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

Answer: (C)

6

Answer 2

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

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

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

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

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

Step 2 : Total Amount After Deposit in Bank A
The total amount after investing in bank A will be the principal plus the interest:

$A_A = 10000 + 500x$

Step 3: Interest Calculation in Bank B
Now, this total amount is deposited in bank B at $6\%$ for 5 years.

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

Step 4: Using the Given Ratio of Interests
The problem states that the ratio of the interests from bank A and bank B is 10 : 13. Therefore:

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

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

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

Step 5: Solving the Equation
Cross-multiply to solve for $x$:

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

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