A reduction of 7.5% in the cost price of a commodity enables a shopkeeper to purchase 15 kg more than what he previously purchased for a sum of ₹7,400. In order to make a profit of 32.5% on the pre-reduction cost price of the commodity, at what price (in ₹) per kg should the commodity be sold?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 53
Let the original cost price per kg be x.
So, the shopkeeper previously purchased 7400/x kg.
After the reduction of 7.5%, the new cost price per kg is 0.925x.
So, the shopkeeper can now purchase 7400/(0.925x) kg.
Given that he can purchase 15 kg more now, we have: 7400/(0.925x) - 7400/x = 15
Simplifying this equation, we get: x = 40
Therefore, the original cost price per kg is ₹40.
Now, to make a profit of 32.5% on the original cost price, the selling price per kg should be: 40 + 32.5% of 40 = 40 + 13 = ₹53
So, the commodity should be sold at ₹53 per kg.