Market Value of a share = Rs.9.50
Investment = Rs.4940
Number of shares =$\dfrac {4940}{9.50}$ = 520
Face Value of a share = Rs.10
Dividend = 14%
Dividend per share = $\dfrac{(10 \times 14)}{100}$ = Rs. 1.4
His annual income = 520 × 1.4 = Rs.728
Total number of preferred shares = 1200
Face value = Rs.50
dividend paid on preferred shares is 10%
Dividend per share = $\dfrac{50 \times 10}{100}$ = Rs.5
Total Dividend = 1200 × 5 = 6000
Total number of common shares = 3000
Face value = Rs.50
Semi-annual dividend of 3$\dfrac{1}{2}$% is declared on common shares.
semi-annual dividend per share = $\dfrac{50 \times 7}{2 \times 100}= Rs.\dfrac{7}{4}$
Total semi-annual dividend = $\dfrac{7}{4} \times 3000$= Rs.5250
annual dividend = Rs.5250 × 2 = Rs.10500
Total dividend on all all shares preferred and common = 6000 + 10500 = Rs.16500
Assuming that face value of the first stock = Rs.100 as it is not given in the question
Since it is a 5% stock, we can take the dividend per stock = Rs.5
Market Value of the first stock = Rs.104
Investment on the first stock = Rs.26000
Number of stocks purchases = $\dfrac{26000}{400}$ = 250
His total income from all these stocks = Rs.250 × 5 = Rs.1250
He sells each of this stock at Rs.120
ie, amount he earns = Rs.120 × 250 = Rs.30000
He invest this Rs.30000 in 6% stock [here also face value is not given and hence take it as Rs.100]
His new income = Rs.[1250 + 2500] = Rs.3750
ie, By Rs.30000 of investment , he earns an income of Rs.3750
To get an income of Rs.6, investment needed = $\dfrac{30000 \times 6}{3750} = Rs.48$%
This is the market value of the second stock=Rs 48
Face Value of a share = Rs.60
He bought each share at Rs.60 - Rs.5 = Rs.55
Number of shares = 40
Dividend = 12$\dfrac{1}{2}$% = $\dfrac{25}{2}$%
Dividend per share = $\dfrac{60 \times 25}{2 \times 100} $= Rs. 7.5%
Total dividend = $(40 \times 7.5)$
ie, He got a dividend of $(40 \times 7.5)$ for an investment of Rs.$(40 \times 55)$
Interest obtained = $\dfrac{40 \times 7.5 \times 100}{40 \times 55}$ = 13.64%
Assume that face value = Rs.100.
Dividend per share = Rs.9 [as it is a 9% stock]
By investing Rs. 1800, he earns Rs.120
Investment needed to earn Rs.9 = $\dfrac{1800 \times 9}{120} $= Rs.135%
ie, stock is then quoted [then market value] = Rs.135
Let investment in each case be Rs. $(143 \times 117)$.
| Income in 1st case = Rs.$ \left(\dfrac{11}{143} \times 143 \times 117\right) $= Rs. 1287. |
| Income in 2nd case = Rs.$ \left(\dfrac{39}{4 \times 117} \times 143 \times 117\right) $= Rs. 1394.25 |
| Clearly, 9$ \dfrac{3}{4} $% stock at 117 is better. |
For an income of Rs. 756, investment = Rs. 9000.
| For an income of Rs.$ \dfrac{21}{2} $, investment = Rs.$\dfrac{9000}{756} \times \dfrac{21}{2} $= Rs. 125. |
$\therefore$ For a Rs. 100 stock, investment = Rs. 125.
| Market value of Rs. 100 stock = Rs.$ \left(125 -\dfrac{1}{4} \right) $= Rs. 124.75 |
Let the investment in 9% stock be Rs. $ x $.
Then, investment in 10% stock = Rs. $\left(9800 - x\right)$.
| $ \dfrac{9}{75} \times x $ =$ \dfrac{10}{80} \times \left(9800 - x\right )$ |
| $\Rightarrow \dfrac{3x}{25} $=$ \dfrac{9800 - x}{8} $ |
$\Rightarrow$ 24$ x $ = 9800 x 25 - 25$ x $
$\Rightarrow$ 49$ x $ = 9800 x 25
$\Rightarrow x $ = 5000.
Face value of each share = Rs.20
Market value of each share = Rs.25
Number of shares = 12500
Amount required to purchase the shares = 12500 × 25 = 312500
Mohan further sells the shares at a premium of Rs. 11 each
ie, Mohan further sells the shares at Rs.(20+11) = Rs.31 per share
Total amount he gets by selling all the shares = 12500 × 31 = 387500
His gain = 387500 - 312500 = Rs.75000
Let investment in 12% stock be Rs. $ x $.
Then, investment in 15% stock = Rs.$\left (12000 - x\right)$.
| $\therefore \dfrac{12}{120} \times x $ +$ \dfrac{15}{125} \times \left(12000 - x \right)$ = 1360. |
| $\Rightarrow \dfrac{x}{10} $+$ \dfrac{3}{25} \left(12000 - x\right)$ = 1360. |
$\Rightarrow$ 5$ x $ + 72000 - 6$ x $ = 1360 x 50
$\Rightarrow x $ = 4000.