Saumya borrowed Rs. 15000 at the rate of 12% p.a., for two years and another amount at the rate of 15% p.a for two years. The total interest paid by her was Rs. 9000. Find the amount she borrowed at 15% pa.

Options

A. Rs. 31000
B. Rs. 33000
C. Rs. 28000
D. Rs. 18000

Answer

To solve the problem step by step, we will follow the same approach as in the video transcript.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Amount borrowed at 12% p.a. = Rs. 15,000
- Rate of interest for the first amount = 12% p.a.
- Time period for both loans = 2 years
- Total interest paid = Rs. 9,000
- Let the amount borrowed at 15% p.a. be Rs. X.

2. **Calculate the Interest for the First Amount:**
- Use the formula for simple interest:
\[ I = \frac{P \times R \times T}{100} \]
- For the first amount (Rs. 15,000):
\[ I_1 = \frac{15000 \times 12 \times 2}{100} \]
- Calculate:
\[ I_1 = \frac{15000 \times 24}{100} = \frac{360000}{100} = 3600 \]
- So, the interest for the first amount (I1) is Rs. 3,600.

3. **Calculate the Interest for the Second Amount:**
- For the second amount (Rs. X) at 15% p.a.:
\[ I_2 = \frac{X \times 15 \times 2}{100} \]
- Simplifying:
\[ I_2 = \frac{30X}{100} = \frac{3X}{10} \]

4. **Set Up the Equation for Total Interest:**
- According to the problem, the total interest paid is Rs. 9,000:
\[ I_1 + I_2 = 9000 \]
- Substitute the values of I1 and I2:
\[ 3600 + \frac{3X}{10} = 9000 \]

5. **Solve for X:**
- Rearrange the equation:
\[ \frac{3X}{10} = 9000 - 3600 \]
- Calculate the right side:
\[ \frac{3X}{10} = 5400 \]
- Multiply both sides by 10:
\[ 3X = 54000 \]
- Divide by 3:
\[ X = \frac{54000}{3} = 18000 \]

6. **Conclusion:**
- The amount borrowed at 15% p.a. is Rs. 18,000.

### Final Answer:
The amount Saumya borrowed at 15% p.a. is Rs. 18,000.