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?

Correct option is D

​Given:
Total money = ₹7,400
Reduction in cost price = 7.5%
After reduction, 15 kg more can be bought with the same amount
Required profit = 32.5% on the original (pre-reduction) cost price
Formula Used:
Quantity purchased = $$\frac{\text{Total money}} {\text{Cost price per kg}}$$​​

Selling price per kg = Cost price × $$\left( 1+ \frac{\text{Profit \%}}{100}\right)$$​​
Solution:
Let original cost price = x ₹/kg
Then,
Quantity at original price =  $$\frac{7400}{x}$$

Then, after 7.5% reduction, the new cost price = $$x - 7.5\% \text{ of } x = 0.925x$$​​

Quantity at reduced price = $$\frac{7400}{0.925x}$$​

Difference in quantity = 15 kg
So:
​$$\frac{7400}{0.925x} - \frac{7400}{x} = 15$$​

​$$\frac{7400x}{0.925x} - 7400 = 15x$$​

​$$\Rightarrow \frac{7400}{0.925} - 7400 = 15x$$​

​$$\frac{7400}{0.925} = 8000$$​

​$$\Rightarrow 8000 - 7400 = 15x$$​​
=> 15 x = 600

=> x = $$\frac{600}{15}$$ 40​
So, original cost price per kg = ₹40

Now, required selling price to make 32.5% profit:

SP =  $$40 \times \left(1 + \frac{32.5}{100}\right) = 40 \times 1.325 = ₹53$$​

The selling price should be ₹53 per kg.

Thus, the correct option is (d) ₹53