Anju starts from Lucknow and drives 18 km towards west. She then takes a right turn, drives 14 km, turns right again and drives 9 km. She takes a final right turn, drives 2 km and stops at Point F. What is the shortest distance between Point F and Lucknow?

Let's place Lucknow at the starting point and track Anju's position after each turn.

Starting from Lucknow, we can use directions like a compass:

Movement	Direction	Distance	New Position from Lucknow
Start	-	-	Lucknow (0, 0)
First	West	18 km	18 km west
Right turn → North	North	14 km	18 km west, 14 km north
Right turn → East	East	9 km	9 km west, 14 km north
Right turn → South	South	2 km	9 km west, 12 km north (Point F)

Why 9 km west in row 4? She was 18 km west, then moved 9 km east (back towards Lucknow), so: $18 - 9 = 9$ km west

Why 12 km north in row 5? She was 14 km north, then moved 2 km south (back down), so: $14 - 2 = 12$ km north

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Point F is 9 km west and 12 km north of Lucknow. This forms a right triangle where:

• One side (horizontal) = 9 km
• Other side (vertical) = 12 km
• Hypotenuse = shortest distance

Using Pythagoras theorem: $\text{Distance}^2 = 9^2 + 12^2$

$\text{Distance}^2 = 81 + 144 = 225$

$\text{Distance} = \sqrt{225} = 15$ km

Answer: Option 4 (15 km)