[3 marks sum]

Question 13 Marks

Salman buys 50 shares of face value Rs 100 available at Rs 132.
(i) What is his investment?
(ii) If the dividend is 7.5% p.a., what will be his annual income?
(iii) If he wants to increase his annual income by Rs 150, how many extra shares should he

Answer

Face Value $=$ Rs 100
(i) Market Value $=$ Rs 132
No. of shares $=50$
Investment
$=$ no. of shares $x$ Market value
$=50 \times 132$
$=$ Rs 6600
(ii) Income per share
$=7.5 \%$ of Face value
$=\frac{75}{10 \times 100}$
$=\text { ₹ }7.5$
$\therefore$ Annual income
$=7.5 \times 50$
$=\text { ₹ } 375$
(iii) New anuual income
$
\begin{aligned}
& =375+150 \\
& =\text { ₹ } 525
\end{aligned}
$
$\therefore$ No of shares
$
=\frac{525}{7.5}
$
$
=70
$
$\therefore$ No. of extra share to be increased
$
\begin{aligned}
& =70-50 \\
& =20 .
\end{aligned}
$

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Question 23 Marks

A man invests Rs. 6750, partly in shares of 6% at Rs. 140 and partly in shares of 5% at Rs. 125. If his total income is Rs. 280, how much has he invested in each?

Answer

Let the investment in first case $=x$
Then investment in second case $=(6750-x)$
In first case, the dividend
$
=x \times \frac{6}{140}=\text { Rs. } \frac{3}{70} x
$
and dividend in second case
$
\begin{aligned}
& =(6750-x) \times \frac{5}{125}=\text { RS. } \frac{750-x}{25} \\
& \therefore \text { Total divided }=\frac{3}{70} x+\frac{6750-x}{25} \\
& \therefore \frac{3}{70} x+\frac{6750-x}{25}=280 \\
& \Rightarrow 15 x+14(6750-x)=280 \times 350 \ldots(\text { L.C.M. }=350) \\
& \Rightarrow 15 x+14 \times 6750-14 x=280 \times 350 \\
& \Rightarrow x=280 \times 350-14 \times 6750 \\
& =98000-94500=\text { Rs. } 3500
\end{aligned}
$
$\therefore$ Investment in first case $=$ Rs. 3500
and investment in second case
$
\begin{aligned}
& =6750-3500 \\
& =\text { Rs. } 3250 .
\end{aligned}
$

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Question 33 Marks

By selling at Rs. 77 , some $2 \frac{1}{4} \%$ shares of face value Rs. 100 , and investing the proceeds in $6 \%$ shares of face value Rs. 100, selling at 110, a person increased his income by Rs, 117 per annum. How many shares did he sell?

Answer

Let the number of shares $=x$
On selling at Rs.77, the amt received $x \times 77=$ Rs. $77 x$
and dividend received $=77 x \times \frac{9}{4 \times 77}=\frac{9}{4} x$
Again investing Rs. $77 x$ for the purchase of shares of market value Rs. 110
$=\frac{77 x}{110}$ shares
Dividend $=\frac{77 x}{110} \times 6=\frac{42}{10} x$
Difference in income
$
\begin{aligned}
& =\frac{42}{10} x-\frac{9}{4} x \\
& =\frac{84 x-45 x}{20} \\
& =\frac{39}{20} x \\
& \therefore \frac{39}{20} x=117 \\
& \Rightarrow x=\frac{117 \times 20}{39}=60
\end{aligned}
$
Hence No. of shares sold $=60$.

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Question 43 Marks

A man sold some Rs. 100 shares paying 10% dividend at a discount of 25% and invested the proceeds in Rs. 100 shares paying 16% dividend quoted at Rs. 80 and thus increased his income by Rs. 2000. Find the number of shares sold by him.

Answer

Face value of each share $=$ Rs. 100
Market value of each share
$
\begin{aligned}
& =\text { Rs. } 100-\text { Rs. } 25 \\
& =\text { Rs. } 75
\end{aligned}
$Rate of dividend $=10 \%$
Let no. of shares $=x$
Selling price $=x \times 75=$ Rs. $75 x$
Face value of $x$ share $=100 x$
Dividend annually $=100 x \times \frac{10}{100}=10 x$
No. of shares purchased $=\frac{75 x}{80}=\frac{15 x}{16}$
Face value of $\frac{15 x}{16}$ shares $=\frac{15}{16} \times 100=\frac{1500}{16} x$
Dividend $=\frac{1500}{16} x \times \frac{16}{100}=15 x$
$\therefore$ Increase in income $=15 x -10 x =5 x$
Now $5 x =2000$
$
\therefore x=\frac{2000}{5}=400
$
$\therefore$ No. of shares purchased $=400$.

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Question 53 Marks

A person invests Rs. 4368 and buys certain hundred-rupee shares at 91. He sells out shares worth Rs. 2400 when they have t risen to 95 and the remainder when they have fallen to 85. Find the gain or loss on the total transaction,

Answer

$
\begin{aligned}
& \text { Investment }=\text { Rs. } 4368 \\
& \text { Market value of each share }=\text { Rs. } 91 \\
& \text { Face value of each share }=\text { Rs. } 100 \\
& \therefore \text { No. of shares }=\frac{4368}{91}=48 \\
& \text { Face value of } 24 \text { shares } \\
& =24 \times 100 \\
& =\text { Rs. } 2400
\end{aligned}
$
Sale price of share worth Rs. 2400
$
=\frac{2400 \times 95}{100}=\text { Rs. } 2280
$
Face value of remaining shares
$
\begin{aligned}
& =24 \times 100 \\
& =\text { Rs. } 2400
\end{aligned}
$
Sale price of shares of remaining amount
$
=\frac{2400 \times 85}{100}=\text { Rs. } 2040
$
Total amount received
$
\begin{aligned}
& =\text { Rs. } 2280+\text { Rs. } 2040=\text { Rs. } 4320 \\
& \therefore \text { Loss } \\
& =\text { Rs. } 4368-\text { Rs. } 4320 \\
& =\text { Rs. } 48 .
\end{aligned}
$

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Question 63 Marks

A man invests Rs -10080 in 6% hundred- rupee shares at Rs. 112. Find his annual income. When the shares fall to Rs. 96 he sells out the shares and invests the proceeds in 10% ten-rupee shares at Rs. 8. Find the change in his annual income.

Answer

Investment = Rs. 10080
Face value of each share $=$ Rs. 100
Market value of each share $=$ Rs. 112
Rate of dividend $=6 \%$
Total income for the year
$
=\frac{10080 \times 6}{112}=\text { Rs. } 540
$
No. of shares $=\frac{10080}{112}=90$
Selling price of 90 shares at the rate of Rs. 96 each $=90 \times 96=$ Rs. 8640
Rate of dividend in new shares $=10 \%$
Face value of each share $=$ Rs. 10
and market value of each share $=$ Rs. 8
No of shares $=\frac{8640}{8}=1080$
Face value of 1080 shares
$
=1080 \times 10
$
= Rs. 10800
$\therefore$ Dividend $=$ Rs. $\frac{1080010}{100}=$ Rs. 1080
Dlfference in income = Rs. 1080 - Rs. 540 $=$ Rs. 540 more.

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Question 73 Marks

A man buys 400 ten-rupee shares at a premium of Rs. 2.50 on each share. If the rate of dividend is 8%, Find,
(i) his investment
(ii) dividend received
(iii) yield.

Answer

No. of shares $=400$
Face value of each share $=$ Rs. 10
Market value of each share
$
\begin{aligned}
& =\text { Rs. } 10+\text { Rs. } 2.50 \\
& =\text { Rs. } 12.50
\end{aligned}
$
Rate of dividend $=8 \%$
$\therefore$ Face value of 400 shares
$
=\text { Rs. } 10 \times 400
$
$
=\text { Rs. } 4000
$
(i) Total investment
$
\begin{aligned}
& =\text { Rs. } 12.50 \times 400 \\
& =\text { Rs. } 5000
\end{aligned}
$
(ii) Total dividend
$
\begin{aligned}
& =\text { Rs. } 4000 \times \frac{8}{100} \\
& =\text { Rs. } 320
\end{aligned}
$
(iii) Yield percent
$
\begin{aligned}
& =\frac{320 \times 100}{5000} \\
& =\frac{32}{5} \\
& =6.4 \%
\end{aligned}
$

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Question 83 Marks

A man invests Rs. 8000 in a company paying 8% dividend when a share of face value of Rs. 100 is selling at Rs. 60 premium,
(i) What is his annual income,
(ii) What percent does he get on his money?

Answer

Amount invested by the man in a company = Rs. 8000
Face value $=$ Rs. 100 and Selling Price $=$ Rs. 60
$\Rightarrow$ Market value $=100+60=$ Rs. 160
So, No. of shares $=\frac{\text { investment }}{\text { market value }}$
$
=\frac{8000}{160}
$
$
=50
$
(i) Therefore, Income $=$ (dividend $\times$ face value $\times$ No of shares)
$
\begin{aligned}
& =0.08 \times 100 \times 50 \\
& =\text { Rs. } 400
\end{aligned}
$
Hence, Annual Income = Rs. 400
Rate of dividend $=8 \%$ p.a.
(ii) Rate of interest on his money
$
\begin{aligned}
& =\frac{400 \times 100}{8000} \\
& =5 \% .
\end{aligned}
$

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Question 93 Marks

A company with 4000 shares of nominal value of Rs.110 declares annual dividend of 15%. Calculate :
(i) the total amount of dividend paid by the company,
(ii) the annual income of Shah Rukh who holds 88 shares in the company,
(iii) if he received only 10% on his investment, find the price Shah Rukh paid for each share.

Answer

Number of shares $=4000$
Nominal (face) value of each share $=$ Rs. 110
Total face value of 4000 shares
$
\begin{aligned}
& =\text { Rs. } 110 \times 4000 \\
& =\text { Rs, } 440000
\end{aligned}
$
Rate of annual dividend $=15 \%$
(i) Annual of dividend
$
\begin{aligned}
& =\frac{440000 \times 15}{100} \\
& =\text { Rs. } 66000
\end{aligned}
$
(ii) Number of shares, Shah Rukh has $=88$
$\therefore$ Face value of 88 shares
$
=88 \times 110
$
$
=\text { Rs. } 9680
$
and annual dividend
$
\begin{aligned}
& =\text { Rs. } \frac{9680 \times 15}{100} \\
& =\text { Rs. } 1452
\end{aligned}
$
(iii) Rate of annual incomes on his investment $=10 \%$
$\therefore$ His investment
$
\begin{aligned}
& =\frac{1452 \times 100}{10} \\
& =\text { Rs. } 14520
\end{aligned}
$
and market value of each share
$
\begin{aligned}
& =\frac{14520}{88} \\
& =\text { Rs. } 165 .
\end{aligned}
$

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Question 103 Marks

A company with 10000 shares of nominal value of Rs.100 declares an annual dividend of 8% to the share holders.
(i) Calculate the total amount of dividend paid by the company.
(ii) Ramesh bought 90 shares of the company at Rs. 150 per share.
Calculate the dividend he received and the percentage return on his investment.

Answer

$\begin{aligned} & \text { (i) Number of shares }=10000 \\ & \text { Nominal value of each share }=\text { Rs. } 100 \\ & \text { Rate of annual dividend }=8 \% \\ & \text { Total face value of } 10000 \text { shares } \\ & =\text { Rs. } 100 \times 10000 \\ & =\text { Rs. } 1000000 \\ & \text { and amount dividend } \\ & =\text { Rs. } \frac{1000000 \times 8}{100} \\ & =\text { Rs. } 80000 \\ & \text { (ii) Number of shares }=90 \\ & \text { Face value of each share }=\text { Rs. } 150 \\ & \text { Total face value of } 90 \text { shades } \\ & =100 \times 90 \\ & =\text { Rs. } 9000 \\ & \therefore \text { Amount of dividend } \\ & =\text { Rs. } \frac{9000 \times 8}{100} \\ & =\text { Rs. } 720 \\ & \text { Market value of } 90 \text { shares } \\ & =90 \times 150 \\ & =\text { Rs. } 13500 \\ & \therefore \text { Rate of interest } \\ & =\frac{720 \times 100}{13500 \times 1} \\ & =\frac{16}{3} \\ & =5 \frac{1}{3} \% .\end{aligned}$

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Question 113 Marks

A man invested Rs. 45000 in 15% Rs. 100 shares quoted at Rs. 125. When the market value of these shares rose to Rs. 140, he sold some shares, just enough to raise Rs. 8400. Calculate :
(i) the number of shares he still holds.
(ii) the dividend due to him on these shares.

Answer

$\begin{aligned} & \text { Investment on shares }=\text { Rs. } 45000 \\ & \text { Face value of each share }=\text { Rs. } 125 \\ & \therefore \text { Total number of shares } \\ & =\frac{45000}{125} \\ & =360 \text { shares } \\ & \text { Income from sold shares }=\text { Rs. } 8400 \\ & \text { No. of shares sold } \\ & =\frac{\text { Income from shares }}{\text { Market value of each share }} \\ & =\frac{8400}{140} \\ & =60 \\ & \therefore 60 \text { shares were sold. } \\ & \text { (i) No. of shares he still hold } \\ & =\text { Total number of shares }- \text { sold shares } \\ & =360-60 \\ & =300 \text { shares. } \\ & \therefore \text { Number of shares he still holds }=300 \\ & \text { (ii) Market value of } 300 \text { shares } \\ & =\text { Rs. } 300 \times 140 \\ & =\text { Rs. } 42000 \\ & \text { Face value of } 300 \text { shares } \\ & =\text { Rs. } 300 \times 125 \\ & =\text { Rs. } 37500 \\ & \text { Difference } \\ & =\text { Market value }- \text { Face value } \\ & =\text { Rs. } 42000-\text { Rs. } 37500 \\ & =\text { Rs. } 4500 .\end{aligned}$

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Mathematics [3 marks sum]

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