In some code, letters P, Q, R, S, T represent numbers 4, 5, 10, 12, 15. It is not known which letter represents which number. If Q − S = 2S and T = R + S + 3, then what is the value of P + R − T?
Answer & explanation
Answer: (b) 2
Q − S = 2S means Q = 3S, so (Q, S) is (15, 5) or (12, 4). Only (15, 5) lets T = R + S + 3 work, with R = 4 and T = 12, which leaves P = 10. So P + R − T = 10 + 4 − 12 = 2.
- Q − S = 2S gives Q = 3S. From 4, 5, 10, 12, 15, the options are (Q, S) = (15, 5) or (12, 4).
- Case Q = 12, S = 4: T = R + 7 with R and T from 5, 10, 15; no pair works.
- Case Q = 15, S = 5: T = R + 8 with R and T from 4, 10, 12; R = 4, T = 12 works, leaving P = 10.
- P + R − T = 10 + 4 − 12 = 2.
Remember · Use the tightest equation first to list the cases, then eliminate cases with the second equation.
Question and answer: UPSC's official GS Paper II (2024, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·