Question : A shopkeeper sold 24 shirts, each at a profit of 20% and 16 shirts, each at a profit of 10%. If he had sold all 40 shirts, each at a profit of 15%, then his overall profit would have been reduced by INR 36. What is the cost price of each shirt?
Option 1: INR 100
Option 2: INR 220
Option 3: INR 90
Option 4: INR 150
Correct Answer: INR 90
Solution :
Given :
A shopkeeper sold 24 shirts at a 20% profit and 16 shirts at a 10% profit.
Let the cost price of each shirt be INR 100.
The selling price of each shirt at 20% profit $=100\times (\frac{100+20}{100})= 120$
Total amount received after selling 24 shirts $=120\times 24=2880$
The selling price of each shirt at 10% profit $=100\times (\frac{100+10}{100})= 110$
Total amount received after selling 16 shirts $=110\times 16= 1760$
Total amount received after selling 40 shirts $=2880+1760= 4640$
The selling price of each shirt at 15% profit $=100\times (\frac{100+15}{100})=115$
Total amount received after selling 40 shirts $=115\times 40=4600$
The difference in the profit $=4640-4600=40$
When the difference in sale amount is INR 40, the cost price is INR 100
So, when the difference in sale amount is INR 36, the cost price of each shirt $=\frac{100}{40}\times 36=90$
Hence, the correct answer is INR 90.
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