Question 12.

We are told that, 10000 is deposited in bank A for a certain number of years at a simple interest of 5% per annum. 

Let us say that the number of years is x

Total value of the deposit after x years is, $10000\left(1+x\left(0.05\right)\right)$

On maturity, the total amount received is deposited in bank B for another 5 years at a simple interest of 6% per annum

Here we know the years and the interest rate, 

$10000\left(1+x\left(0.05\right)\right)\left(1+5\left(0.06\right)\right)$

$10000\left(1+\left(0.05\right)x\right)\left(1.3\right)$

Interest received from Bank A is $\left(x\left(0.05\right)\right)10000$

Interest received from Bank B is $0.3\left(10000\left(1+x\left(0.05\right)\right)\right)$

This ratio is given to be 10:13. 

$\dfrac{x\left(0.05\right)}{0.3\left(1+x\left(0.05\right)\right)}=\dfrac{10}{13}$

$0.65x=3+0.15x$

$0.5x=3$

$x=6$

Hence the number of years the money was invested in Bank A is 6 years.