Neeta borrowed some money at the rate of 6% per annum for the first 3 yr, at the rate of 9% per annum for the next 5 yr and at the rate of 13% per annum for the period beyond 8 yr. If she pays a total interest of ? 8160 at the end of 11 yr, how much money did she borrow?

Options

A. X1200
B. X1000
C. X800
D. Data is inadequate

Answer

To solve the problem step by step, we need to calculate the total interest Neeta paid over the 11 years at different interest rates and find out how much money she borrowed.

### Step 1: Define the variables
Let the amount of money Neeta borrowed be \( X \).

### Step 2: Calculate the interest for the first 3 years at 6%
The formula for simple interest is:
\[ \text{Simple Interest} = \frac{P \times R \times T}{100} \]
For the first 3 years at 6%:
\[ \text{Interest}_1 = \frac{X \times 6 \times 3}{100} = \frac{18X}{100} = 0.18X \]

### Step 3: Calculate the interest for the next 5 years at 9%
For the next 5 years at 9%:
\[ \text{Interest}_2 = \frac{X \times 9 \times 5}{100} = \frac{45X}{100} = 0.45X \]

### Step 4: Calculate the interest for the last 3 years at 13%
For the last 3 years (from year 8 to year 11) at 13%:
\[ \text{Interest}_3 = \frac{X \times 13 \times 3}{100} = \frac{39X}{100} = 0.39X \]

### Step 5: Add all the interests together
Now, we can add all the interests:
\[ \text{Total Interest} = \text{Interest}_1 + \text{Interest}_2 + \text{Interest}_3 \]
\[ \text{Total Interest} = 0.18X + 0.45X + 0.39X = 1.02X \]

### Step 6: Set up the equation with the total interest paid
We know that the total interest paid at the end of 11 years is \( 8160 \):
\[ 1.02X = 8160 \]

### Step 7: Solve for \( X \)
To find \( X \), divide both sides by \( 1.02 \):
\[ X = \frac{8160}{1.02} \]
Calculating this gives:
\[ X = 8000 \]

### Conclusion
Neeta borrowed **₹8000**.

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