Sanjay borrowed Rs 900 at4%annum and Rs 1100 at 5% per annum for the same duration. He had to pay Rs 364 in all as interest. What is the time period in years?

Options

A. 5 years
B. 3 years
C. 2 years
D. 4 years

Answer

To solve the problem step by step, we will use the formula for Simple Interest (SI):

\[ SI = \frac{P \times R \times T}{100} \]

Where:
- \( SI \) = Simple Interest
- \( P \) = Principal amount
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

### Step 1: Calculate the Simple Interest for each loan

1. **For the first loan of Rs 900 at 4% per annum:**
\[ SI_1 = \frac{900 \times 4 \times T}{100} = \frac{3600T}{100} = 36T \]

2. **For the second loan of Rs 1100 at 5% per annum:**
\[ SI_2 = \frac{1100 \times 5 \times T}{100} = \frac{5500T}{100} = 55T \]

### Step 2: Write the equation for total interest

According to the problem, the total interest paid is Rs 364. Therefore, we can write the equation:

\[ SI_1 + SI_2 = 364 \]

Substituting the values we calculated:

\[ 36T + 55T = 364 \]

### Step 3: Combine like terms

Combine the terms on the left side:

\[ 91T = 364 \]

### Step 4: Solve for T

To find \( T \), divide both sides by 91:

\[ T = \frac{364}{91} = 4 \]

### Conclusion

The time period \( T \) is 4 years.

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