Stocks & Shares

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

1. Rs. 3100
2. Rs. 6240
3. Rs. 6500
4. Rs. 9600

Answer:Option 1

Explanation:

Solution:

To obtain Rs. 10, investment = Rs. 96.
To obtain Rs. 650, investment =

\begin{aligned} R s . (\frac{96}{10} \times 650) \\ = R s . 6240 \end{aligned}

$\eqalign{ & Rs.\,\left( {\frac{{96}}{{10}} \times 650} \right) \cr & = Rs.\,6240 \cr}$

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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:

1. 12¹/₂%
2. 13¹/₂%
3. 15%
4. 16²/₃%

Answer:Option 1

Explanation:

Solution:

\begin{aligned} Investment \\ = R s . [20 \times (50 - 5)] \\ = R s . 900. \\ FaceValue \\ = R s . (50 \times 20) \\ = R s . 1000. \\ Dividend \\ = R s . (\frac{27}{2} \times \frac{1000}{100}) \\ = R s . 135. \\ Interest Obtained \\ = (\frac{135}{900} \times 100) % \\ = 15 % \end{aligned}

$\eqalign{ & {\text{Investment}} \cr & = Rs.\,\left[ {20 \times \left( {50 - 5} \right)} \right] \cr & = Rs.\,900. \cr & {\text{FaceValue}} \cr & = Rs.\,\left( {50 \times 20} \right) \cr & = Rs.\,1000. \cr & {\text{Dividend}} \cr & = Rs.\,\left( {\frac{{27}}{2} \times \frac{{1000}}{{100}}} \right) \cr & = Rs.\,135. \cr & {\text{Interest}}\,{\text{Obtained}} \cr & = \left( {\frac{{135}}{{900}} \times 100} \right)\% \cr & = 15\% \cr}$

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

1. 11% stock at 143
2. 9³/₄% stock at 117
3. Both are equally good
4. Cannot be compared, as the total amount of investment is not given.

Answer:Option 1

Explanation:

Solution:

\begin{aligned} Let investment in each case be \\ R s . (143 \times 117) . \\ Income in 1^{st} case \\ = R s . (\frac{11}{143} \times 143 \times 117) \\ = R s . 1287. \\ Income in 2^{nd} case \\ = R s . (\frac{39}{4 \times 117} \times 143 \times 117) \\ = R s . 1394.25 \\ Clearly, 9 \frac{3}{4} % stock at 117 is better . \end{aligned}

$\eqalign{ & {\text{Let}}\,{\text{investment}}\,{\text{in}}\,{\text{each}}\,{\text{case}}\,{\text{be}} \cr & Rs.\,\left( {143 \times 117} \right). \cr & {\text{Income}}\,{\text{in}}\,{{\text{1}}^{{\text{st}}}}\,{\text{case}} \cr & = Rs.\left( {\frac{{11}}{{143}} \times 143 \times 117} \right) \cr & = Rs.\,1287. \cr & {\text{Income}}\,{\text{in}}\,{{\text{2}}^{{\text{nd}}}}\,{\text{case}} \cr & = Rs.\,\left( {\frac{{39}}{{4 \times 117}} \times 143 \times 117} \right) \cr & = Rs.\,1394.25 \cr & {\text{Clearly,}}\,9\frac{3}{4}\% \,{\text{stock}}\,{\text{at}}\,117\,{\text{is}}\,{\text{better}}. \cr}$

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

1. Rs. 5640
2. Rs. 5760
3. Rs. 7500
4. Rs. 9600

Answer:Option 1

Explanation:

Solution:

To earn Rs. ⁵⁰/₃, investment = Rs. 64.
To earn Rs. 1500, investment =

\begin{aligned} R s . (64 \times \frac{3}{50} \times 1500) \\ = R s . 5760 \end{aligned}

$\eqalign{ & Rs.\,\left( {64 \times \frac{3}{{50}} \times 1500} \right) \cr & = Rs.\,5760 \cr}$

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

1. Rs. 48
2. Rs. 75
3. Rs. 96
4. Rs. 133.33

Answer:Option 1

Explanation:

Solution:

For an income of Rs. 8, investment = Rs. 100.
For an income of Rs. 6, investment =

\begin{aligned} R s . (\frac{100}{8} \times 6) \\ = R s . 75 \end{aligned}

$\eqalign{ & Rs.\,\left( {\frac{{100}}{8} \times 6} \right) \cr & = Rs.\,75 \cr}$ ∴ Market value of Rs. 100 stock = Rs. 75.

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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:

1. Rs. 207.40
2. Rs. 534.60
3. Rs. 648
4. Rs. 655.60

Answer:Option 1

Explanation:

Solution:

\begin{aligned} Number of shares \\ = (\frac{4455}{8.25}) \\ = 540. \\ Face value \\ = R s . (540 \times 10) \\ = R s . 5400. \\ Annual income \\ = R s . (\frac{12}{100} \times 5400) \\ = R s . 648. \end{aligned}

$\eqalign{ & {\text{Number}}\,{\text{of}}\,{\text{shares}} \cr & = \left( {\frac{{4455}}{{8.25}}} \right) \cr & = 540. \cr & {\text{Face}}\,{\text{value}} \cr & = Rs.\,\left( {540 \times 10} \right) \cr & = Rs.\,5400. \cr & {\text{Annual}}\,{\text{income}} \cr & = Rs.\,\left( {\frac{{12}}{{100}} \times 5400} \right) \cr & = Rs.\,648. \cr}$

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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:

1. Rs. 4800
2. Rs. 5000
3. Rs. 5400
4. Rs. 5600

Answer:Option 1

Explanation:

Solution:

\begin{aligned} Let the ivestment in 9 % stock be R s . x . \\ Then, investment in 10 % stock \\ = R s . (9800 - x) . \\ \frac{9}{75} \times x = \frac{10}{80} \times (9800 - x) \\ \Rightarrow \frac{3 x}{25} = \frac{9800 - x}{8} \\ \Rightarrow 24 x = 9800 \times 25 - 25 x \\ \Rightarrow 49 x = 9800 \times 25 \\ \Rightarrow x = 5000. \end{aligned}

$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{ivestment}}\,{\text{in}}\,9\% \,{\text{stock}}\,{\text{be}}\,Rs.\,x. \cr & {\text{Then,}}\,{\text{investment}}\,{\text{in}}\,10\% \,{\text{stock}} \cr & = Rs.\,\left( {9800 - x} \right). \cr & \frac{9}{{75}} \times \,x\, = \frac{{10}}{{80}}\, \times \,\left( {9800 - x} \right) \cr & \Rightarrow \frac{{3x}}{{25}} = \frac{{9800 - x}}{8} \cr & \Rightarrow 24x = 9800 \times 25 - 25x \cr & \Rightarrow 49x = 9800 \times 25 \cr & \Rightarrow x = 5000. \cr}$

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

1. Rs. 80
2. Rs. 96
3. Rs. 106
4. Rs. 108

Answer:Option 1

Explanation:

Solution:

\begin{aligned} To earn Rs . 135,investment = R s . 1620. \\ To earn Rs . 8, investment = \\ R s . (\frac{1620}{135} \times 8) = R s . 96. \\ ∴ Market value of Rs . 100 stock \\ = R s . 96. \end{aligned}

$\eqalign{ & {\text{To}}\,{\text{earn}}\,{\text{Rs}}{\text{.}}\,{\text{135,investment}} = Rs.\,1620. \cr & {\text{To}}\,{\text{earn}}\,{\text{Rs}}{\text{.}}\,{\text{8,}}\,{\text{investment}} = \cr & Rs.\,\left( {\frac{{1620}}{{135}} \times 8} \right) = Rs.\,96. \cr & \therefore {\text{Market}}\,{\text{value}}\,{\text{of}}\,{\text{Rs}}{\text{.}}\,{\text{100}}\,{\text{stock}} \cr & = Rs.\,96. \cr}$

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

1. 7.5%
2. 8%
3. 9.7%
4. None of these

Answer:Option 1

Explanation:

Solution:

\begin{aligned} By investing Rs . 1552, \\ income = R s . 128. \\ By investing R s . 97, \\ income = R s . (\frac{128}{1552} \times 97) \\ = R s . 8. \\ ∴ Dividend = 8 % \end{aligned}

$\eqalign{ & {\text{By}}\,{\text{investing}}\,{\text{Rs}}{\text{.}}\,{\text{1552,}} \cr & {\text{income}} = Rs.\,128. \cr & {\text{By}}\,{\text{investing}}\,Rs.\,97, \cr & {\text{income}} = Rs.\,\left( {\frac{{128}}{{1552}} \times 97} \right) \cr & = Rs.\,8. \cr & \therefore {\text{Dividend}} = 8\% \cr}$

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

1. Rs. 83.33
2. Rs. 110
3. Rs. 112
4. Rs. 120

Answer:Option 1

Explanation:

Solution:

\begin{aligned} To earn Rs . 10, money invested \\ = R s . 100. \\ To earn Rs . 12, money invested \\ = R s . (\frac{100}{10} \times 12) = R s . 120. \\ ∴ Market value of R s . 100 stockas = R s . 120 \end{aligned}

$\eqalign{ & {\text{To}}\,{\text{earn}}\,{\text{Rs}}{\text{.}}\,{\text{10,}}\,{\text{money}}\,{\text{invested}} \cr & = Rs.\,100. \cr & {\text{To}}\,{\text{earn}}\,{\text{Rs}}{\text{.}}\,{\text{12,}}\,{\text{money}}\,{\text{invested}} \cr & = Rs.\,\left( {\frac{{100}}{{10}} \times 12} \right) = Rs.\,120. \cr & \therefore {\text{Market}}\,{\text{value}}\,{\text{of}}\,Rs.\,100\,{\text{stockas}} = Rs.\,120 \cr}$

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