Directions: Read the following information carefully and answer the questions given below:

Anita starts cycling from point A in the west direction. After travelling 4m, she reaches point B. From point B, she takes a left turn and rides 3m to reach point C. From point C, she turns right and travels 6m to reach point D. From point D, she takes a right turn and travels 9m to reach point E.

Benny starts cycling from point P in the north direction. After travelling 6m, he reaches point Q. From point Q, he takes a left turn and rides 5m to reach point R. From point R, he takes a left turn and rides 10m to reach point S. Now, from point S, he takes a right turn and travels 3m to reach point E.

Which of the following statement(s) is/are true?

I. The total distance covered by Benny is greater than the total distance covered by Anita.

II. Point R is to the west of point Q.

III. The shortest distance between point P and point S is $\sqrt{65}$ m.

The correct option is Both I and II.

Let us analyze the movements of Anita and Benny step-by-step to evaluate each statement.

1. Distance covered by Anita:
- Path: Point A → West 4 m → Point B → South 3 m (left turn) → Point C → West 6 m (right turn) → Point D → North 9 m (right turn) → Point E.
- Total distance covered by Anita:

$=4+3+6+9=22$ m

2. Distance covered by Benny:
- Path: Point P → North 6 m → Point Q → West 5 m (left turn) → Point R → South 10 m (left turn) → Point S → West 3 m (right turn) → Point E.
- Total distance covered by Benny:

$=6+5+10+3=24$ m

3. Evaluation of Statement I:
Statement I states: "The total distance covered by Benny is greater than the total distance covered by Anita."
Since Benny covered 24 m and Anita covered 22 m:

$24>22$

Therefore, Statement I is true.

4. Evaluation of Statement II:
Statement II states: "Point R is to the west of point Q."
From point Q, Benny turned left (facing North), which is towards the West direction, to reach point R. Thus, point R lies to the West of point Q.
Therefore, Statement II is true.

5. Evaluation of Statement III:
Statement III states: "The shortest distance between point P and point S is
$\sqrt{65}$
m."
Let us calculate the horizontal and vertical displacements from P to S:
- Horizontal distance (West) $=5$ m
- Vertical distance (South) $=10-6=4$ m

Using the Pythagoras theorem, the shortest distance between P and S is:

$\text{Distance}=\sqrt{5^2+4^2}=\sqrt{25+16}=\sqrt{41}$ m

Since $\sqrt{41}\ne \sqrt{65}$, Statement III is false.

Hence, only statements I and II are true.