If the Price of Rice is Reduced by 24%, It Enables Alok to Buy 10 kg More Rice for ₹2,500. Find the Reduced Rate of Rice per kg

Alok is looking to buy rice, and with a 24% reduction in price, he can buy 10 kg more rice for ₹2,500. Let's solve the problem and find out the reduced rate of rice per kg.

Step 1: Defining Variables

Let the original price of rice per kg be ₹x. After a 24% reduction, the new price per kg is 76% of the original price, which is 0.76x.

Step 2: Setting Up the Equation

At the original price, Alok can buy:

Quantity at original price = 2500 / x

At the reduced price, Alok can buy:

Quantity at reduced price = 2500 / (0.76x)

The difference in the quantity of rice he can buy is 10 kg, so we have the equation:

(2500 / (0.76x)) - (2500 / x) = 10

Step 3: Simplifying the Equation

Factor out 2500 from the equation:

2500 * (1 / (0.76x) - 1 / x) = 10

Now, simplify the expression inside the parentheses:

(1 / (0.76x)) - (1 / x) = (1 / x) * (1 / 0.76 - 1)

We get:

(1 / (0.76x)) - (1 / x) = (1 / x) * (0.24 / 0.76)

Substitute this back into the equation:

2500 * (0.24 / (0.76 * x)) = 10

Step 4: Solving for x

Now, solve for x:

x = 600 / 7.6 = 78.95

Step 5: Finding the Reduced Price

The original price of rice is ₹78.95. Therefore, the reduced price per kg is:

Reduced price = 0.76 * 78.95 = ₹60

Conclusion

The reduced price of rice per kg is ₹60, allowing Alok to buy 10 kg more rice for ₹2,500!