Stocks and Shares Questions in English

(B) The face value of the share is $Rs. 50$ and the dividend rate is $10\%$.
Dividend on each share $= \frac{10}{100} \times 50 = Rs. 5$.
Let the market price at which he bought the share be $Rs. x$.
The return on investment is given as $12.5\%$.
Therefore,the return on investment formula is: $\frac{\text{Dividend}}{\text{Market Price}} \times 100 = \text{Return percentage}$.
$\frac{5}{x} \times 100 = 12.5$.
$x = \frac{5 \times 100}{12.5} = \frac{500}{12.5} = Rs. 40$.
Thus,the man bought the shares at $Rs. 40$.

(B) The market value of one share is $Rs. 25$.
Brokerage is $2\%$ of the market value.
Brokerage per share $= 2\% \text{ of } 25 = \frac{2}{100} \times 25 = Rs. 0.50$.
Total cost price of one share including brokerage $= 25 + 0.50 = Rs. 25.50$.
Total amount available for investment $= Rs. 12750$.
Number of shares that can be purchased $= \frac{\text{Total Investment}}{\text{Cost price per share}} = \frac{12750}{25.50} = 500$ shares.

(C) The face value of the stock is $Rs. 100$.
Since the stock is at a $4$ discount,the market price is $Rs. (100 - 4) = Rs. 96$.
The brokerage is $\frac{1}{4}\%$ of the face value,which is $\frac{1}{4}\% \text{ of } 100 = Rs. 0.25$.
The cost price is the sum of the market price and the brokerage.
Cost price $= Rs. 96 + Rs. 0.25 = Rs. 96.25$.

(C) Cost price of $1$ share $= (100 - 4) = Rs. 96$.
Total investment for $20$ shares $= 20 \times 96 = Rs. 1920$.
Dividend is calculated on the face value of the share.
Dividend per share $= 12 \% \text{ of } 100 = Rs. 12$.
Total dividend for $20$ shares $= 20 \times 12 = Rs. 240$.
Rate of interest (return) $= \left( \frac{\text{Total Dividend}}{\text{Total Investment}} \right) \times 100$.
Rate of interest $= \left( \frac{240}{1920} \right) \times 100 = \frac{1}{8} \times 100 = 12.5 \%$.

(B) The face value of one share is $Rs. 100$.
Since the shares are at $20\%$ premium,the market price of one share is $100 + (20\% \text{ of } 100) = Rs. 120$.
Total number of shares purchased = $\frac{\text{Total Investment}}{\text{Market Price per share}} = \frac{14400}{120} = 120$ shares.
The company declares a $5\%$ dividend on the face value of the shares.
Dividend per share = $5\% \text{ of } 100 = Rs. 5$.
Total dividend received = $\text{Number of shares} \times \text{Dividend per share} = 120 \times 5 = Rs. 600$.

(B) Annual dividend on one share $= 10 \% \text{ of } Rs. 10 = Rs. (10 \times \frac{10}{100}) = Rs. 1$.
Annual dividend of Ram owning $1500$ shares $= (1500 \times 1) = Rs. 1500$.
Alternatively,we can calculate the total par value of $1500$ shares first and then find the dividend at $10 \%$ of it:
Total par value of $1500$ shares $= Rs. (1500 \times 10) = Rs. 15000$.
$\therefore$ Total annual dividend of Ram $= (15000 \times \frac{10}{100}) = Rs. 1500$.

(B) Annual dividend on one share $= 10 \%$ of $Rs. 100$.
$= Rs. \left(\frac{10}{100} \times 100\right) = Rs. 10$.
$\therefore$ Annual dividend on $4000$ shares $= Rs. (4000 \times 10) = Rs. 40000$.

(C) Number of shares purchased by Jatin = $\frac{27260}{116} = 235$.
Face value of $235$ shares = $235 \times 100 = Rs. 23500$.
Annual income from dividend = $16 \%$ of Face Value.
Annual income = $\frac{16}{100} \times 23500 = 16 \times 235 = Rs. 3760$.

(B) Number of shares $= 50000$
Par value of one share $= Rs. 10$
Total par value of $50000$ shares $= 50000 \times 10 = Rs. 500000$
Total dividend declared $= Rs. 62500$
Rate of dividend is calculated on the total par value (face value) of the shares.
Rate of dividend $= \left( \frac{\text{Total Dividend}}{\text{Total Par Value}} \times 100 \right) \%$
Rate of dividend $= \left( \frac{62500}{500000} \times 100 \right) \%$
Rate of dividend $= \frac{62500}{5000} \% = \frac{625}{50} \% = 12.5 \% = 12\frac{1}{2} \%$

(A) The semi-annual dividend is $7 \frac{1}{2} \% = 7.5 \%$.
Since the dividend is declared semi-annually,the annual dividend rate is $2 \times 7.5 \% = 15 \%$.
The par value of one share is $Rs. 10$.
Annual dividend on one share $= 15 \% \text{ of } Rs. 10 = \frac{15}{100} \times 10 = Rs. 1.50$.
Chetan owns $1250$ shares.
Therefore,the total annual dividend for Chetan $= 1250 \times 1.50 = Rs. 1875$.

(A) Number of shares $= 125000$
Par value of one share $= Rs. 20$
Total par value of all shares $= 125000 \times 20 = Rs. 2500000$
Total dividend declared $= Rs. 375000$
The rate of dividend is calculated on the total par value (face value) of the shares.
Rate of dividend $= \left( \frac{\text{Total Dividend}}{\text{Total Par Value}} \times 100 \right) \%$
Rate of dividend $= \left( \frac{375000}{2500000} \times 100 \right) \% = \left( \frac{3750}{25000} \times 100 \right) \% = \frac{375}{25} \% = 15 \%$

(B) Dividend on $50$ preferred shares $= 50 \times 100 \times \frac{10}{100} = Rs. 500$.
Dividend on $400$ common shares: Since the semiannual dividend is $7.5\%$,the annual dividend rate is $7.5\% \times 2 = 15\%$.
Dividend on $400$ common shares $= 400 \times 100 \times \frac{15}{100} = Rs. 6000$.
Total annual dividend received by Seema $= 500 + 6000 = Rs. 6500$.

(A) Dividend on $200$ preferred shares:
$= 10 \% \text{ of } Rs. (200 \times 100)$
$= Rs. \left( \frac{10}{100} \times 20000 \right) = Rs. 2000$
Dividend on $1000$ common shares:
$= 12 \frac{1}{2} \% \text{ of } Rs. (1000 \times 100)$
$= Rs. \left( \frac{25/2}{100} \times 100000 \right)$
$= Rs. \left( \frac{25}{2} \times 1000 \right) = Rs. 12500$
$\therefore$ Total dividend received:
$= Rs. (2000 + 12500) = Rs. 14500$

(B) Total dividend declared $= Rs. 125000$.
Amount kept in reserve fund $= Rs. 50000$.
Net amount paid as dividend to the shareholders $= Rs. (125000 - 50000) = Rs. 75000$.
Total par value of $50000$ shares $= 50000 \times 100 = Rs. 5000000$.
Rate of dividend paid by the company $= (\frac{75000}{5000000} \times 100) \% = \frac{75}{50} \% = \frac{3}{2} \% = 1 \frac{1}{2} \%$.

(B) Dividend on $1200$ preferred shares:
$= 10 \%$ of $Rs. (1200 \times 50)$
$= Rs. (\frac{10}{100} \times 60000) = Rs. 6000$
Dividend on $3000$ common shares:
Since the dividend is semi-annual at $3 \frac{1}{2} \%$,the annual dividend rate is $3 \frac{1}{2} \% \times 2 = 7 \%$.
$= 7 \%$ of $Rs. (3000 \times 50)$
$= Rs. (\frac{7}{100} \times 150000) = Rs. 10500$
Total dividend received by Nishita:
$= Rs. (6000 + 10500) = Rs. 16500$

(A) Market value of one share $= Rs.\, 25$.
$\therefore$ Total amount required to purchase $12500$ shares $= 12500 \times 25 = Rs.\, 312500$.
Mohan sells the shares at a premium of $Rs.\, 11$ over the par value of $Rs.\, 20$.
$\therefore$ Selling price per share $= 20 + 11 = Rs.\, 31$.
Total selling price for $12500$ shares $= 12500 \times 31 = Rs.\, 387500$.
Gain $= \text{Selling Price} - \text{Cost Price} = 387500 - 312500 = Rs.\, 75000$.

(A) The par value of $200$ shares is $200 \times 10 = Rs. 2000$.
The annual dividend is $8 \%$ of the par value.
Dividend received $= \frac{8}{100} \times 2000 = Rs. 160$.
Let the total market value of $200$ shares be $x$.
According to the problem,the return on investment is $10 \%$,so $10 \%$ of $x = 160$.
$\frac{10}{100} \times x = 160 \Rightarrow x = 1600$.
The total market value of $200$ shares is $Rs. 1600$.
Therefore,the market value of one share $= \frac{1600}{200} = Rs. 8$.

(B) The par value of $12000$ shares is $12000 \times 10 = Rs. 120000$.
The annual dividend received is $15\%$ of the par value:
Dividend $= \frac{15}{100} \times 120000 = Rs. 18000$.
Let the total market value of $12000$ shares be $x$.
Shyam gets a $10\%$ return on her investment,so:
$10\%$ of $x = 18000$.
$\frac{10}{100} \times x = 18000$
$x = 18000 \times 10 = 180000$.
Thus,the total market value of $12000$ shares is $Rs. 180000$.
The market value of one share $= \frac{180000}{12000} = Rs. 15$.

(C) Total profit of the company $= Rs. 180000$.
Amount kept in reserve fund $= Rs. 30000$.
Net amount available for distribution as dividend $= Rs. (180000 - 30000) = Rs. 150000$.
Dividend paid on $50000$ preferred shares at $20 \%$ of par value $(Rs. 10)$:
Dividend on preferred shares $= 50000 \times (20 \% \text{ of } 10) = 50000 \times 2 = Rs. 100000$.
Dividend available for common shareholders $= Rs. (150000 - 100000) = Rs. 50000$.
Dividend per common share $= \frac{50000}{20000} = Rs. 2.50$.
Dividend percentage on common share $= \left( \frac{2.50}{10} \times 100 \right) \% = 25 \%$.

(A) $1$. Calculate the dividend on preferred shares:
Dividend on preferred shares $= 12 \% \text{ of } (10000 \times 100) = \frac{12}{100} \times 1000000 = Rs. 120000$.
$2$. Calculate the dividend on common shares:
Dividend on common shares $= 17.6 \% \text{ of } (50000 \times 100) = \frac{17.6}{100} \times 5000000 = Rs. 880000$.
$3$. Calculate the total dividend paid:
Total dividend $= Rs. 120000 + Rs. 880000 = Rs. 1000000 = Rs. 10 \text{ Lakhs}$.
$4$. Calculate the amount kept in the reserve fund:
Reserve fund $=$ Total profit $-$ Total dividend paid
Reserve fund $= Rs. 15 \text{ Lakhs} - Rs. 10 \text{ Lakhs} = Rs. 5 \text{ Lakhs}$.

(B) The man sells $5000$ shares of Company $X$ at a market price of $Rs. 30$ per share.
Total sale proceeds $= 5000 \times 30 = Rs. 150000$.
He invests this entire amount of $Rs. 150000$ in shares of Company $Y$.
The market value of one share of Company $Y$ is $Rs. 40$.
Number of shares of Company $Y$ purchased $= \frac{\text{Total Investment}}{\text{Market Value per share of } Y} = \frac{150000}{40} = 3750$ shares.

(C) Par value of a share $= Rs. 10$.
Market value of a share $= Rs. (10 + 20\% \text{ of } 10) = Rs. (10 + 2) = Rs. 12$.
The amount paid by the buyer to purchase $2500$ shares $= 2500 \times 12 = Rs. 30000$.
Selling price per share $= Rs. 20$.
Gain per share $= Rs. (20 - 12) = Rs. 8$.
Total gain on selling $2500$ shares $= 2500 \times 8 = Rs. 20000$.

(A) The face value of the stock is $Rs.\, 60000$.
The dividend or income is calculated on the face value of the stock,regardless of the purchase price.
Given that the stock is $12\%$,it means the annual income on $Rs.\, 100$ face value is $Rs.\, 12$.
Therefore,the income on $Rs.\, 60000$ face value is calculated as:
$\text{Income} = \left( \frac{12}{100} \right) \times 60000$
$\text{Income} = 12 \times 600 = Rs.\, 7200$.
The purchase price of $Rs.\, 110$ is irrelevant for calculating the annual income,as income is always based on the face value.

(C) Face value of the stock $= Rs.\, 20000$.
Income on $Rs.\, 100$ stock $= Rs.\, 7 \frac{1}{2} = Rs.\, 7.50$.
Income on $Rs.\, 1$ stock $= Rs.\, \frac{7.50}{100} = Rs.\, 0.075$.
Income on $Rs.\, 20000$ stock $= Rs.\, 0.075 \times 20000 = Rs.\, 1500$.
Note: The purchase price of $Rs.\, 120$ is irrelevant for calculating the income,as income is always calculated on the face value of the stock.

(C) The total amount invested is $Rs. 81000$.
The market value of the stock is $Rs. 135$ per $Rs. 100$ face value.
The dividend rate is $9 \%$,which means an investment of $Rs. 100$ (face value) yields an income of $Rs. 9$.
First,calculate the total face value of the stock purchased:
$\text{Face Value} = \left( \frac{\text{Total Investment}}{\text{Market Value}} \right) \times 100 = \left( \frac{81000}{135} \right) \times 100 = 600 \times 100 = Rs. 60000$.
Now,calculate the income on this face value:
$\text{Income} = \left( \frac{9}{100} \right) \times 60000 = 9 \times 600 = Rs. 5400$.

(A) The market value of the investment is $Rs. 90000$.
The stock is available at $112 \frac{1}{2}$,which means for a face value of $Rs. 100$,the market price is $Rs. \frac{225}{2}$.
The number of shares (or stock) purchased = $\frac{\text{Total Investment}}{\text{Market Price of } Rs. 100 \text{ stock}} = \frac{90000}{225/2} = 90000 \times \frac{2}{225} = 800$.
The dividend (income) is calculated on the face value of the stock. The dividend rate is $7 \frac{1}{2} \% = \frac{15}{2} \%$.
Income = $\text{Face Value} \times \text{Dividend Rate} = (800 \times 100) \times \frac{15}{2 \times 100} = 80000 \times \frac{15}{200} = 400 \times 15 = Rs. 6000$.

(B) The face value of the stock is $Rs.\, 72000$.
The dividend rate is $9 \frac{1}{2} \% = \frac{19}{2} \%$.
The annual income is calculated on the face value of the stock.
Annual Income $= \text{Face Value} \times \text{Dividend Rate}$
Annual Income $= 72000 \times \frac{19}{2 \times 100}$
Annual Income $= 720 \times \frac{19}{2} = 360 \times 19 = 6840$.
Therefore,the annual income is $Rs.\, 6840$.

(B) The market value of $Rs. 100$ stock is the sum of the face value and the brokerage.
Market value of $Rs. 100$ stock $= Rs. (91 + 1) = Rs. 92$.
Total investment made by Mr. Lal is $Rs. 92000$.
The number of shares (stock) purchased $= \frac{92000}{92} = 1000$ units of $Rs. 100$ stock.
The annual dividend rate is $9\frac{1}{2}\% = 9.5\%$.
Annual income $= \text{Total face value} \times \text{Dividend rate}$.
Annual income $= (1000 \times 100) \times \frac{9.5}{100} = 100000 \times 0.095 = Rs. 9500$.

(D) The market value of $Rs. 100$ stock including brokerage is $Rs. (81 \frac{1}{2} + 1) = Rs. 82 \frac{1}{2} = Rs. \frac{165}{2}$.
The annual dividend (income) on $Rs. 100$ stock is $7 \frac{1}{2} = Rs. \frac{15}{2}$.
Total investment made by Raja is $Rs. 99000$.
The number of shares purchased is $\frac{99000}{165/2} = 99000 \times \frac{2}{165} = 1200$.
Since each share represents $Rs. 100$ face value,the total face value is $1200 \times 100 = Rs. 120000$.
The annual income is calculated on the face value: $\text{Income} = \frac{15}{2} \% \text{ of } 120000 = \frac{15}{200} \times 120000 = 15 \times 600 = Rs. 9000$.

(C) The market value of $Rs.\, 100$ stock is the sum of the quoted price and the brokerage.
Market value of $Rs.\, 100$ stock $= Rs.\, (112 + 2) = Rs.\, 114$.
The annual income on $Rs.\, 100$ stock is $9 \frac{1}{2} = \frac{19}{2} = Rs.\, 9.5$.
Therefore,the income on $Rs.\, 114$ investment is $Rs.\, 9.5$.
To find the income on an investment of $Rs.\, 88008$,we use the unitary method:
Income $= \frac{19}{2} \times \frac{1}{114} \times 88008$.
Income $= \frac{19}{228} \times 88008$.
Income $= \frac{1}{12} \times 88008 = Rs.\, 7334$.

(A) The market value of $Rs.\, 100$ stock is given as $Rs.\, 92$.
To find the investment required for $Rs.\, 125000$ stock,we use the proportion:
$\text{Investment} = \left(\frac{\text{Market Value}}{\text{Face Value}}\right) \times \text{Total Stock Value}$
$\text{Investment} = \left(\frac{92}{100} \times 125000\right)$
$\text{Investment} = 92 \times 1250 = Rs.\, 115000$
Therefore,an investment of $Rs.\, 115000$ is required to purchase $Rs.\, 125000$ of $8 \%$ stock at $92$.

(B) The market value of $Rs.\, 100$ stock is $Rs.\, 110$.
To find the investment required for $Rs.\, 90000$ of stock,we use the ratio:
$\text{Investment} = \left( \frac{\text{Market Value}}{\text{Face Value}} \right) \times \text{Face Value of Stock}$
$\text{Investment} = \left( \frac{110}{100} \times 90000 \right)$
$\text{Investment} = 110 \times 900 = Rs.\, 99000$
Therefore,an investment of $Rs.\, 99000$ is required.

(C) The face value of the stock is $Rs. 100$.
Brokerage is $1 \%$ of the market price of $Rs. 90$,which is $Rs. 0.90$.
Therefore,the total cost (investment) to purchase $Rs. 100$ stock is $Rs. 90 + Rs. 0.90 = Rs. 90.90$.
The annual income from $Rs. 100$ stock is $9 \frac{1}{2} \% = Rs. 9.50$.
For an income of $Rs. 9.50$,the investment required is $Rs. 90.90$.
For an income of $Rs. 1938$,the investment required is calculated as:
$\text{Investment} = \frac{90.90}{9.50} \times 1938 = \frac{90.90}{19/2} \times 1938 = \frac{90.90 \times 2}{19} \times 1938$.
$\text{Investment} = 90.90 \times 2 \times 102 = 181.80 \times 102 = Rs. 18543.60$.

(B) Investment made by the man in buying $Rs. 20000$ of $5\%$ stock at $90 = Rs. \left(\frac{90}{100} \times 20000\right) = Rs. 18000$.
When the price rose to $Rs. 93 \frac{3}{4} = Rs. \frac{375}{4}$,the man sold the stock. Thus,money realized from selling the stock is:
$= Rs. \left(\frac{375}{4} \times \frac{1}{100} \times 20000\right) = Rs. 18750$.
$\therefore$ Gain in the transaction $= Rs. (18750 - 18000) = Rs. 750$.
$\therefore$ Gain percent $= \left(\frac{750}{18000} \times 100\right) \% = \frac{75}{18} \% = 4 \frac{3}{18} \% = 4 \frac{1}{6} \%$.

(A) Investment made by Meena in buying $Rs. 36000$ of $7 \frac{1}{2} \%$ stock at $92 = Rs. \left(\frac{92}{100} \times 36000\right) = Rs. 33120$.
When the price rose to $Rs. 93 \frac{3}{4} = Rs. 93.75$,Meena sold the stock.
Money realized from selling the stock $= Rs. \left(\frac{93.75}{100} \times 36000\right) = Rs. 33750$.
Gain in the transaction $= Rs. (33750 - 33120) = Rs. 630$.
Gain percent $= \left(\frac{630}{33120} \times 100\right) \% \approx 1.902 \% \approx 1.9 \%$.

(A) Stock purchased by investing $Rs. 27600$ in $4 \%$ stock at $92$ is calculated as:
$= Rs. \left(\frac{27600 \times 100}{92}\right) = Rs. 30000$.
Money realized by selling $Rs. 20000$ stock at a market value of $Rs. 96$ is:
$= Rs. \left(\frac{20000 \times 96}{100}\right) = Rs. 19200$.
Remaining stock $= Rs. (30000 - 20000) = Rs. 10000$.
Money realized by selling the remaining $Rs. 10000$ stock at $Rs. 90$ is:
$= Rs. \left(10000 \times \frac{90}{100}\right) = Rs. 9000$.
Total money realized by selling the whole stock $= Rs. (19200 + 9000) = Rs. 28200$.
Money invested $= Rs. 27600$.
Gain $= Rs. (28200 - 27600) = Rs. 600$.

(B) Stock purchased by investing $Rs.\, 28500$ in $5\%$ stock at $95$ is calculated as:
$= Rs.\, \left(\frac{100}{95} \times 28500\right) = Rs.\, 30000$.
Money realized by selling $Rs.\, 15000$ stock at a market value of $Rs.\, 98$ is:
$= Rs.\, \left(\frac{98}{100} \times 15000\right) = Rs.\, 14700$.
Remaining stock $= Rs.\, (30000 - 15000) = Rs.\, 15000$.
Money realized by selling the remaining $Rs.\, 15000$ stock at $Rs.\, 90$ is:
$= Rs.\, \left(\frac{90}{100} \times 15000\right) = Rs.\, 13500$.
Total money realized $= Rs.\, (14700 + 13500) = Rs.\, 28200$.
Money invested $= Rs.\, 28500$.
Since the total money realized is less than the money invested,there is a loss.
Loss $= Rs.\, (28500 - 28200) = Rs.\, 300$.

(C) Income from the first stock $= Rs.\, \left(\frac{7}{98} \times 245000\right) = Rs.\, 17500$.
Next,we calculate the amount realized after selling the stock at $Rs.\, 100$.
Amount realized on selling $Rs.\, 98$ stock $= Rs.\, 100$.
Amount realized on selling $Rs.\, 245000$ stock $= Rs.\, \left(\frac{100}{98} \times 245000\right) = Rs.\, 250000$.
This amount is then invested in $9\%$ stock at $125$.
Income from the second stock $= Rs.\, \left(\frac{9}{125} \times 250000\right) = Rs.\, 18000$.
Therefore,the increase in income $= Rs.\, (18000 - 17500) = Rs.\, 500$.

(B) Initial investment $= Rs.\, 32400$ at $90$.
Face value of stock purchased $= (32400 / 90) \times 100 = Rs.\, 36000$.
Initial income $= (8 / 100) \times 36000 = Rs.\, 2880$.
Sale proceeds from $Rs.\, 18000$ stock at $95 = (95 / 100) \times 18000 = Rs.\, 17100$.
Sale proceeds from remaining $Rs.\, 18000$ stock at $98 = (98 / 100) \times 18000 = Rs.\, 17640$.
Total sale proceeds $= 17100 + 17640 = Rs.\, 34740$.
New investment $= Rs.\, 34740$ in $10 \%$ stock at $96.5$ (or $193/2$).
Face value of new stock $= (34740 / 96.5) \times 100 = 36000$.
New income $= (10 / 100) \times 36000 = Rs.\, 3600$.
Change in income $= 3600 - 2880 = Rs.\, 720$.

(A) $1$. Purchase price of the first stock (including brokerage) $= Rs. (99 + 3) = Rs. 102$.
$2$. Number of shares purchased $= \frac{50490}{102} = 495$.
$3$. Income from the first stock $= 5\% \text{ of } (495 \times 100) = \frac{5}{100} \times 49500 = Rs. 2475$.
$4$. Sale price of the first stock (after deducting brokerage) $= Rs. (102 - 3) = Rs. 99$.
$5$. Total amount received from the sale $= 495 \times 99 = Rs. 49005$.
$6$. Purchase price of the second stock (including brokerage) $= Rs. (96 + 3) = Rs. 99$.
$7$. Number of shares purchased in the second stock $= \frac{49005}{99} = 495$.
$8$. Income from the second stock $= 8\% \text{ of } (495 \times 100) = \frac{8}{100} \times 49500 = Rs. 3960$.
$9$. Change in income $= Rs. (3960 - 2475) = Rs. 1485$.

(C) Income on the first stock $= Rs. \left(\frac{5}{104} \times 260000\right) = Rs. 12500$.
Money realized by selling the stock when the price rose to $Rs. 125$:
$= Rs. \left(\frac{125}{104} \times 260000\right) = Rs. 312500$.
Income on the second stock is $Rs. 2500$ more than the first stock.
Therefore,income on the second stock $= Rs. (12500 + 2500) = Rs. 15000$.
Let $Rs. x$ be the market value of the second stock.
Therefore,$\frac{312500 \times 6}{x} = 15000$.
$x = \frac{312500 \times 6}{15000} = 125$.
Thus,the man purchased the second stock at $Rs. 125$.

(A) The face value of the debenture is $Rs.\, 100$.
Given that the debenture is $5 \%$,the annual income on the face value is $5 \%$ of $Rs.\, 100 = Rs.\, 5$.
The market value of the debenture is $Rs.\, 125$.
The income percent (or yield) is calculated as: $\text{Income Percent} = \left( \frac{\text{Annual Income}}{\text{Market Value}} \right) \times 100$.
Substituting the values: $\text{Income Percent} = \left( \frac{5}{125} \right) \times 100$.
$\text{Income Percent} = \frac{1}{25} \times 100 = 4 \%$.
Note: The provided options and original solution contained a calculation error regarding the face value. Based on standard financial definitions,the income percent is $4 \%$.

(B) The par value of the debenture is $Rs.\, 120$ and the interest rate is $10 \%$.
Therefore,the annual income on one debenture $= 10 \% \text{ of } Rs.\, 120 = \frac{10}{100} \times 120 = Rs.\, 12$.
However,the market value of the debenture is $Rs.\, 150$.
The income percent (or yield) is calculated on the market value of the investment.
$\text{Income percent} = \left( \frac{\text{Annual Income}}{\text{Market Value}} \right) \times 100$
$\text{Income percent} = \left( \frac{12}{150} \right) \times 100 = \frac{1200}{150} = 8 \%$.
Thus,the income percent on the debentures is $8 \%$.

(A) Annual dividend on $800$ shares $= Rs. \left(\frac{800 \times 50 \times 6}{100}\right) = Rs. 2400$.
Annual interest on $600$ debentures $= Rs. \left(\frac{600 \times 100 \times 12}{100}\right) = Rs. 7200$.
Total annual income of Brij $= Rs. (2400 + 7200) = Rs. 9600$.
Total investment of Brij $= Rs. (800 \times 50 + 600 \times 100) = Rs. (40000 + 60000) = Rs. 100000$.
Rate of return $= \left(\frac{9600}{100000} \times 100\right) \% = 9.6 \%$.

(C) Face value of $20$ shares $= Rs. (50 \times 20) = Rs. 1000$.
Market price of one share $= Rs. (50 - 5) = Rs. 45$.
Total investment $= Rs. (45 \times 20) = Rs. 900$.
Rate of dividend $= 4 \frac{3}{4} \% = \frac{19}{4} \%$.
Annual dividend $= \frac{19}{4} \% \text{ of } Rs. 1000 = \frac{19}{400} \times 1000 = Rs. 47.5$.
Rate of interest (return) $= \left( \frac{\text{Annual Dividend}}{\text{Total Investment}} \times 100 \right) \% = \left( \frac{47.5}{900} \times 100 \right) \% = \frac{47.5}{9} \% \approx 5.28 \%$.

(C) Let the investments of $A, B$,and $C$ be $4x, 6x$,and $5x$ respectively.
$A$ invested for $12$ months,while $B$ and $C$ invested for $12 - 4 = 8$ months.
The ratio of their profit shares is calculated as: (Investment $\times$ Time).
Profit ratio of $A: B: C = (4x \times 12) : (6x \times 8) : (5x \times 8)$.
$= 48x : 48x : 40x$.
Dividing by $8x$,the ratio becomes $6 : 6 : 5$.
Let the profit shares be $6k, 6k$,and $5k$.
Given that $A$'s share is $Rs. 250$ more than $C$'s share:
$6k - 5k = 250 \Rightarrow k = 250$.
Total annual profit $= 6k + 6k + 5k = 17k$.
Total profit $= 17 \times 250 = Rs. 4250$.

(C) Let the total sum be $x$.
According to the problem:
$A = \frac{1}{2}x + 40$
$B = \frac{3}{8}x - 120$
$C = 200$
Since the sum of $A, B,$ and $C$ equals the total sum $x$,we have:
$(\frac{1}{2}x + 40) + (\frac{3}{8}x - 120) + 200 = x$
Combine the terms:
$(\frac{4}{8}x + \frac{3}{8}x) + (40 - 120 + 200) = x$
$\frac{7}{8}x + 120 = x$
$120 = x - \frac{7}{8}x$
$120 = \frac{1}{8}x$
$x = 120 \times 8 = 960$
Thus,the total sum is $Rs. 960$.

(D) To find the profit share,we calculate the equivalent investment for one month for each partner:
$A$ invested $Rs. 18,000$ for $12$ months: $18,000 \times 12 = 216,000$.
$B$ invested $Rs. 24,000$ for $8$ months (from month $1$ to $8$) and then rejoined for $2$ months (month $11$ and $12$): $24,000 \times 8 + 24,000 \times 2 = 192,000 + 48,000 = 240,000$.
$C$ invested $Rs. 15,000$ for $4$ months (from month $5$ to $8$) and then $Rs. 15,000 + 3,000 = 18,000$ for $4$ months (from month $9$ to $12$): $15,000 \times 4 + 18,000 \times 4 = 60,000 + 72,000 = 132,000$.
Ratio of investments $(A:B:C) = 216,000 : 240,000 : 132,000 = 216 : 240 : 132$.
Dividing by $12$,we get $18 : 20 : 11$.
Total ratio parts $= 18 + 20 + 11 = 49$.
$B$'s share of profit $= \frac{20}{49} \times 12,005 = 20 \times 245 = Rs. 4,900$.

(B) To determine the better investment,we calculate the return percentage for each stock.
$(i)$ For $4 \%$ stock at $Rs. 120$:
Return $= (4 / 120) \times 100 = 100 / 30 = 3.33 \%$.
$(ii)$ For $3 \%$ stock at $Rs. 80$:
Return $= (3 / 80) \times 100 = 300 / 80 = 3.75 \%$.
Comparing the two,$3.75 \% > 3.33 \%$.
Therefore,the $3 \%$ stock at $Rs. 80$ is a better investment.

(C) The $LCM$ of $4, 5, 6$ is $60$.
The correct ratio is $\frac{1}{4} \times 60 : \frac{1}{5} \times 60 : \frac{1}{6} \times 60 = 15 : 12 : 10$.
The total parts in the correct ratio $= 15 + 12 + 10 = 37$.
$C$'s actual share $= \frac{10}{37} \times 555 = 10 \times 15 = 150$.
The incorrect ratio is $4 : 5 : 6$.
The total parts in the incorrect ratio $= 4 + 5 + 6 = 15$.
$C$'s share by mistake $= \frac{6}{15} \times 555 = 6 \times 37 = 222$.
The excess amount received by $C = 222 - 150 = 72$.