If the length of the rectangular plot is increased by `50%` then how many per cent should its breadth be increased so that its new area is `75%` more than its original area ?

Options

A. `20%`
B. `17 1/4%`
C. `16%`
D. `16 2/3%`

Answer

To solve the problem, we need to determine how much the breadth of a rectangular plot should be increased if the length is increased by 50% and the new area is to be 75% more than the original area.

### Step-by-Step Solution:

1. **Define Original Dimensions:**
Let the original length of the rectangle be \( L \) and the original breadth be \( B \).
- Original Area \( A = L \times B \).

2. **Increase Length by 50%:**
The new length after a 50% increase will be:
\[ L' = L + 0.5L = 1.5L \]

3. **Determine New Area Requirement:**
The new area should be 75% more than the original area. Therefore, the new area \( A' \) is:
\[ A' = A + 0.75A = 1.75A = 1.75(L \times B) \]

4. **Express New Area in Terms of New Breadth:**
Let the new breadth be \( B' \). The new area can also be expressed as:
\[ A' = L' \times B' = (1.5L) \times B' \]

5. **Set the Two Expressions for New Area Equal:**
Now we set the two expressions for the new area equal to each other:
\[ 1.5L \times B' = 1.75(L \times B) \]

6. **Cancel \( L \) from Both Sides:**
Assuming \( L \neq 0 \), we can divide both sides by \( L \):
\[ 1.5B' = 1.75B \]

7. **Solve for New Breadth \( B' \):**
Now, solve for \( B' \):
\[ B' = \frac{1.75B}{1.5} = \frac{1.75}{1.5}B = \frac{7}{6}B \]

8. **Calculate the Increase in Breadth:**
The increase in breadth is:
\[ \text{Increase} = B' - B = \frac{7}{6}B - B = \left(\frac{7}{6} - 1\right)B = \frac{1}{6}B \]

9. **Determine Percentage Increase in Breadth:**
The percentage increase in breadth is given by:
\[ \text{Percentage Increase} = \left(\frac{\text{Increase}}{B}\right) \times 100\% = \left(\frac{\frac{1}{6}B}{B}\right) \times 100\% = \frac{1}{6} \times 100\% \approx 16.67\% \]

### Final Answer:
The breadth should be increased by approximately **16.67%**.