UPSC Prelims 2019·CSAT·Quantitative Aptitude·Geometry and Mensuration

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?

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Last updated 23 May 2026, 3:31 pm IST
  1. A140km
  2. B130km
  3. C10km
  4. D100kmCorrect

Explanation

The problem describes the relative positions of three towns P, Q, and R, forming a right-angled triangle. 1. Q is in the West of P, and R is in the South of P. This means that the lines PQ and PR are perpendicular to each other, with P being the vertex of the right angle (90 degrees). 2. The distance between P and Q (PQ) is 60 km. 3. The distance between P and R (PR) is 80 km. 4. We need to find the distance between Q and R (QR), which is the hypotenuse of the right-angled triangle PQR. 5. Using the Pythagorean theorem (a^2 + b^2 = c^2): QR^2 = PQ^2 + PR^2 QR^2 = 60^2 + 80^2 QR^2 = 3600 + 6400 QR^2 = 10000 QR = sqrt(10000) QR = 100 km. Therefore, the distance between Q and R is 100 km. Analyzing the options: A) 140km: This would be the sum of the two distances (60 + 80), which is incorrect for a right-angled triangle. B) 130km: Incorrect. C) 10km: Incorrect. D) 100km: Correct, as calculated by the Pythagorean theorem. The final answer is D.
Quantitative Aptitude: 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 i
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