Solving the Plot Area Percentage Problem

This problem involves calculating the area of a plot of land based on percentage increases relative to other plots. We are given the area of Nakul's plot and the percentage relationships between Tarun's and Basab's plots, and Tarun's and Nakul's plots.

Understanding the Relationships

Let's define the areas:

• Area of Basab's plot = \(B\) square feet
• Area of Tarun's plot = \(T\) square feet
• Area of Nakul's plot = \(N\) square feet

According to the problem statement:

• Tarun's area was 10% more than Basab's area.
• Nakul's area was 40% more than Tarun's area.
• Nakul's area (\(N\)) was 2695 square feet.

Setting up the Equations

We can write these relationships as equations:

1. Tarun's area (\(T\)) is Basab's area (\(B\)) plus 10% of \(B\).
   \(T = B + 0.10B\)
   \(T = 1.10B\)
2. Nakul's area (\(N\)) is Tarun's area (\(T\)) plus 40% of \(T\).
   \(N = T + 0.40T\)
   \(N = 1.40T\)
3. We are given the value of \(N\).
   \(N = 2695\)

Solving for Basab's Area

We need to find the value of \(B\). We can use the given value of \(N\) and work backwards through the equations.

Step 1: Find Tarun's Area (\(T\))

We know that \(N = 1.40T\) and \(N = 2695\). So, we can write:

\(2695 = 1.40T\)

To find \(T\), we divide 2695 by 1.40:

\(T = \frac{2695}{1.40}\)

\(T = \frac{2695}{\frac{140}{100}} = \frac{2695 \times 100}{140} = \frac{2695 \times 10}{14}\)

Let's perform the division:

\(T = \frac{26950}{14}\)

Dividing 26950 by 14:

So, Tarun's area (\(T\)) is 1925 square feet.

Step 2: Find Basab's Area (\(B\))

Now we know that \(T = 1.10B\) and \(T = 1925\). So, we can write:

\(1925 = 1.10B\)

To find \(B\), we divide 1925 by 1.10:

\(B = \frac{1925}{1.10}\)

\(B = \frac{1925}{\frac{110}{100}} = \frac{1925 \times 100}{110} = \frac{1925 \times 10}{11}\)

Let's perform the division:

\(B = \frac{19250}{11}\)

Dividing 19250 by 11:

So, Basab's area (\(B\)) is 1750 square feet.

Conclusion

The area of the plot owned by Basab was 1750 square feet.

Revision Table: Plot Area Problem

Additional Information: Percentage Calculations

When a quantity is increased by a certain percentage, you can calculate the new quantity by multiplying the original quantity by \((1 + \text{percentage increase as a decimal})\). For example:

• A 10% increase means multiplying by \((1 + 0.10) = 1.10\).
• A 40% increase means multiplying by \((1 + 0.40) = 1.40\).

Conversely, if you know the new quantity after a percentage increase and want to find the original quantity, you divide the new quantity by \((1 + \text{percentage increase as a decimal})\).

In this problem, Nakul's area is 140% of Tarun's area (\(N = 1.40T\)), and Tarun's area is 110% of Basab's area (\(T = 1.10B\)). We used the division method to find the original values.