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

✅ Correct Option: 2

Let's recall that Simple Interest = Principal × Rate × Time ÷ 100

Principal (P) = Rs 10000

Rate (R) = 5% per annum

Time = T years (this is what we need to find!)

Using Simple Interest formula: $SI = \tfrac{P \times R \times T}{100}$

Interest from Bank A = $\tfrac{10000 \times 5 \times T}{100} = 500T$

Maturity amount from Bank A = Original Principal + Interest Earned

= $10000 + 500T$

Important: This entire maturity amount becomes the new principal for Bank B.

Now this entire amount goes to Bank B:

New Principal = $10000 + 500T$

Rate = 6% per annum

Time = 5 years

Interest from Bank B = $\tfrac{(10000 + 500T) \times 6 \times 5}{100}$

$= \tfrac{(10000 + 500T) \times 30}{100}$

$= \tfrac{30(10000 + 500T)}{100}$

$= 3000 + 150T$

We're told that interests from Bank A and Bank B are in ratio 10:13.

$\tfrac{\text{Interest from Bank A}}{\text{Interest from Bank B}} = \tfrac{10}{13}$

$\tfrac{500T}{3000 + 150T} = \tfrac{10}{13}$

$500T \times 13 = (3000 + 150T) \times 10$

$6500T = 30000 + 1500T$

$6500T - 1500T = 30000$

$5000T = 30000$

$T = 6$ years

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