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A shopkeeper sold a book at a loss of 7%. If the selling price had been increased by тВ╣120, there would have been a gain of 17%. What was the cost price (in тВ╣) of the book? 1764
500
495
505
510
500
Directly add the percentages (17% + 7% = 24%) because one is a loss and the other is a gain. Divide the price difference (120) by this sum (24%) to get the cost price: (120 / 0.24) = 500.
Initial loss percentage = 7%, final gain percentage = 17%, and increase in selling price = тВ╣120.
CP=Gain%┬а-┬аLoss%Difference┬аin┬аSPтАЛ├Ч100
Directly add the percentages (17% + 7% = 24%) because one is a loss and the other is a gain. Divide the price difference (120) by this sum (24%) to get the cost price: (120 / 0.24) = 500.
Students often incorrectly calculate the difference as (17% - 7%) = 10% instead of (17% - (-7%)) = 24%, failing to account for the movement across the break-even point.
Define Cost Price
Let the cost price of the book be CP. The initial selling price is SP1тАЛ=CP├Ч(1тИТ0.07)=0.93CP.
SP1тАЛ=0.93CP
Define New Selling Price
The new selling price after a gain of 17% is SP2тАЛ=CP├Ч(1+0.17)=1.17CP.
SP2тАЛ=1.17CP
Equate the Difference
Given that SP2тАЛтИТSP1тАЛ=120, we set up the equation 1.17CPтИТ0.93CP=120.
0.24CP=120
Solve for CP
Dividing both sides by 0.24 gives CP=0.24120тАЛ=500.
CP=500
A is correct because the difference of 24% of the cost price corresponds to тВ╣120, making the cost price тВ╣500.
This logic is identical to problems involving 'Time and Distance' where you move from 'late' to 'early', requiring you to add the time intervals.
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