Mayuri took a loan at simple interest rate of 6 p.c.p.a in the first year and it increased by 1.5 p.c.p.a. every year. If she pays Rs. 8190 as interest at the end of 3 years, what was her loan amount?

Options

A. A)Rs. 36000
B. B)Rs. 35400
C. C)Rs. 36800
D. D)None of these

Answer

To solve the problem, we need to determine Mayuri's loan amount based on the interest she paid over 3 years. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Interest Rates
- In the first year, the interest rate is 6% per annum.
- In the second year, the interest rate increases by 1.5%, making it 7.5% per annum.
- In the third year, the interest rate increases again by 1.5%, making it 9% per annum.

### Step 2: Calculate the Interest for Each Year
Let the principal amount (loan amount) be represented as \( P \).

- Interest for the first year:
\[ \text{Interest}_1 = P \times \frac{6}{100} = 0.06P \]

- Interest for the second year:
\[ \text{Interest}_2 = P \times \frac{7.5}{100} = 0.075P \]

- Interest for the third year:
\[ \text{Interest}_3 = P \times \frac{9}{100} = 0.09P \]

### Step 3: Calculate Total Interest Paid Over 3 Years
Now, we can sum the interest from all three years:
\[ \text{Total Interest} = \text{Interest}_1 + \text{Interest}_2 + \text{Interest}_3 \]
\[ \text{Total Interest} = 0.06P + 0.075P + 0.09P = 0.225P \]

### Step 4: Set Up the Equation
According to the problem, Mayuri paid Rs. 8190 as interest at the end of 3 years. Therefore, we can set up the equation:
\[ 0.225P = 8190 \]

### Step 5: Solve for \( P \)
To find \( P \), divide both sides of the equation by 0.225:
\[ P = \frac{8190}{0.225} \]
Calculating the right side:
\[ P = 36400 \]

### Conclusion
Thus, the loan amount that Mayuri took was Rs. 36,400.

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