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

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Accepted Answer

The problem involves determining the investment period in bank A, given the interest rates and the ratio of interests earned from two banks. Here's the step-by-step solution:

**Interest from Bank A:**

- The principal amount deposited in bank A is Rs. 10,000.
   - The simple interest formula is:
     $$
     	ext{Interest} = \frac{	ext{Principal} 	imes 	ext{Rate} 	imes 	ext{Time}}{100}
     $$
   - For bank A:
     $$
     	ext{Interest from A} = \frac{10000 	imes 5 	imes n}{100} = 500n
     $$
     where $$n$$ is the number of years the amount is invested in bank A.

**Interest from Bank B:**

- On maturity, the total amount received from bank A becomes the principal for bank B. This total amount is:
     $$
     	ext{Principal for B} = 10000 + 500n
     $$
   - The investment period in bank B is 5 years, and the interest rate is 6% per annum. The interest from bank B is:
     $$
     	ext{Interest from B} = \frac{	ext{Principal for B} 	imes 6 	imes 5}{100}
     $$
     Substituting the principal:
     $$
     	ext{Interest from B} = \frac{(10000 + 500n) 	imes 6 	imes 5}{100}
     $$
     Simplify:
     $$
     	ext{Interest from B} = 3000 + 150n
     $$

**Ratio of Interests:**

- The ratio of interests from bank A and bank B is given as $$10 : 13$$. Thus:
     $$
     \frac{	ext{Interest from A}}{	ext{Interest from B}} = \frac{10}{13}
     $$
   - Substituting values:
     $$
     \frac{500n}{3000 + 150n} = \frac{10}{13}
     $$

**Solve for $$n$$:**

- Cross-multiply to eliminate the fraction:
     $$
     13(500n) = 10(3000 + 150n)
     $$
   - Simplify:
     $$
     6500n = 30000 + 1500n
     $$
   - Rearrange terms:
     $$
     5000n = 30000
     $$
   - Solve for $$n$$:
     $$
     n = \frac{30000}{5000} = 6
     $$

### Final Answer:

The investment period in bank A is **6 years**.  
Correct option: **C**

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