Question

The ratio of length and breadth of a rectangular park is 3:2. 'X' is walking along the boundary of the park at the speed of 6 km/hr and completes one round in 20 minutes. find the area of the park in square meters.

• A. 220000
• B. 240000
• C. 260000

Hint:

In problems involving speed, distance, and time with geometric figures, the first and most crucial step is to ensure all units are consistent. Converting km/hr to m/s or m/min at the beginning prevents errors in later calculations.

Answer 1

The Correct Option is C

Step 1: Understanding the Given Information
We are given the following information:


Ratio of Length (L) to Breadth (B) = \(3:2\).

Speed of walking = 6 km/hr.

Time to complete one round = 20 minutes.

One round along the boundary is the perimeter of the park.

We need to find the area of the park in square meters.

Step 2: Key Formula or Approach
\begin{enumerate}
Convert all units to be consistent (meters and minutes).

Calculate the perimeter using the formula: Distance = Speed \(\times\) Time.

Use the perimeter and the given ratio to find the length and breadth.

Calculate the area using the formula: Area = Length \(\times\) Breadth.
\end{enumerate}
Step 3: Detailed Explanation
1. Convert Units:
The speed is given in km/hr and the time in minutes. Let's convert the speed to meters per minute.
\[ \text{Speed} = 6 \frac{\text{km}}{\text{hr}} = \frac{6 \times 1000 \text{ meters}}{60 \text{ minutes}} = 100 \text{ meters/minute} \] The time is given as 20 minutes.
2. Calculate the Perimeter:
The distance covered in one round is the perimeter of the park.
\[ \text{Perimeter (P)} = \text{Speed} \times \text{Time} \] \[ P = 100 \text{ m/min} \times 20 \text{ min} = 2000 \text{ meters} \] 3. Find Length and Breadth:
The formula for the perimeter of a rectangle is \(P = 2(L + B)\).
\[ 2000 = 2(L + B) \] \[ L + B = \frac{2000}{2} = 1000 \text{ meters} \] We are given the ratio \(L:B = 3:2\). Let \(L = 3k\) and \(B = 2k\).
Substituting these values into the equation:
\[ 3k + 2k = 1000 \] \[ 5k = 1000 \] \[ k = \frac{1000}{5} = 200 \] Now we can find the actual length and breadth:
\[ L = 3k = 3 \times 200 = 600 \text{ meters} \] \[ B = 2k = 2 \times 200 = 400 \text{ meters} \] 4. Calculate the Area:
The formula for the area of a rectangle is Area = \(L \times B\).
\[ \text{Area} = 600 \text{ m} \times 400 \text{ m} = 240000 \text{ square meters} \]
Step 4: Final Answer
The area of the park is 240,000 square meters. Therefore, option (C) is the correct answer.