A person buys three articles P, Q and R for ₹ 3,330. If P costs 25% more than R and R costs 20% more than Q, then what is the cost of P?

(a) ₹ 1,000
(b) ₹ 1,200
(c) ₹ 1,250
(d) ₹ 1,350 ✓ UPSC's answer

Why the answer is (d)

• Let the cost of article Q be x.

• Since R costs 20% more than Q, the cost of R is 1.20x.

• Since P costs 25% more than R, the cost of P is 1.25 * 1.20x = 1.50x.

• The total cost is the sum of P, Q, and R: 1.50x + x + 1.20x = 3.70x.

• Given the total cost is ₹3,330, we solve 3.70x = 3,330, which gives x = 900.

• The cost of P is 1.50x = 1.50 * 900 = ₹1,350, matching option (d).

Why the other options are wrong

(a) ₹ 1,000: ₹1,000 is incorrect because it does not satisfy the ratio relationship where P is 1.5 times Q.
(b) ₹ 1,200: ₹1,200 is incorrect because it corresponds to a different base value that does not sum to ₹3,330 with the given percentages.
(c) ₹ 1,250: ₹1,250 is incorrect because it fails to meet the condition that P is 25% more than R when R is 20% more than Q.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2024, held on 16 June 2024. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.