P, Q and R are three towns. The distance between P and Q is 60 km, whereas the distance between P and R is 80 km. Q is in the West of P and R is in the South of P. What is the distance between Q and R?
Answer & explanation
Answer: (d) 100 km
West and South are at right angles, so Q, P and R form a right triangle with the right angle at P. QR is the hypotenuse of a 60–80–100 triangle.
- Q is due West and R due South of P, so angle QPR = 90°.
- QR² = 60² + 80² = 3600 + 6400 = 10000.
- QR = 100 km.
- Check: 60 : 80 : 100 = 3 : 4 : 5.
Remember · Perpendicular directions make a right triangle; spot 3–4–5 multiples before squaring.
Question and answer: UPSC's official GS Paper II (2019, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·