A reduction of 10% in the price of mangoes enables a person to buy 10 mangoes more for ₹2250. What is the price per dozen after reduction?

Correct option is D

Given:

Reduction in price = 10%

Total money = ₹2250

Increase in quantity = 10 mangoes

Solution:​

Let the original price per mango be ₹x. Then after a 10% reduction, the new price = ₹0.9x.
Using the money equation:

​$$\frac{2250}{0.9x} - \frac{2250}{x} = 10 \\ \ \\2250 \left( \frac{1}{0.9x} - \frac{1}{x} \right) = 10 \\ \ \\2250 \left( \frac{x - 0.9x}{0.9x^2} \right) = 10 \\ \ \\2250 \left( \frac{0.1x}{0.9x^2} \right) = 10 \\ \ \\2250 \times \frac{0.1}{0.9x} = 10 \\ \ \\\frac{225}{0.9x} = 10 \\ \ \\\frac{225}{10} = 0.9x \\ \ \\22.5 = 0.9x \\ \ \\x = \frac{22.5}{0.9} = 25$$​​

Original price per mango = ₹25

Reduced price per mango = ₹25 × 0.9 = ₹22.5
Price per dozen after reduction = ₹22.5 × 12 = ₹270 per dozen