An amount of Rs. 1,00,000 is invested in two types of shares. The first yields an interest of 9% p.a. and second, 11% p.a. If the total interest at the end of one year is $$9\frac{3}{4}$$ %, then the amount invested in each share was -

Explanation:-

Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (100000 - x).
Then,
$$\eqalign{ & = \left( {\frac{{x \times 9 \times 1}}{{100}}} \right) + \left[ {\frac{{\left( {100000 - x} \right) \times 11 \times 1}}{{100}}} \right] \cr & = \left( {100000 \times \frac{{39}}{4} \times \frac{1}{{100}}} \right) \cr & \Leftrightarrow \frac{{9x + 100000 - 11x}}{{100}} = \frac{{39000}}{4} = 9750 \cr & \Leftrightarrow 2x = \left( {1100000 - 975000} \right) = 125000 \cr & \Leftrightarrow x = 62500 \cr & \therefore {\text{Sum invested at 9}}\% \cr & = {\text{Rs}}{\text{. }}62500. \cr & {\text{Sum invested at 11% }} \cr & {\text{ = Rs}}{\text{.}}\left( {100000 - 62500} \right) \cr & = {\text{Rs}}{\text{. }}37500. \cr}$$