As a result of 25% hike in the price of rice per kg, a person is able to purchase 6 kg less rice for ₹ 1,200. What was the original price of rice per kg?

(a) ₹ 30
(b) ₹ 40 ✓ UPSC's answer
(c) ₹ 50
(d) ₹ 60

Why the answer is (b)

• Let the original price of rice per kg be ₹x.

• The new price after a 25% hike is x + 0.25x = 1.25x.

• The quantity of rice purchased at the original price is 1200/x kg.

• The quantity of rice purchased at the new price is 1200/(1.25x) kg.

• The difference in quantity is given as 6 kg, so 1200/x - 1200/(1.25x) = 6.

• Solving the equation: 1200/x - 960/x = 6, which simplifies to 240/x = 6, resulting in x = 40.

Why the other options are wrong

(a) ₹ 30: If the original price were ₹30, the quantity difference would be approximately 6.67 kg, not 6 kg.
(c) ₹ 50: If the original price were ₹50, the quantity difference would be 4.8 kg, not 6 kg.
(d) ₹ 60: If the original price were ₹60, the quantity difference would be 4 kg, not 6 kg.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2020, held on 4 October 2020. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.