, which satisfies the condition that a 5% increase in profit corresponds to a Rs. 40 increase in selling price.
This logic is identical to problems involving speed/time where a change in speed results in a change in time (e.g., reaching a destination 10 minutes early).
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