As a result of 25% hike in the price of rice per kg, a person is able to purchase 6 kg less rice for Rs 1200. What was the original price of rice per kg.

EXPLANATION

Let the original price of rice per kg be P and the original quantity of rice purchased be Q kg.

The total expenditure is Rs 1200. Therefore, the initial relationship is:

P × Q = 1200 (Equation 1)

The price of rice increases by 25%. The new price per kg will be:

New Price = P + 0.25P = 1.25P = (5/4)P

Due to the price hike, the person purchases 6 kg less rice. The new quantity purchased is (Q - 6) kg.

The total expenditure remains Rs 1200. So, the new relationship is:

(5/4)P × (Q - 6) = 1200 (Equation 2)

From Equation 1, we have P = 1200/Q. Substitute this into Equation 2:

(5/4) × (1200/Q) × (Q - 6) = 1200

Divide both sides by 1200:

(5/4) × (1/Q) × (Q - 6) = 1

Multiply by 4Q:

5(Q - 6) = 4Q

5Q - 30 = 4Q

Q = 30 kg

Now, substitute the value of Q back into Equation 1 to find the original price P:

P × 30 = 1200

P = 1200 / 30

P = Rs 40

Thus, the original price of rice per kg was Rs 40.

The other options are incorrect because they do not satisfy the conditions stated in the problem.

If the original price was Rs 30 (Option 1), the original quantity would be 1200/30 = 40 kg. A 25% hike makes the new price Rs 37.5 (30 × 1.25). The new quantity purchased would be 1200/37.5 = 32 kg. The difference in quantity (40 - 32 = 8 kg) is not 6 kg.
If the original price was Rs 50 (Option 3), the original quantity would be 1200/50 = 24 kg. A 25% hike makes the new price Rs 62.5 (50 × 1.25). The new quantity purchased would be 1200/62.5 = 19.2 kg. The difference in quantity (24 - 19.2 = 4.8 kg) is not 6 kg.
If the original price was Rs 60 (Option 4), the original quantity would be 1200/60 = 20 kg. A 25% hike makes the new price Rs 75 (60 × 1.25). The new quantity purchased would be 1200/75 = 16 kg. The difference in quantity (20 - 16 = 4 kg) is not 6 kg.