If the length of a rectangle is increased in the ratio `4:5` and its breadth is decreased in the ratio `3:2` , then its area will be decrease in the ratio `"………"` .

Options

A. `2:1`
B. `4:3`
C. `10:3`
D. `6:5`

Answer

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

### Step 1: Understand the problem
We need to find the ratio of the area of a rectangle before and after changes in its dimensions. The length is increased in the ratio 4:5, and the breadth is decreased in the ratio 3:2.

### Step 2: Assign initial dimensions
Let's assign initial dimensions to the rectangle:
- Initial Length (L1) = 4 units
- Initial Breadth (B1) = 3 units

### Step 3: Calculate the initial area
The area of a rectangle is calculated using the formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]
So, the initial area (A1) can be calculated as:
\[ A1 = L1 \times B1 = 4 \times 3 = 12 \text{ square units} \]

### Step 4: Determine the new dimensions
Now, we will calculate the new dimensions based on the given ratios:
- New Length (L2) = 5 units (since it increased from 4 to 5)
- New Breadth (B2) = 2 units (since it decreased from 3 to 2)

### Step 5: Calculate the final area
Using the new dimensions, we can calculate the final area (A2):
\[ A2 = L2 \times B2 = 5 \times 2 = 10 \text{ square units} \]

### Step 6: Find the ratio of the initial area to the final area
Now, we need to find the ratio of the initial area to the final area:
\[ \text{Ratio} = \frac{A1}{A2} = \frac{12}{10} = \frac{6}{5} \]

### Step 7: Conclusion
The area of the rectangle decreases in the ratio of 6:5.

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