Sakshi invests a part of Rs. 12,000 in 12% stock at Rs. 120 and the remainder in 15% stock at Rs. 125. If his total dividend per annum is Rs. 1360, how much does he invest in 12% stock at Rs. 120?

1Rs. 4000
2Rs. 4500
3Rs. 5500
4Rs. 6000

Answer:- 1

Explanation:-

Solution:

\begin{aligned} Let investment in 12 % stock be R s . x . \\ Then, investment in 15 % stock \\ = R s . (12000 - x) . \\ ∴ \frac{12}{120} \times x + \frac{15}{125} \times (12000 - x) \\ = 1360 \\ \Rightarrow \frac{x}{10} + \frac{3}{25} (12000 - x) = 1360 \\ \Rightarrow 5 x + 72000 - 6 x = 1360 \times 50 \\ \Rightarrow x = 4000. \end{aligned}

$\eqalign{ & {\text{Let}}\,{\text{investment}}\,{\text{in}}\,12\% \,{\text{stock}}\,{\text{be}}\,Rs.x. \cr & {\text{Then,}}\,{\text{investment}}\,{\text{in}}\,15\% \,{\text{stock}} \cr & = Rs.\,\left( {12000 - x} \right). \cr & \therefore \frac{{12}}{{120}} \times x + \frac{{15}}{{125}} \times \left( {12000 - x} \right) \cr & = 1360 \cr & \Rightarrow \frac{x}{{10}} + \frac{3}{{25}}\left( {12000 - x} \right) = 1360 \cr & \Rightarrow 5x + 72000 - 6x = 1360 \times 50 \cr & \Rightarrow \,x = 4000. \cr}$