CSAT 2021

Q. There are three points P,Q and R on a straight line such that PQ:QR-3:5. If n is the number of possible values of PQ:PR, then what is n equal to ?

(a) 1
(b) 2
(c) 3
(d) 4
Correct Answer: (b) 2

Question from UPSC Prelims 2021 CSAT Paper

Explanation : 

Three points P,Q and R on straight line

CASE – 1
Assuming PQ = 3x, QR = 5x and PR = PQ + QR, we get
PQ : PR = 3x : (3x + 5x)
⇒ PQ : PR = 3 : 8

Three points P, Q, R on a line

CASE – 2
Assuming PQ = 3x, QR = 5x and PR = QR – PQ, we get
PQ : PR = 3x : (5x – 3x)
⇒ PQ : PR = 3 : 2

So, we have n = 2 possible values.

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