Question

Mr.Suman Bhndari invested $1/3^{rd}$ of his savings in $20\%$ Rs.50 shares quoted at Rs.60 and the remained of his savings in $10\%$ Rs.100 shares quoted at Rs.110, if his total income from these investment is Rs.4600.
Find:
i) total savings,
ii) no. of Rs.50 shares,
iii) no of Rs.100 shares

Answer 1

$CaseI:$

Let Mr. Suman total saving is $Rs.y$

$\Rightarrow$ His saving $=\frac{1}{3}\times y=Rs.\frac{y}{3}$

$\Rightarrow$ Market price of $1$ share $=Rs.60$

$\Rightarrow$ Then, shares purchased $=\frac{y}{3\times 60}=Rs.\frac{y}{180}$

$\Rightarrow$ Dividend on $1$ share $=20\%$ of $Rs.50=\frac{20}{100}\times Rs.50=Rs.10$

$\Rightarrow$ Total dividend $=\frac{y}{180}\times 10=Rs.\frac{y}{18}$

$CaseII:$

$\Rightarrow$ His savings $=\frac{2}{3}\times y=Rs.\frac{2y}{3}$

$\Rightarrow$ Market price of $1$ share $=Rs.110$

$\Rightarrow$ Then, shares purchased $=\frac{2y}{3\times 110}=\frac{y}{165}$

$\Rightarrow$ Dividend on $1$ share $=10\%$ of $Rs.100=Rs.10$

$\Rightarrow$ Total dividend $=\frac{y}{165}\times 10=Rs.\frac{2y}{33}$

$\Rightarrow$ Total income $=Rs.4600$

According to question,

$\Rightarrow$ $\frac{y}{18}+\frac{2y}{33}=Rs.4600$

$\Rightarrow$ $\frac{23}{198}y=Rs.4600$

$\Rightarrow$ $y=Rs.\frac{4600\times 198}{23}$

$\Rightarrow$ $y=Rs.39600$

$\Rightarrow$ The number of $Rs.50$ share $=\frac{39600}{180}=220$

$\Rightarrow$ The number of $Rs.100$ share $=\frac{39600}{165}=240$