Question

An amount of Rs 10000 is deposited in bank A for a certain number of years at a simple interest of 5% per annum. On maturity, the total amount received is deposited in bank B for another 5 years at a simple interest of 6% per annum. If the interests received from bank A and bank B are in the ratio 10 : 13, then the investment period, in years, in bank A is

• A. 5
• B. 3
• C. 6
• D. 4

Answer 1

The Correct Option is C

Let $x$ be the number of years the amount is invested in bank A.

Step 1: Calculate Interest in Bank A
The simple interest formula is:

$\text{SI} = \frac{P \cdot R \cdot T}{100}$

Here: - $P = 10000$ (principal), - $R = 5\%$ (annual interest rate), - $T = x$ years (time).
The interest earned from bank A is:

$\text{SI}_A = \frac{10000 \cdot 5 \cdot x}{100} = 500x$ (Rs)

Step 2: Calculate Total Amount After Investment in Bank A
The total amount in bank A after the investment period is the principal plus the interest:

$A_A = 10000 + 500x$

Step 3: Calculate Interest in Bank B
This total amount ($A_A$) is then deposited in bank B at a 6% interest rate for 5 years.

$\text{SI}_B = \frac{(10000 + 500x) \cdot 6 \cdot 5}{100} = 300(10000 + 500x) = 300000 + 150000x$

Step 4: Use the Given Ratio of Interests
The problem states that the ratio of the interest earned from bank A to the interest earned from bank B is 10 : 13. Therefore:

$\frac{\text{SI}_A}{\text{SI}_B} = \frac{10}{13}$

Substitute the calculated expressions for $\text{SI}_A$ and $\text{SI}_B$:

$\frac{500x}{300000 + 150000x} = \frac{10}{13}$

Step 5: Solve for $x$
Cross-multiply to solve the equation for $x$:

$13 \cdot 500x = 10 \cdot (300000 + 150000x)$
$6500x = 3000000 + 1500000x$
$6500x - 1500000x = 3000000$
$-1493500x = 3000000$
$x = \frac{3000000}{1493500} \approx 3.02$

Therefore, the investment period in bank A is approximately 3 years.