Correct Option (2)
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.
Incorrect Options:
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.