Mr. Gupta has a choice to invest in ten-rupee shares of two firms at Rs13 or at Rs16. If the first firm pays 5% dividend and the second firm pays 6% dividend per annum, find: (i) which firm is paying better. (ii) if Mr. Gupta invests equally in both the firms and the difference between the returns from them is Rs 30, find how much, in all, does he invest.

(I) The primary firm:

$\begin{array}{*{35}{l}} Profit\text{ }=\text{ }5%\text{ }of\text{ }Rs\text{ }10\text{ }=\text{ }Rs\text{ }0.50 \\ In\text{ }this\text{ }way,\text{ }the\text{ }pay\text{ }%\text{ }=\text{ }Income/Investment\text{ }x\text{ }100 \\ =\text{ }0.50/13\text{ }x\text{ }100\text{ }=\text{ }3.846\text{ }% \\ \end{array}$

Presently,

The subsequent firm:

$\begin{array}{*{35}{l}} Nominal\text{ }worth\text{ }of\text{ }1\text{ }offer\text{ }=\text{ }Rs\text{ }10 \\ Market\text{ }worth\text{ }of\text{ }1\text{ }offer\text{ }=\text{ }Rs\text{ }16 \\ Profit\text{ }%\text{ }=\text{ }6\text{ }% \\ In\text{ }this\text{ }manner,\text{ }pay\text{ }%\text{ }=\text{ }pay/venture\text{ }x\text{ }100 \\ =\text{ }0.60/16\text{ }x\text{ }100 \\ =\text{ }3.75\text{ }% \\ \end{array}$

Accordingly, the primary firm is paying better compared to second firm

(ii) Let cash put resources into each firm

$=\text{ }Rs\text{ }y$

For first firm

$\begin{array}{*{35}{l}} Number\text{ }of\text{ }offers\text{ }bought\text{ }=\text{ }y/13\text{ }offers \\ Complete\text{ }profit\text{ }=\text{ }Rs\text{ }0.50\text{ }x\text{ }y/13\text{ }=\text{ }Rs\text{ }y/26 \\ \end{array}$

For second firm

$\begin{array}{*{35}{l}} Number\text{ }of\text{ }offers\text{ }bought\text{ }=\text{ }y/16\text{ }offers \\ Complete\text{ }profit\text{ }=\text{ }Rs\text{ }0.60\text{ }x\text{ }y/16\text{ }=\text{ }Rs\text{ }3y/80 \\ \end{array}$

Given the distinction of both profit

$=\text{ }Rs\text{ }30$

$\begin{array}{*{35}{l}} y/26\text{ }\text{ }3y/80\text{ }=\text{ }Rs\text{ }30 \\ y/1040\text{ }=\text{ }Rs\text{ }30 \\ y\text{ }=\text{ }Rs\text{ }30\text{ }x\text{ }1040\text{ }=\text{ }Rs\text{ }31,200 \\ \end{array}$

Hence, absolute cash put resources into both firm

$=\text{ }Rs\text{ }31,200\text{ }x\text{ }2$

$=\text{ }Rs\text{ }62,400$

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