Which is better investment: 11% stock at 143 or 9³/₄% stock at 117?

111% stock at 143
29³/₄% stock at 117
3Both are equally good
4Cannot be compared, as the total amount of investment is not given.

Answer:- 1

Explanation:-

Solution:

\begin{aligned} Let investment in each case be \\ R s . (143 \times 117) . \\ Income in 1^{st} case \\ = R s . (\frac{11}{143} \times 143 \times 117) \\ = R s . 1287. \\ Income in 2^{nd} case \\ = R s . (\frac{39}{4 \times 117} \times 143 \times 117) \\ = R s . 1394.25 \\ Clearly, 9 \frac{3}{4} % stock at 117 is better . \end{aligned}

$\eqalign{ & {\text{Let}}\,{\text{investment}}\,{\text{in}}\,{\text{each}}\,{\text{case}}\,{\text{be}} \cr & Rs.\,\left( {143 \times 117} \right). \cr & {\text{Income}}\,{\text{in}}\,{{\text{1}}^{{\text{st}}}}\,{\text{case}} \cr & = Rs.\left( {\frac{{11}}{{143}} \times 143 \times 117} \right) \cr & = Rs.\,1287. \cr & {\text{Income}}\,{\text{in}}\,{{\text{2}}^{{\text{nd}}}}\,{\text{case}} \cr & = Rs.\,\left( {\frac{{39}}{{4 \times 117}} \times 143 \times 117} \right) \cr & = Rs.\,1394.25 \cr & {\text{Clearly,}}\,9\frac{3}{4}\% \,{\text{stock}}\,{\text{at}}\,117\,{\text{is}}\,{\text{better}}. \cr}$