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)
• Q is due west of P and R is due south of P, so the angle QPR is a right angle.
• QR² = PQ² + PR² = 60² + 80² = 3600 + 6400 = 10000.
• QR = √10000 = 100 km, option (d).
Why the other options are wrong
- (a) 140 km
- 140 km is PQ + PR, the distance via P, not the straight-line distance.
- (b) 130 km
- 130 km is not the hypotenuse of a right triangle with sides 60 km and 80 km.
- (c) 110 km
- 110 km is not the hypotenuse of a right triangle with sides 60 km and 80 km.
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.