Question

Mr. Shameem invested $33\frac{1}{3}\%$ of his savings in e 20% Rs. 50 shares quoted at Rs. 60 and the remainder of the savings in 10% Rs.100 shares quoted at Rs. 110. If his total income from these investments is Rs. 9,200; find his total savings

• A. 79,200
• B. 78,200
• C. 77,200
• D. 76,200

Answer 1

The correct option is A 79,200

Let the total savings be $Rs.x$

Let the $2$ parts of total savings be $\mathrm{Rs}.\left(\frac{x}{3}\right)$ and $Rs.\left(\frac{2x}{3}\right)$.

FOR FIRST PART :

Sum invested $=Rs.\left(\frac{x}{3}\right)$

Nominal value of 1 share $=Rs.50$

Market value of 1 share $=Rs.60$

Number of shares bought $=\frac{\text{sum invested}}{\text{Market value of}1\text{share}}=\frac{\frac{x}{3}}{60}=\frac{x}{180}$

Rate of dividend $=20\%$

Dividend on $1$ share $=20\%$ of $Rs.50=Rs.10$

Dividend on $\frac{x}{180}$ shares $=\mathrm{Rs}[10\times \frac{x}{180}]=\mathrm{Rs}\left(\frac{x}{18}\right)$

FOR SECOND PART :

Sum invested $=Rs.\left(\frac{2x}{3}\right)$

Nominal value of $1$ share $=Rs.100$

Market value of $1$ share $=Rs.110$.

Number of shares bought $=\frac{\text{sum invested}}{\text{Market value of}1\text{share}}=\frac{\frac{2x}{3}}{110}=\frac{x}{165}$

Rate of dividend $=10\%$

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

Dividend on $\frac{x}{165}$ shares $=\mathrm{Rs}[10\times \frac{x}{165}]=\mathrm{Rs}\left(\frac{2x}{33}\right)$

Total dividend $=Rs.9200$

$\Rightarrow \frac{x}{18}+\frac{2x}{33}=9200$

$\Rightarrow \frac{11x+12x}{198}=9200$

$\Rightarrow \frac{23x}{198}=9200$

$\Rightarrow x=79200$

So, total savings $=Rs.79200$

Hence $\text{A}$ is the correct option.