MAH-CET 2026 — Reasoning PYQ

1. Understand the Movement:

   • Let the starting point of the man be $O$.

   • He first walks $5\text{ km}$ South to reach point $A$. So, $OA=5\text{ km}$.

   • From point $A$, he turns left and walks $5\text{ km}$ East to reach the final point $B$. So, $AB=5\text{ km}$.

2. Forming a Right-Angled Triangle:

   • The path forms a right-angled triangle $\Delta OAB$ where the right angle is at $A$ ($\angle OAB=90^{\circ }$).

   • We need to find the shortest distance between the starting point $O$ and the final point $B$, which is the hypotenuse $OB$.

3. Applying Pythagoras Theorem:

   $${\text{Hypotenuse}}^2={\text{Base}}^2+{\text{Perpendicular}}^2$$

   $$O{B}^2=O{A}^2+A{B}^2$$

   $$O{B}^2=5^2+5^2$$

   $$O{B}^2=25+25$$

   $$O{B}^2=50$$

   $$OB=\sqrt{50}$$

   $$OB=5\sqrt{2}\text{ km}$$

4. Calculating the Decimal Value:

   • Since $\sqrt{2}\approx 1.414$:

     $$OB=5\times 1.414=7.07\text{ km}$$

Therefore, the distance from his starting point is $7.07\text{ km}$.