A borrowed Rs 1500 at 4 % per annum and Rs 1400 at 5 % per annum for the same period. He paid Rs 390 as total inteset. Find the time for which he borrowed the sum.

Options

A. 3.5 years
B. 2.5 years
C. 3 years
D. 4 years

Answer

To find the time for which the amounts were borrowed, we will use the formula for simple interest:

\[ \text{Simple Interest (SI)} = \frac{P \times R \times T}{100} \]

where:
- \( P \) = Principal amount (the initial amount borrowed)
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

### Step 1: Calculate the interest for the first amount

For the first loan of Rs 1500 at 4% per annum:

\[ SI_1 = \frac{1500 \times 4 \times T}{100} = 60T \]

### Step 2: Calculate the interest for the second amount

For the second loan of Rs 1400 at 5% per annum:

\[ SI_2 = \frac{1400 \times 5 \times T}{100} = 70T \]

### Step 3: Set up the equation for total interest

According to the problem, the total interest paid is Rs 390. Therefore, we can write the equation:

\[ SI_1 + SI_2 = 390 \]

Substituting the values we found:

\[ 60T + 70T = 390 \]

### Step 4: Combine like terms

Combine the terms on the left side:

\[ 130T = 390 \]

### Step 5: Solve for \( T \)

Now, divide both sides by 130 to find \( T \):

\[ T = \frac{390}{130} = 3 \]

### Conclusion

The time for which he borrowed the sum is **3 years**.

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