SSC CGL 2024 PYQ — Question 68

SSC CGL - 18 Sep 2024 - Shift 3 • Quantitative Aptitude • Q68

The side MN of a parallelogram MNOP is produced to Q such that MN = NQ. PQ intersects ON at R. The point R divides ON in the ratio:

Show answer & explanation

Correct answer: D

Explanation

The correct answer is option 4 i.e. 1 : 1.

MN = NQ

Here, MN = PO then, MN = PO = NQ

PO || MN then, PO || NQ

In ΔPOR and ΔNQR,

PO = NQ

∠OPR = ∠RQN (Alternate interior angles)

∠PRO = ∠QRN (Vertically opposite angles)

So, ΔOPR ≅ ΔNQR (ASA Rule)

Then, OR = RN

OR : RN = 1 : 1

Therefore, the point R divides ON in the ratio of 1 : 1.