CUET UG 2025 — General Test Logical Reasoning

Let Home be the starting point and track Kanika's movements.

Starting from Home:

• Drives 6 km west
• Turns left (now facing south) and drives 3 km
• Turns left again (now facing east) and drives 10 km to reach Office

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Place Home at coordinates (0, 0) and track the position after each movement:

Starting position: Home = (0, 0)

After 6 km west: Position = (-6, 0)

After turning left and driving 3 km south: Position = (-6, -3)

After turning left and driving 10 km east: Position = (-6 + 10, -3) = (4, -3)

Therefore, Office = (4, -3)

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The shortest distance is the straight line from Home to Office.

Home: (0, 0)

Office: (4, -3)

Using the distance formula:

$$\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$Distance=(x2​−x1​)2+(y2​−y1​)2​

$$= \sqrt{(4 - 0)^2 + (-3 - 0)^2}$$=(4−0)2+(−3−0)2​

$$= \sqrt{16 + 9}$$=16+9​

$$= \sqrt{25}$$=25​

$$= 5$$=5

Therefore, the shortest distance between home and office is 5 km.