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?
- (a) 140 km
- (b) 130 km
- (c) 110 km
- (d) 100 km ✓ UPSC's answer
Why the answer is (d)
• P, Q, and R form a right-angled triangle with the right angle at P because Q is directly West and R is directly South of P.
• The distance PQ is given as 60 km, which serves as one leg of the triangle.
• The distance PR is given as 80 km, which serves as the other leg of the triangle.
• The distance QR is the hypotenuse, calculated using the Pythagorean theorem: $\sqrt{60^2 + 80^2}$.
• This simplifies to $\sqrt{3600 + 6400} = \sqrt{10000} = 100$ km.
• Therefore, the distance between Q and R is 100 km, corresponding to option (d).
Why the other options are wrong
- (a) 140 km
- 140 km is the simple sum of the two distances (60 + 80), which ignores the perpendicular geometry.
- (b) 130 km
- 130 km does not correspond to the hypotenuse of a 60-80 right triangle.
- (c) 110 km
- 110 km is an arbitrary value that does not result from the Pythagorean calculation.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2019, held on 2 June 2019. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.