# 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.