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
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.