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?

The correct option is 53.

Step 1: Formulate equations for the quantity of commodity purchased.
Let the pre-reduction cost price of the commodity per kg be P rupees.
Total amount spent = ₹7,400.

The original quantity purchased (in kg) at price P is:

$\text{Original Quantity}=\frac{7400}{P}$

A reduction of 7.5% in the cost price means the new cost price per kg becomes:

$\text{New Cost Price}=P\times (1-0.075)=0.925P$

The new quantity purchased (in kg) for ₹7,400 at this reduced price is:

$\text{New Quantity}=\frac{7400}{0.925P}$

Simplifying the fraction for the new quantity:

$\frac{7400}{0.925P}=\frac{7400\times 1000}{925P}=\frac{8000}{P}$

Step 2: Calculate the pre-reduction cost price per kg (P).
It is given that the reduced price allows the shopkeeper to buy 15 kg more than before:

$\text{New Quantity}-\text{Original Quantity}=15$

$\frac{8000}{P}-\frac{7400}{P}=15$

$\frac{600}{P}=15$

$P=\frac{600}{15}=40$

So, the pre-reduction cost price of the commodity is ₹40 per kg.

Step 3: Determine the selling price per kg to earn a profit of 32.5%.
To earn a 32.5% profit on the pre-reduction cost price (₹40), the selling price per kg is:

$\text{Selling Price}=40\times \left(1+\frac{32.5}{100}\right)$

$\text{Selling Price}=40\times 1.325=53$

Therefore, the commodity should be sold at ₹53 per kg.