A playground is in the shape of a rectangle. A sum of Rs. 1,000 was spent to make the ground usable at the rate of 25 paise per sq.m. The breadth of the ground is 50 m. If the length of the ground is increased by 20 m, what will be the expenditure (in rupees) at the same rate per sq.m. ?

Options

A. 1250
B. 1000
C. 1500
D. 2250

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the Area of the Playground
The amount spent to make the ground usable is Rs. 1,000 at the rate of Rs. 0.25 (25 paise) per square meter.

To find the area of the playground, we use the formula:
\[ \text{Area} = \frac{\text{Total Cost}}{\text{Cost per sq.m}} \]

Substituting the values:
\[ \text{Area} = \frac{1000}{0.25} = 4000 \text{ sq.m} \]

### Step 2: Determine the Dimensions of the Playground
We know the breadth of the playground is 50 m. Let the length be \( L \).

The area of a rectangle is given by:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]
Thus, we have:
\[ 4000 = L \times 50 \]

To find \( L \):
\[ L = \frac{4000}{50} = 80 \text{ m} \]

### Step 3: Increase the Length of the Playground
The problem states that the length of the ground is increased by 20 m. Therefore, the new length \( L' \) will be:
\[ L' = 80 + 20 = 100 \text{ m} \]

### Step 4: Calculate the New Area of the Playground
Now, we can calculate the new area with the updated length:
\[ \text{New Area} = L' \times \text{Breadth} = 100 \times 50 = 5000 \text{ sq.m} \]

### Step 5: Calculate the Expenditure for the New Area
Finally, we calculate the expenditure for the new area at the same rate of Rs. 0.25 per sq.m:
\[ \text{Expenditure} = \text{New Area} \times \text{Cost per sq.m} = 5000 \times 0.25 = 1250 \text{ Rs.} \]

### Final Answer
The expenditure for the new area will be Rs. 1,250.

---