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Stocks & Shares
1.In order to obtain an income of Rs. 650 from 10% stock at Rs. 96, one must make an investment of:

Explanation:

Solution:
To obtain Rs. 10, investment = Rs. 96.
To obtain Rs. 650, investment =
$\begin{array}{rl}& Rs.\phantom{\rule{thinmathspace}{0ex}}\left(\frac{96}{10}×650\right)\\ & =Rs.\phantom{\rule{thinmathspace}{0ex}}6240\end{array}$

2.A man bought 20 shares of Rs. 50 at 5 discount, the rate of dividend being 131/2. The rate of interest obtained is:

Explanation:

Solution:
$\begin{array}{rl}& \text{Investment}\\ & =Rs.\phantom{\rule{thinmathspace}{0ex}}\left[20×\left(50-5\right)\right]\\ & =Rs.\phantom{\rule{thinmathspace}{0ex}}900.\\ & \text{FaceValue}\\ & =Rs.\phantom{\rule{thinmathspace}{0ex}}\left(50×20\right)\\ & =Rs.\phantom{\rule{thinmathspace}{0ex}}1000.\\ & \text{Dividend}\\ & =Rs.\phantom{\rule{thinmathspace}{0ex}}\left(\frac{27}{2}×\frac{1000}{100}\right)\\ & =Rs.\phantom{\rule{thinmathspace}{0ex}}135.\\ & \text{Interest}\phantom{\rule{thinmathspace}{0ex}}\text{Obtained}\\ & =\left(\frac{135}{900}×100\right)\mathrm{%}\\ & =15\mathrm{%}\end{array}$

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

Explanation:

Solution:
$\begin{array}{rl}& \text{Let}\phantom{\rule{thinmathspace}{0ex}}\text{investment}\phantom{\rule{thinmathspace}{0ex}}\text{in}\phantom{\rule{thinmathspace}{0ex}}\text{each}\phantom{\rule{thinmathspace}{0ex}}\text{case}\phantom{\rule{thinmathspace}{0ex}}\text{be}\\ & Rs.\phantom{\rule{thinmathspace}{0ex}}\left(143×117\right).\\ & \text{Income}\phantom{\rule{thinmathspace}{0ex}}\text{in}\phantom{\rule{thinmathspace}{0ex}}{\text{1}}^{\text{st}}\phantom{\rule{thinmathspace}{0ex}}\text{case}\\ & =Rs.\left(\frac{11}{143}×143×117\right)\\ & =Rs.\phantom{\rule{thinmathspace}{0ex}}1287.\\ & \text{Income}\phantom{\rule{thinmathspace}{0ex}}\text{in}\phantom{\rule{thinmathspace}{0ex}}{\text{2}}^{\text{nd}}\phantom{\rule{thinmathspace}{0ex}}\text{case}\\ & =Rs.\phantom{\rule{thinmathspace}{0ex}}\left(\frac{39}{4×117}×143×117\right)\\ & =Rs.\phantom{\rule{thinmathspace}{0ex}}1394.25\\ & \text{Clearly,}\phantom{\rule{thinmathspace}{0ex}}9\frac{3}{4}\mathrm{%}\phantom{\rule{thinmathspace}{0ex}}\text{stock}\phantom{\rule{thinmathspace}{0ex}}\text{at}\phantom{\rule{thinmathspace}{0ex}}117\phantom{\rule{thinmathspace}{0ex}}\text{is}\phantom{\rule{thinmathspace}{0ex}}\text{better}.\end{array}$

4.By investing in 162/3% stock at 64, one earns Rs. 1500. The investment made is:

Explanation:

Solution:
To earn Rs. 50/3, investment = Rs. 64.
To earn Rs. 1500, investment =
$\begin{array}{rl}& Rs.\phantom{\rule{thinmathspace}{0ex}}\left(64×\frac{3}{50}×1500\right)\\ & =Rs.\phantom{\rule{thinmathspace}{0ex}}5760\end{array}$

5.A 6% stock yields 8%. The market value of the stock is:

Explanation:

Solution:
For an income of Rs. 8, investment = Rs. 100.
For an income of Rs. 6, investment =
$\begin{array}{rl}& Rs.\phantom{\rule{thinmathspace}{0ex}}\left(\frac{100}{8}×6\right)\\ & =Rs.\phantom{\rule{thinmathspace}{0ex}}75\end{array}$
∴ Market value of Rs. 100 stock = Rs. 75.

6.A man invested Rs. 4455 in Rs. 10 shares quoted at Rs. 8.25. If the rate of dividend be 12%, his annual income is:

Explanation:

Solution:
$\begin{array}{rl}& \text{Number}\phantom{\rule{thinmathspace}{0ex}}\text{of}\phantom{\rule{thinmathspace}{0ex}}\text{shares}\\ & =\left(\frac{4455}{8.25}\right)\\ & =540.\\ & \text{Face}\phantom{\rule{thinmathspace}{0ex}}\text{value}\\ & =Rs.\phantom{\rule{thinmathspace}{0ex}}\left(540×10\right)\\ & =Rs.\phantom{\rule{thinmathspace}{0ex}}5400.\\ & \text{Annual}\phantom{\rule{thinmathspace}{0ex}}\text{income}\\ & =Rs.\phantom{\rule{thinmathspace}{0ex}}\left(\frac{12}{100}×5400\right)\\ & =Rs.\phantom{\rule{thinmathspace}{0ex}}648.\end{array}$

7.Rs. 9800 are invested partly in 9% stock at 75 and 10% stock at 80 to have equal amount of incomes. The investment in 9% stock is:

Explanation:

Solution:
$\begin{array}{rl}& \text{Let}\phantom{\rule{thinmathspace}{0ex}}\text{the}\phantom{\rule{thinmathspace}{0ex}}\text{ivestment}\phantom{\rule{thinmathspace}{0ex}}\text{in}\phantom{\rule{thinmathspace}{0ex}}9\mathrm{%}\phantom{\rule{thinmathspace}{0ex}}\text{stock}\phantom{\rule{thinmathspace}{0ex}}\text{be}\phantom{\rule{thinmathspace}{0ex}}Rs.\phantom{\rule{thinmathspace}{0ex}}x.\\ & \text{Then,}\phantom{\rule{thinmathspace}{0ex}}\text{investment}\phantom{\rule{thinmathspace}{0ex}}\text{in}\phantom{\rule{thinmathspace}{0ex}}10\mathrm{%}\phantom{\rule{thinmathspace}{0ex}}\text{stock}\\ & =Rs.\phantom{\rule{thinmathspace}{0ex}}\left(9800-x\right).\\ & \frac{9}{75}×\phantom{\rule{thinmathspace}{0ex}}x\phantom{\rule{thinmathspace}{0ex}}=\frac{10}{80}\phantom{\rule{thinmathspace}{0ex}}×\phantom{\rule{thinmathspace}{0ex}}\left(9800-x\right)\\ & ⇒\frac{3x}{25}=\frac{9800-x}{8}\\ & ⇒24x=9800×25-25x\\ & ⇒49x=9800×25\\ & ⇒x=5000.\end{array}$

8.By investing Rs. 1620 in 8% stock, Michael earns Rs. 135. The stock is then quoted at:

Explanation:

Solution:
$\begin{array}{rl}& \text{To}\phantom{\rule{thinmathspace}{0ex}}\text{earn}\phantom{\rule{thinmathspace}{0ex}}\text{Rs}\text{.}\phantom{\rule{thinmathspace}{0ex}}\text{135,investment}=Rs.\phantom{\rule{thinmathspace}{0ex}}1620.\\ & \text{To}\phantom{\rule{thinmathspace}{0ex}}\text{earn}\phantom{\rule{thinmathspace}{0ex}}\text{Rs}\text{.}\phantom{\rule{thinmathspace}{0ex}}\text{8,}\phantom{\rule{thinmathspace}{0ex}}\text{investment}=\\ & Rs.\phantom{\rule{thinmathspace}{0ex}}\left(\frac{1620}{135}×8\right)=Rs.\phantom{\rule{thinmathspace}{0ex}}96.\\ & \therefore \text{Market}\phantom{\rule{thinmathspace}{0ex}}\text{value}\phantom{\rule{thinmathspace}{0ex}}\text{of}\phantom{\rule{thinmathspace}{0ex}}\text{Rs}\text{.}\phantom{\rule{thinmathspace}{0ex}}\text{100}\phantom{\rule{thinmathspace}{0ex}}\text{stock}\\ & =Rs.\phantom{\rule{thinmathspace}{0ex}}96.\end{array}$

9.A man invested Rs. 1552 in a stock at 97 to obtain an income of Rs. 128. The dividend from the stock is:

Explanation:

Solution:
$\begin{array}{rl}& \text{By}\phantom{\rule{thinmathspace}{0ex}}\text{investing}\phantom{\rule{thinmathspace}{0ex}}\text{Rs}\text{.}\phantom{\rule{thinmathspace}{0ex}}\text{1552,}\\ & \text{income}=Rs.\phantom{\rule{thinmathspace}{0ex}}128.\\ & \text{By}\phantom{\rule{thinmathspace}{0ex}}\text{investing}\phantom{\rule{thinmathspace}{0ex}}Rs.\phantom{\rule{thinmathspace}{0ex}}97,\\ & \text{income}=Rs.\phantom{\rule{thinmathspace}{0ex}}\left(\frac{128}{1552}×97\right)\\ & =Rs.\phantom{\rule{thinmathspace}{0ex}}8.\\ & \therefore \text{Dividend}=8\mathrm{%}\end{array}$

10.A 12% stock yielding 10% is quoted at:

$\begin{array}{rl}& \text{To}\phantom{\rule{thinmathspace}{0ex}}\text{earn}\phantom{\rule{thinmathspace}{0ex}}\text{Rs}\text{.}\phantom{\rule{thinmathspace}{0ex}}\text{10,}\phantom{\rule{thinmathspace}{0ex}}\text{money}\phantom{\rule{thinmathspace}{0ex}}\text{invested}\\ & =Rs.\phantom{\rule{thinmathspace}{0ex}}100.\\ & \text{To}\phantom{\rule{thinmathspace}{0ex}}\text{earn}\phantom{\rule{thinmathspace}{0ex}}\text{Rs}\text{.}\phantom{\rule{thinmathspace}{0ex}}\text{12,}\phantom{\rule{thinmathspace}{0ex}}\text{money}\phantom{\rule{thinmathspace}{0ex}}\text{invested}\\ & =Rs.\phantom{\rule{thinmathspace}{0ex}}\left(\frac{100}{10}×12\right)=Rs.\phantom{\rule{thinmathspace}{0ex}}120.\\ & \therefore \text{Market}\phantom{\rule{thinmathspace}{0ex}}\text{value}\phantom{\rule{thinmathspace}{0ex}}\text{of}\phantom{\rule{thinmathspace}{0ex}}Rs.\phantom{\rule{thinmathspace}{0ex}}100\phantom{\rule{thinmathspace}{0ex}}\text{stockas}=Rs.\phantom{\rule{thinmathspace}{0ex}}120\end{array}$