CAT Exam Model Paper 8 with solutions for free online practice

The area of APRS is half the area of APQS which means that PR is a median.
So QR = RS
Also QR = PR (∴∆PQR is an equilateral triangle)
Hence, PR = RS
Now ∠PRQ = 60° ⇒ ∠PRS = 120°
So, ∠RPS + ∠PSR = 60°
But ∠RPS = ∠PSR (∴ PR = RS)
=∠RPS =30°
Therefore, ZQPS = 60° + 30° = 90°