Question

Due to a 10% reduction in the price of sugar, Iqbal can now buy 7 kg more sugar without changing his total expenditure on sugar. If he spends ₹2520 on sugar, find the original price of sugar.

a) ₹3000
b) ₹3500
c) ₹2800
d) ₹3200

Answer 1

Final Answer:

The original price of sugar was ₹3000.

Thus the correct option is (A).

Step-by-step explanation:

Let the original price of sugar be P per kg, and let the quantity of sugar bought be Q kg. The total expenditure is given by the product of the price and quantity, i.e.,
`\( P * Q \)`. With a 10% reduction in price, the new price becomes 0.9P .

The problem states that with the reduction in price, Iqbal can now buy 7 kg more sugar without changing his total expenditure. Mathematically, this is expressed as:

`\[ P * Q = 0.9P * (Q + 7) \]`

Given that the total expenditure is ₹2520, we can write the equation:

`\[ P * Q = 2520 \]`

Now, substituting this into the previous equation, we get:

`\[ 2520 = 0.9P * (Q + 7) \]`

Solving for \( P \), we find:

`\[ P = (2520)/(0.9 * (Q + 7)) \]`

If we assume Q = 7 (as given in the problem), we can calculate Pto be ₹3000. Therefore, the original price of sugar was ₹3000.

Thus the correct option is (A).

Answer 2

To find the original price of sugar, we set up an equation based on the given 10% price reduction and the fact that Iqbal can purchase 7 kg more for the same cost of ₹2520. Solving this equation gives us the original price per kg of sugar, which when multiplied by the original quantity purchased, equals the total expenditure. Hence, the original price spent on sugar is ₹2520.

Step-by-step explanation:

Due to a 10% reduction in the price of sugar, Iqbal can now buy 7 kg more sugar without changing his total expenditure of ₹2520. We are looking to find the original price of sugar before the reduction. Let the original price per kg of sugar be x. Therefore, the number of kgs Iqbal could buy originally was ₹2520 / x. After the price reduction, the new price is 0.9x, so the number of kgs he can now buy is ₹2520 / 0.9x. Since he can buy 7 kgs more with the new price, we set up the equation: ₹2520 / x + 7 = ₹2520 / 0.9x. By solving this equation, we can calculate that the original price per kg was ₹36.

Given this original price of ₹36 per kg, the original total amount Iqbal spent on sugar (₹2520) allows him to buy 2520 / 36 = 70 kgs of sugar originally. Therefore, the correct answer to the original price of sugar would be calculated as the original quantity (70 kgs) multiplied by the original price per kg (₹36), which results in ₹2520. This means the original price of sugar spent by Iqbal was ₹2520.