UPSC CDS I 2025 Mathematics Paper

Distance traveled East =x meters
Distance traveled South =40 meters
Distance traveled West =60 meters
Distance traveled North =200 meters
PR =200 meters
Formula used:
Pythagoras theorem: In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Calculation:
PR =200 meters
Horizontal distance between P and R=x−60
Vertical distance between P and R = 200-40=160
Using Pythagoras theorem:
⇒(PR)2=(‌ Horizontal distance ‌)2+(‌ Vertical distance ‌)2
⇒2002=(x−60)2+1602
⇒40000=(x−60)2+25600
⇒(x−60)2=40000−25600
⇒(x−60)2=14400
⇒x−60=√‌14400
⇒x−60=120
⇒x=120+60
⇒x=180