Rs. 9800 are invested partly in 9% stock at 75 and 10% stock at 80 to have equal amount of incomes. The investment in 9% stock is:

1Rs. 4800
2Rs. 5000
3Rs. 5400
4Rs. 5600

Answer:- 1

Explanation:-

Solution:

\begin{aligned} Let the ivestment in 9 % stock be R s . x . \\ Then, investment in 10 % stock \\ = R s . (9800 - x) . \\ \frac{9}{75} \times x = \frac{10}{80} \times (9800 - x) \\ \Rightarrow \frac{3 x}{25} = \frac{9800 - x}{8} \\ \Rightarrow 24 x = 9800 \times 25 - 25 x \\ \Rightarrow 49 x = 9800 \times 25 \\ \Rightarrow x = 5000. \end{aligned}

$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{ivestment}}\,{\text{in}}\,9\% \,{\text{stock}}\,{\text{be}}\,Rs.\,x. \cr & {\text{Then,}}\,{\text{investment}}\,{\text{in}}\,10\% \,{\text{stock}} \cr & = Rs.\,\left( {9800 - x} \right). \cr & \frac{9}{{75}} \times \,x\, = \frac{{10}}{{80}}\, \times \,\left( {9800 - x} \right) \cr & \Rightarrow \frac{{3x}}{{25}} = \frac{{9800 - x}}{8} \cr & \Rightarrow 24x = 9800 \times 25 - 25x \cr & \Rightarrow 49x = 9800 \times 25 \cr & \Rightarrow x = 5000. \cr}$