Question

Amit and richa invest rs 12000 each in buying shares of two companies . amit buys 15% rs 100 shares at a discount of rs 20, while richa buys rs 25 shares at a premium of 20%. if both receive equal dividend at the end of the year , find the rate % of the dividend declared by richa's company

Answer 1

Answer:

Market value of one share purchased by Amit

=₹100-₹20=₹80.

Investment by Amit=₹12000.

=>$number \: of \: shares \: purchased \: by \: </em></strong><strong><em>A</em></strong><strong><em>mit = \frac{</em></strong><strong><em>12000}{</em></strong><strong><em>80} = 150.$

$</em></strong><strong><em>A</em></strong><strong><em>nnual \: dividend \: recieved \: by \: </em></strong><strong><em>A</em></strong><strong><em>mit = \\ number \: of \: shares \: held \: by \: </em></strong><strong><em>A</em></strong><strong><em>mit \times rate \: of \: dividend \times face \: value \: of \: one \: share \: held \: by \: </em></strong><strong><em>A</em></strong><strong><em>mit.$

$= 150 \times \frac{15}{100} \times </em></strong><strong><em>100</em></strong><strong><em> = </em></strong><strong><em>2250$

=>$</em></strong><strong><em>A</em></strong><strong><em>nnual \: dividend \: recived \: by \: </em></strong><strong><em>Ri</em></strong><strong><em>cha = </em></strong><strong><em>2250$

$(</em></strong><strong><em>B</em></strong><strong><em>oth \: </em></strong><strong><em>A</em></strong><strong><em>mit \: and \: </em></strong><strong><em>R</em></strong><strong><em>icha \: get \: equal \: dividends)$

$</em></strong><strong><em>R</em></strong><strong><em>icha \: purchased \: </em></strong><strong><em>25 \: shares \: at \: premium \: of \: 20\%$

=>$</em></strong><strong><em>M</em></strong><strong><em>arket \: value \: of \: one \: share \: purchased \: by \: </em></strong><strong><em>R</em></strong><strong><em>icha = (1 + \frac{20}{100} ) \: of \: </em></strong><strong><em>2</em></strong><strong><em>5$

$= </em></strong><strong><em>(25 \times \frac{6}{5} ) = </em></strong><strong><em>30.$

$</em></strong><strong><em>I</em></strong><strong><em>nvestment \: by \: </em></strong><strong><em>R</em></strong><strong><em>icha = </em></strong><strong><em>12000.$

=>$</em></strong><strong><em>N</em></strong><strong><em>umber \: of \: shares \: purchased \: by \: </em></strong><strong><em>R</em></strong><strong><em>icha = \frac{</em></strong><strong><em>12000}{</em></strong><strong><em>30} = 400.$

$</em></strong><strong><em>L</em></strong><strong><em>et \: r\% \: be \: the \: rate \: of \: dividend \: declared \: by \: richa</em></strong><strong><em>'</em></strong><strong><em>s \: company \: then$

$annual \: dividend \: of \: </em></strong><strong><em>Ri</em></strong><strong><em>cha =$

$number \: of \: shares \: held \: by \: </em></strong><strong><em>R</em></strong><strong><em>icha \times rate \: of \: dividend \: of \: </em></strong><strong><em>R</em></strong><strong><em>icha</em></strong><strong><em>'</em></strong><strong><em>s \: company \times face \: value \: of \: one \: share \: held \: by \: </em></strong><strong><em>Ri</em></strong><strong><em>cha$

$=> </em></strong><strong><em>2250 = 400 \times \frac{r}{100} \times </em></strong><strong><em>25$

$=> 2250 = 100r$

$r = 22.5$

$</em></strong><strong><em>H</em></strong><strong><em>ence \: </em></strong><strong><em>,</em></strong><strong><em>the \: rate \: percent \: of \: the \: dividend \: declared \: by \: richas \: company = 22.5\%$.

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