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 the 40 shirts, each at a profit of 15%, then his overall profit would have been reduced by ₹36. What is the cost price of each shirt?
Answer & explanation
Correct answer: option 1
Let the price of each shirt = 1 rupee
Then the cost price of 24 shirts = 24
Profit = 20%
Then the selling price of 24 shirts = 120% of 24 = 28.8
The cost price of 16 shirts = 16
Profit = 10%
Then the selling price of each shirt = 110% of 16 = 17.6
The total selling price = 17.6 + 28.8 = 46.4
The total cost price = 24 + 16 = 40
If he had sold all the 40 shirts, each at a profit of 15%, then his overall profit would have been reduced by ₹36.
The new selling price of the shirts = 115% of 50 = 46
Reduction in profit = 46.4 - 46 = 0.4
Now it is given = 0.4 = 36
cost price of 24 shirts = 36 × \(\frac{40}{0.4}\) = 3600
the cost price of 1 shirt = \(\frac{3600}{40}\) = 90