ICSE Class 10 Mathematics · ML Aggarwal Mathematics · 55 solved questions
Find the dividend received on 60 shares of ₹20 each if 9% dividend is declared.
Dividend on 1 share
$$\begin{aligned}= 9% \text{ of ₹20} \\[0.5em] = \frac{9}{100} \times 20 \\[0.5em] = ₹1.8\end{aligned}$$
∴ Dividend on 60 shares
= ₹1.8 * 60
= ₹108
A company declares 8 percent dividend to the share holders. If a man receives ₹2840 as his dividend, find the nominal value of his shares.
Hint — Let the nominal value of his shares be ₹x, then 8% of ₹x = ₹2840.
Let nominal value of shares be ₹x
According to the given,
$$\begin{aligned}8% \text{ of } x = 2840 \\[0.5em] \Rightarrow \frac{8}{100} \times x = 2840 \\[0.5em] \Rightarrow x = \frac{2840 \times 100}{8} \\[0.5em] \Rightarrow x = 35500\end{aligned}$$
∴ Nominal value of the man's shares = ₹35500
A man buys 250, ten-rupee shares each at ₹12.50. If the rate of dividend is 7%, find the :
(a) dividend he receives annually.
(b) percentage return on his investment.
(a) Nominal Value of 1 share = ₹10
Market Value of 1 share = ₹12.50
Number of shares purchased = 250
Nominal Value of 250 shares = 250 x 10 = ₹2500
Rate of dividend = 7%
∴ Dividend received = 7% of 2500
= $\frac{7}{100} \times 2500$
= ₹175.
Hence, annual dividend = ₹175.
(b) Amount Invested = No. of shares x Market Value
= 250 x 12.50
= ₹3125
$$\begin{aligned}\text{Return percentage } = \frac{\text{Dividend received}}{\text{Investment}} \times 100 \\[1em] = \frac{175}{3125} \times 100 \\[1em] = \frac{17500}{3125} \\[1em] = 5.6%.\end{aligned}$$
Hence, return percentage = 5.6%.
Find the market price of 5% ₹100 share when a person gets a dividend of ₹65 by investing ₹1430.
Let the number of shares purchased be x
Nominal Value per share = ₹100
Rate of Dividend = 5%
Annual Dividend = No. of shares x Rate of Dividend x Nominal Value per share
According to the given,
$$\begin{aligned}65 = x \times \frac{5}{100} \times 100 \\[0.5em] 65 = 5x \\[0.5em] x = \frac{65}{5} \\[0.5em] x = 13\end{aligned}$$
∴ No. of shares purchased = 13
Total Investment = ₹1430
∴ Market Price of one share
$$\begin{aligned}= \frac{\text{Total Investment}}{\text{No. of shares}} \\[0.7em] = \frac{1430}{13} \\[0.5em] = \bold{₹110}\end{aligned}$$
Govind buys 50 shares of face value ₹100 available at ₹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 ₹150, how many extra shares should he buy?
Number of shares = 50
Face value per share = ₹100
Market value per share = ₹132
(i)
Total Investment = No. of shares x Market value per share
$$\begin{aligned}= 50 \times 132 \\ = 6600\end{aligned}$$
∴ Govind investment = ₹6600
(ii)
Annual Dividend = No. of shares x Rate of Dividend x Nominal Value per share
$$\begin{aligned}= 50 \times \frac{7.5}{100} \times 100 \\[0.5em] = 375\end{aligned}$$
∴ Govind Annual Income = ₹375
(iii)
Increase in Annual Income = ₹150
New Annual Income = ₹375 + ₹150 = ₹525
Let the new number of shares by x
Annual Dividend = No. of shares x Rate of Dividend x Nominal Value per share
According to the given,
$$\begin{aligned}525 = x \times \frac{7.5}{100} \times 100 \\[0.5em] 525 = 7.5x \\[0.5em] x = \frac{5250}{75} \\[0.5em] x = 70\end{aligned}$$
∴ New number of shares = 70
Extra shares Govind should buy
= 70 - 50
= 20
A lady holds 1800, ₹100 shares of a company that pays 15% dividend annually. Calculate her annual dividend. If she had bought these shares at 40% premium, what percentage return does she get on her investment?
No. of shares held = 1800
Nominal Value per share = ₹100
Rate of Dividend = 15%
Annual Dividend = No. of shares x Rate of Dividend x Nominal Value per share
$$\begin{aligned}= 1800 \times \frac{15}{100} \times 100 \\[0.5em] = 27000\end{aligned}$$
∴ Annual Dividend = ₹27000
As Shares are bought at 40% premium,
Market Value of one share
$$\begin{aligned}= 100 + \Big(\frac{40}{100} \times 100\Big) \\[0.5em] = 100 + 40 \\[0.5em] = ₹140\end{aligned}$$
Total Investment = No. of shares x Market Value per share
= 1800 x 140
= ₹252000
% $\text{Return}= \Big(\frac{\text{Annual Inc.}}{\text{Investment}} \times 100\Big)$ %
$= \Big(\frac{27000}{252000} \times 100\Big)$ %
$= \Big(\frac{2700}{252} \Big)$ %
$= \Big(\frac{75}{7} \Big)$ %
$= \bold{10\frac{5}{7}}$ %
What sum should a person invest in ₹25 shares, selling at ₹36, obtain an income of ₹720, if the dividend declared is 12%? Also find the percentage return on his income.
Let the number of shares purchased be x.
Nominal Value per share = ₹25
Market Value per share = ₹36
Rate of Dividend = 12%
Annual Dividend = No. of shares x Rate of Dividend x Nominal Value per share
According to the given,
$$\begin{aligned}720 = x \times \frac{12}{100} \times 25 \\[0.5em] 720 = 3x \\[0.5em] x = \frac{720}{3} \\[0.5em] x = 240\end{aligned}$$
∴ Total Investment Required = No. of shares x Market Value per share
= 240 x 36
= ₹8640
% $\text{Return} = \Big(\frac{\text{Annual Inc.}}{\text{Investment}} \times 100\Big)$ %
$= \Big(\frac{720}{8640} \times 100\Big)$ %
$= \Big(\frac{72000}{8640} \Big)$ %
$= \Big(\frac{25}{3} \Big)$ %
$= \bold{8\frac{1}{3}}$ %
Ashok invests ₹26400 on 12% ₹25 shares of a company. If he receives a dividend of ₹2475, find:
(i) the number of shares he bought.
(ii) the market value of each share.
Let the number of shares purchased be x.
Nominal Value per share = ₹25
Rate of Dividend = 12%
Total Investment = ₹26400
Annual Dividend = ₹2475
Annual Dividend = No. of shares x Rate of Dividend x Nominal Value per share
According to the given,
$$\begin{aligned}2475 = x \times \frac{12}{100} \times 25 \\[0.5em] 2475 = 3x \\[0.5em] x = \frac{2475}{3} \\[0.5em] x = 825\end{aligned}$$
∴ Number of shares bought = 825
Market value of each share
$$\begin{aligned}= \frac{\text{Total Investment}}{\text{No. of shares}} \\[0.7em] = \frac{26400}{825} \\[0.5em] = \bold{₹32}\end{aligned}$$
A man invests ₹4500 in shares of a company which is paying 7.5% dividend. If ₹100 shares are available at a discount of 10%, find
(i) the number of shares he purchases.
(ii) his annual income.
Nominal Value per share = ₹100
Rate of Dividend = 7.5%
Total Investment = ₹4500
As the shares are bought at a discount of 10%,
Market Value per share = ₹100 - ₹(10% of 100)
$$\begin{aligned}= ₹100 - ₹\Big(\frac{10}{100} \times 100 \Big) \\[0.5em] = ₹100 - ₹10 \\[0.5em] = ₹90\end{aligned}$$
(i) Number of shares purchased
$$\begin{aligned}= \frac{\text{Total Investment}}{\text{MV per share}} \\[0.7em] = \frac{4500}{90} \\[0.5em] = \bold{50}\end{aligned}$$
(ii) Annual Dividend = No. of shares x Rate of Dividend x Nominal Value per share
$$\begin{aligned}= 50 \times \frac{7.5}{100} \times 100 \\[0.5em] = \bold{₹375}\end{aligned}$$
Hence, his annual income = ₹375
Amit invests ₹36000 in buying ₹100 shares at ₹20 premium. The dividend is 15% per annum. Find:
(i) the number of shares he buys
(ii) his yearly dividend
(iii) the percentage return on his investment.
Nominal Value per share = ₹100
Rate of Dividend = 15%
Total Investment = ₹36000
As Amit buys the shares at ₹20 premium,
Market Value per share = ₹100 + ₹20 = ₹120
∴ Number of shares he buys
$$\begin{aligned}= \frac{\text{Total Investment}}{\text{MV per share}} \\[0.7em] = \frac{36000}{120} \\[0.5em] = \bold{300}\end{aligned}$$
Annual Dividend = No. of shares x Rate of Dividend x Nominal Value per share
$$\begin{aligned}= 300 \times \frac{15}{100} \times 100 \\[0.5em] = \bold{₹4500}\end{aligned}$$
% $\text{Return} = \Big(\frac{\text{Annual Inc.}}{\text{Investment}} \times 100\Big)$ %
$= \Big(\frac{4500}{36000} \times 100\Big)$ %
$= \Big(\frac{450000}{36000} \Big)$ %
$= \Big(\frac{25}{2} \Big)$ %
$= \bold{12.5}$ %
Mr. Gupta invested ₹33000 in buying ₹100 shares of a company at 10% premium. The dividend declared by the company is 12%.
Find:
(a) the number of shares purchased by him.
(b) his annual dividend.
Money invested = ₹33000
N.V. of share = ₹100
M.V. = N.V + Premium
= ₹100 + $\frac{10}{100} \times 100$
= ₹100 + ₹10
= ₹110.
(a) Number of shares = $\frac{\text{Money invested}}{\text{M.V.}} = \frac{33000}{110}$ = 300.
Hence, no. of shares purchased = 300.
(b) By formula,
Annual dividend = Number of shares × Rate of dividend × N.V.
= 300 × $\frac{12}{100} \times 100$
= ₹3600.
Hence, annual dividend = ₹3600.
A man buys shares at the par value of ₹10 yielding 8% dividend at the end of a year. Find the number of shares bought if he receives a dividend of ₹300.
As shares are bought at par,
Market value per share = Nominal value per share = ₹10
Rate of Dividend = 8%
Annual Dividend = ₹300
Let the number of shares purchased be x.
Annual Dividend = No. of shares x Rate of Dividend x Nominal Value per share
According to the given,
$$\begin{aligned}300 = x \times \frac{8}{100} \times 10 \\[0.5em] x = \frac{300 \times 10}{8} \\[0.5em] x = 375\end{aligned}$$
∴ Number of shares bought = 375
A man invests ₹8800 on buying shares of face value of rupees hundred each at a premium of 10%. If he earns ₹1200 at the end of year as dividend, find:
(i) the number of shares he has in this company
(ii) the dividend percentage per share.
Nominal Value per share = ₹100
Total Investment = ₹8800
Annual Dividend = ₹1200
(i)
As the shares were bought at 10% premium,
Market Value of one share
$$\begin{aligned}= 100 + \Big(\frac{10}{100} \times 100\Big) \\[0.5em] = 100 + 10 \\[0.5em] = ₹110\end{aligned}$$
Number of shares bought
$$\begin{aligned}= \frac{\text{Total Investment}}{\text{MV per share}} \\[0.7em] = \frac{8800}{110} \\[0.5em] = \bold{80}\end{aligned}$$
∴ Number of shares the man has in the company = 80
(ii)
Let the dividend percentage per share be r%
Annual Dividend = No. of shares x Rate of Dividend x Nominal Value per share
According to the given,
$$\begin{aligned}1200 = 80 \times \frac{r}{100} \times 100 \\[0.5em] 1200 = 80r \\[0.5em] r = \frac{1200}{80} \\[0.5em] r = 15\end{aligned}$$
∴ Dividend percentage per share = 15%
A man invested ₹45000 in 15% ₹100 shares quoted at ₹125. When the market value of these shares rose to ₹140, he sold some shares, just enough to raise ₹8400. Calculate:
(i) The number of shares he still holds.
(ii) The dividend due to him on these shares.
(i)
Nominal Value per share = ₹100
Market Value per share = ₹125
Total Investment = ₹45000
Rate of Dividend = 15%
No. of shares bought at MV of ₹125
$$\begin{aligned}= \frac{\text{Total Investment}}{\text{MV per share}} \\[0.5em] = \frac{45000}{125} \\[0.5em] = 360\end{aligned}$$
∴ Total number of shares = 360
Market Value per share of shares sold = ₹140
Amount raised from sale = ₹8400
$$\begin{aligned}\text{No. of shares sold} \\[0.5em] = \frac{\text{Amt raised from sale}}{\text{MV per share}} \\[0.5em] = \frac{8400}{140} \\[0.5em] = 60\end{aligned}$$
No. of shares remaining = Total shares - Shares sold
= 360 - 60
= 300
∴ Number of shares the man still holds = 300
(ii)
Annual Dividend = No. of shares x Rate of Dividend x Nominal Value per share
$$\begin{aligned}= 300 \times \frac{15}{100} \times 100 \\[0.5em] = \bold{₹4500}\end{aligned}$$
∴ Dividend due to the man on remaining shares = ₹4500
Ajay owns 560 shares of a company. The face value of each share is ₹25. The company declares a dividend 0f 9%. Calculate:
(i) the dividend that Ajay will get
(ii) the rate of interest, on his investment, if Ajay has paid ₹30 for each share.
Nominal Value per share = ₹25
Rate of Dividend = 9%
No. of shares owned = 560
(i)
Annual Dividend = No. of shares x Rate of Dividend x Nominal Value per share
$$\begin{aligned}= 560 \times \frac{9}{100} \times 25 \\[0.5em] = ₹1260\end{aligned}$$
∴ The dividend that Ajay will get = ₹1260
(ii)
Market Value per share = ₹30
Total Investment = No. of shares x Market Value per share
= 560 x 30
= 16800
% $\text{Return} = \Big(\frac{\text{Annual Inc.}}{\text{Investment}} \times 100\Big)$ %
$= \Big(\frac{1260}{16800} \times 100\Big)$ %
$= \Big(\frac{1260}{168} \Big)$ %
$= \Big(\frac{15}{2} \Big)$ %
$= \bold{7\frac{1}{2}}$ %
∴ Rate of return on Ajay's investment = 7½%
A company with 10000 shares of nominal value of ₹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 ₹150 per share. Calculate the dividend he received and the percentage return on his investment.
(i)
No. of shares = 10000
Nominal Value per share = ₹100
Rate of Dividend = 8%
Annual Dividend = No. of shares x Rate of Dividend x Nominal Value per share
$$\begin{aligned}= 10000 \times \frac{8}{100} \times 100 \\[0.5em] = ₹80000\end{aligned}$$
∴ Total amount of dividend paid by the company = ₹80000
(ii)
No. of shares Ramesh bought = 90
Nominal Value per share = ₹100
Rate of Dividend = 8%
Annual Dividend = No. of shares x Rate of Dividend x Nominal Value per share
$$\begin{aligned}= 90 \times \frac{8}{100} \times 100 \\[0.5em] = ₹720\end{aligned}$$
∴ Dividend Ramesh received = ₹720
Total investment of Ramesh = 90 x 150 = ₹13500
% $\text{Return} = \Big(\frac{\text{Annual Inc.}}{\text{Investment}} \times 100\Big)$ %
$= \Big(\frac{720}{13500} \times 100\Big)$ %
$= \Big(\frac{720}{135} \Big)$ %
$= \Big(\frac{16}{3} \Big)$ %
$= \bold{5\frac{1}{3}}$ %
A company with 500 shares of nominal value ₹ 120 declares and annual dividend of 15%. Calculate :
(i) the total amount of dividend paid by the company
(ii) the annual income of Mr Sharma who hold 80 shares of the company.
If the return percent of Mr. Sharma from his shares is 10%, find the market value of each shares.
(i) No. of shares = 500
Nominal Value per share = ₹ 120
Rate of Dividend = 15%
By formula,
Annual Dividend = No. of shares x Rate of Dividend x Nominal Value per share
= 500 x $\frac{15}{100}$ x 120
= ₹ 9,000
Hence, total amount of dividend paid by the company = ₹ 9,000.
(ii) No. of shares held by Mr. Sharma = 80
Nominal Value per share = ₹ 120
Rate of Dividend = 15%
By formula,
Annual Dividend = No. of shares x Rate of Dividend x Nominal Value per share
= 80 x $\frac{15}{100}$ x 120
= ₹ 1,440.
Hence, annual income of Mr. Sharma = ₹ 1,440.
By formula,
Rate of dividend × N.V. = Profit (return%) × M.V.
$$\begin{aligned}\Rightarrow \frac{15}{100} \times 120 = \frac{10}{100} \times M.V. \\[1em] \Rightarrow 15 \times 120 = 10 \times M.V. \\[1em] \Rightarrow M.V. = \frac{15 \times 120}{10} = 180.\end{aligned}$$
Hence, market value of each share = ₹ 180.
By investing ₹7500 in a company paying 10 percent dividend, an income of ₹500 is received. What price is paid for each ₹100 share.
Let the number of shares purchased be x.
Nominal Value per share = ₹100
Rate of Dividend = 10%
Total Investment = ₹7500
Annual Dividend = ₹500
Annual Dividend = No. of shares x Rate of Dividend x Nominal Value per share
According to the given,
$$\begin{aligned}500 = x \times \frac{10}{100} \times 100 \\[0.5em] 500 = 10x \\[0.5em] x = \frac{500}{10} \\[0.5em] x = 50\end{aligned}$$
∴ Number of shares purchased = 50
Market value of each share
$$\begin{aligned}= \frac{\text{Total Investment}}{\text{No. of shares}} \\[0.7em] = \frac{7500}{50} \\[0.5em] = \bold{₹150}\end{aligned}$$
∴ Price paid for each share = ₹150
A man buys 400 ten-rupee shares at a premium of ₹2.50 on each share. If the rate of dividend is 8%, find
(i) his investment
(ii) dividend received
(iii) yield.
(i)
Number of shares = 400
Nominal Value per share = ₹10
As the man buys the shares at ₹2.50 premium,
Market Value per share = ₹10 + ₹2.50 = ₹12.50
Total Investment = No. of shares x MV per share
= 400 x 12.5
= 5000
∴ Investment of man = ₹5000
(ii)
Rate of Dividend = 8%
Annual Dividend = No. of shares x Rate of Dividend x Nominal Value per share
$$\begin{aligned}= 400 \times \frac{8}{100} \times 10 \\[0.5em] = \bold{₹320}\end{aligned}$$
∴ Dividend received = ₹320
(iii)
Yield means the rate of return on investment.
% $\text{Return} = \Big(\frac{\text{Annual Inc.}}{\text{Investment}} \times 100\Big)$ %
$= \Big(\frac{320}{5000} \times 100\Big)$ %
$= \Big(\frac{32}{5} \Big)$ %
$= \bold{6.4}$ %
∴ Yield = 6.4%
A man invests ₹10400 in 6% shares at ₹104 and ₹11440 in 10.4% shares at ₹143. How much income would he get in all? (Assume face value of ₹100)
First Investment:
Total Investment = ₹10400
Market Value per share = ₹104
∴ No. of shares
$$\begin{aligned}= \frac{\text{Total Investment}}{\text{MV per share}} \\[0.7em] = \frac{10400}{104} \\[0.5em] = \bold{100}\end{aligned}$$
Rate of Dividend = 6%
As Nominal value is not given, let's assume it to be ₹100 per share
Annual Dividend = No. of shares x Rate of Dividend x Nominal Value per share
$$\begin{aligned}= 100 \times \frac{6}{100} \times 100 \\[0.5em] = \bold{₹600}\end{aligned}$$
Second Investment:
Total Investment = ₹11440
Market Value per share = ₹143
∴ No. of shares
$$\begin{aligned}= \frac{\text{Total Investment}}{\text{MV per share}} \\[0.7em] = \frac{11440}{143} \\[0.5em] = \bold{80}\end{aligned}$$
Rate of Dividend = 10.4%
As Nominal value is not given, let's assume it to be ₹100 per share
Annual Dividend = No. of shares x Rate of Dividend x Nominal Value per share
$$\begin{aligned}= 80 \times \frac{10.4}{100} \times 100 \\[0.5em] = \bold{₹832}\end{aligned}$$
Total Income = Income from first investment + Income from second investment
= ₹600 + ₹832
= ₹1432
∴ Total Income = ₹1432
Two companies have shares of 7% at ₹116 and 9% at ₹145 respectively. In which of the shares would the investment be more profitable?(Assume face value of ₹100)
Assuming nominal value per share to be ₹100 in both cases.
In the first case:
Income on ₹116 = 7% of ₹100 = ₹7
$\therefore \text{ Income on ₹1} = ₹\frac{7}{116}$
In the second case:
Income on ₹145 = 9% of ₹100 = ₹9
$\therefore \text{ Income on ₹1} = ₹\frac{9}{145}$
Now,
$$\begin{aligned}\frac{7}{116} = \frac{7 \times 5}{116 \times 5} = \frac{35}{580} \\[0.7em] \frac{9}{145} = \frac{9 \times 4}{145 \times 4} = \frac{36}{580}\end{aligned}$$
Since 35 < 36, therefore investment in second case (i.e. 9% at ₹145) is more profitable than the investment in first case.
Which is better investment : 6% ₹100 shares at ₹120 or 8% ₹10 shares at ₹15
In the first case:
Income on ₹120 = 6% of ₹100 = ₹6
$$\begin{aligned}\therefore \text{ Income on ₹1} = ₹\frac{6}{120} \\[0.5em] = ₹\frac{1}{20}\end{aligned}$$
In the second case:
Income on ₹15 = 8% of ₹10 = ₹0.8
$$\begin{aligned}\therefore \text{ Income on ₹1} = ₹\frac{0.8}{15} \\[0.5em] = ₹\frac{8}{150} \\[0.5em] = ₹\frac{4}{75}\end{aligned}$$
Now,
$$\begin{aligned}\frac{1}{20} = \frac{1 \times 15}{20 \times 15} = \frac{15}{300} \\[0.7em] \frac{4}{75} = \frac{4 \times 4}{75 \times 4} = \frac{16}{300}\end{aligned}$$
Since 15 < 16, therefore investment in second case (i.e. 8% ₹10 shares at ₹15) is more profitable than the investment in first case.
A man invests ₹10080 in 6% hundred-rupee shares at ₹112. Find his annual income. When the shares fall to ₹96 he sells out the shares and invests the proceeds in 10% ten-rupee shares at ₹8. Find the change in his annual income.
Total Investment = ₹10080
Market Value per share = ₹112
∴ No. of shares
$$\begin{aligned}= \frac{\text{Total Investment}}{\text{MV per share}} \\[0.7em] = \frac{10080}{112} \\[0.5em] = \bold{90}\end{aligned}$$
Rate of Dividend = 6%
Nominal value per share = ₹100
Annual Dividend = No. of shares x Rate of Dividend x Nominal Value per share
$$\begin{aligned}= 90 \times \frac{6}{100} \times 100 \\[0.5em] = \bold{₹540}\end{aligned}$$
∴ Annual Income = ₹540
Let's calculate the Annual Income of his new investment.
Selling price of 1 share = ₹96
∴ Selling price of 90 shares = ₹(90 x 96) = ₹8640
Hence, sale proceeds = ₹8640
Total Investment in new shares = ₹8640
Market Value per share of new shares = ₹8
∴ No. of new shares
$$\begin{aligned}= \frac{\text{Total Investment}}{\text{MV per share}} \\[0.7em] = \frac{8640}{8} \\[0.5em] = \bold{1080}\end{aligned}$$
Nominal value per share of new shares = ₹10
Rate of Dividend of new shares = 10%
Annual Dividend from new shares = No. of shares x Rate of Dividend x Nominal Value per share
$$\begin{aligned}= 1080 \times \frac{10}{100} \times 10 \\[0.5em] = \bold{₹1080}\end{aligned}$$
∴ Change in Annual Income = ₹1080 - ₹540 = ₹540
Annual Income increased by ₹540
Sachin invests ₹8500 in 10% ₹100 shares at ₹170. He sells the shares when the price of each share rises by ₹30. He invests the proceeds in 12% ₹100 shares at ₹125. Find
(i) the sale proceeds.
(ii) the number of ₹125 shares he buys.
(iii) the change in his annual income.
(i) Total Investment = ₹8500
Market Value per share = ₹170
∴ No. of shares
$$\begin{aligned}= \frac{\text{Total Investment}}{\text{MV per share}} \\[0.7em] = \frac{8500}{170} \\[0.5em] = \bold{50}\end{aligned}$$
Selling price of 1 share = ₹170 + ₹30 = ₹200
∴ Selling price of 50 shares = ₹(50 x 200) = ₹10000
Hence, the sale proceeds = ₹10000
(ii) Market Value of new shares = ₹125
∴ No. of new shares
$$\begin{aligned}= \frac{\text{Total Investment}}{\text{MV per share}} \\[0.7em] = \frac{10000}{125} \\[0.5em] = \bold{80}\end{aligned}$$
Hence, the number of ₹125 shares he buys = 80
(iii) The change in his annual income:
Annual Dividend from 10% ₹100 shares at ₹170
= No. of shares x Rate of Dividend x Nominal Value per share
$$\begin{aligned}= 50 \times \frac{10}{100} \times 100 \\[0.5em] = \bold{₹500}\end{aligned}$$
Annual Dividend from 12% ₹100 shares at ₹125
= No. of shares x Rate of Dividend x Nominal Value per share
$$\begin{aligned}= 80 \times \frac{12}{100} \times 100 \\[0.5em] = \bold{₹960}\end{aligned}$$
∴ Change in Annual Income = ₹960 - ₹500 = ₹460
Annual Income increased by ₹460
A person invests ₹4368 and buys certain hundred-rupee shares at ₹91. He sells out shares worth ₹2400 when they have risen to ₹95 and the remainder when they have fallen to ₹85. Find the gain or loss on the total transaction.
Total Investment = ₹4368
Nominal value per share = ₹100
Market value per share = ₹91
∴ Number of shares purchased
$$\begin{aligned}= \frac{\text{Total Investment}}{\text{MV per share}} \\[0.7em] = \frac{4368}{91} \\[0.5em] = \bold{48}\end{aligned}$$
Number of shares worth (face value) ₹2400
$$\begin{aligned}= \frac{2400}{100} \\[0.5em] = 24\end{aligned}$$
Hence, the person sold 24 shares at ₹95.
∴ The selling value of 24 shares at ₹95 each
= ₹(24 x 95) = ₹2280
The number of remaining shares = 48 - 24 = 24
Hence, the person sold the remaining 24 shares at ₹85.
∴ The selling value of 24 shares at ₹85 each
= ₹(24 x 85) = ₹2040
∴ Total selling value = ₹2280 + ₹2040 = ₹4320
Total Gain/Loss = New Selling Value - Initial Investment
= ₹4320 - ₹4368 = -₹48
As new selling value is less than initial investment hence there is a loss of ₹48 on the total transaction.
By purchasing ₹50 gas shares for ₹80 each, a man gets 4% profit on his investment. What rate percent is company paying? What is his dividend if he buys 200 shares?
Let the rate percent company is paying be x%
Dividend on 1 share of ₹50
$= x$% $\text{of ₹50}$
$$\begin{aligned}= \frac{x}{100} \times 50 \\[0.5em] = \frac{x}{2}\end{aligned}$$
His profit on one share
$= 4$% $\text{of ₹80}$
$$\begin{aligned}= \frac{4}{100} \times 80 \\[0.5em] = \frac{32}{10} \\[0.5em] = \frac{16}{5}\end{aligned}$$
As per the given,
$$\begin{aligned}\frac{x}{2} = \frac{16}{5} \\[0.5em] \Rightarrow x = \frac{16 \times 2}{5} \\[0.5em] \Rightarrow x = 6.4\end{aligned}$$
∴ Rate percent company is paying = 6.4%
Annual Dividend = No. of shares x Rate of Dividend x Nominal Value per share
$$\begin{aligned}= 200 \times \frac{6.4}{100} \times 50 \\[0.5em] = 200 \times \frac{64}{1000} \times 50 \\[0.5em] = 2 \times 64 \times 5 \\[0.5em] = \bold{₹640}\end{aligned}$$
∴ Dividend if he buys 200 shares = ₹640
₹100 shares of a company are sold at a discount of ₹20. If the return on the investment is 15%. Find the rate of dividend declared.
Let Rate of Dividend be x%
Dividend on 1 share of ₹100 = x% of ₹100 = ₹x
Since the shares are sold at a discount of ₹20,
Market Value of 1 share = ₹100 - ₹20 = ₹80
$$\begin{aligned}% \text{Return} = \Big(\frac{\text{Annual Inc.}}{\text{Investment}} \times 100\Big)% \\[0.5em]\end{aligned}$$
As per the given,
$$\begin{aligned}15 = \frac{x}{80} \times 100 \\[0.5em] x = \frac{15 \times 80}{100} \\[0.5em] x = 12\end{aligned}$$
∴ Rate of Dividend = 12%
A company declared a dividend of 14%. Find the market value of ₹50 shares if the return on the investment was 10%.
Let the market value of 1 share be ₹x
Dividend on 1 share of ₹50 = 14% of ₹50 = ₹7
$$\begin{aligned}% \text{Return} = \Big(\frac{\text{Annual Inc.}}{\text{Investment}} \times 100\Big)% \\[0.5em]\end{aligned}$$
As per the given,
$$\begin{aligned}10 = \frac{7}{x} \times 100 \\[0.5em] x = \frac{7 \times 100}{10} \\[0.5em] x = 70\end{aligned}$$
∴ Market Value of each ₹50 share = ₹70
A company with 10000 shares of ₹100 each, declares an annual dividend of 5%.
(i) What is the total amount of dividend paid by the company?
(ii) What would be the annual income of a man, who has 72 shares, in the company?
(iii) If he received only 4% on his investment, find the price he paid for each share.
(i)
Number of shares = 10000
Nominal value per share = ₹100
Rate of Dividend = 5%
Annual Dividend = No. of shares x Rate of Dividend x Nominal Value per share
$$\begin{aligned}= 10000 \times \frac{5}{100} \times 100 \\[0.5em] = \bold{₹50000}\end{aligned}$$
∴ Total amount of dividend paid by the company = ₹50000
(ii)
Number of shares the man has = 72
$$\begin{aligned}\text{Annual Inc.} = 72 \times \frac{5}{100} \times 100 \\[0.5em] = \bold{₹360}\end{aligned}$$
∴ Annual income of man with 72 shares = ₹360
(iii)
Let price paid by man for each share be ₹x
His total investment = ₹72x
$$\begin{aligned}% \text{Return} = \Big(\frac{\text{Annual Inc.}}{\text{Investment}} \times 100\Big)% \\[0.5em]\end{aligned}$$
As per the given,
$$\begin{aligned}4 = \frac{360}{72x} \times 100 \\[0.5em] x = \frac{360 \times 100}{4 \times 72} \\[0.5em] x = 125\end{aligned}$$
∴ Price paid by man for each share = ₹125
A man sold some ₹100 shares paying 10% dividend at a discount of 25% and invested the proceeds in ₹100 shares paying 16% dividend quoted at ₹80 and thus increased his income by ₹2000. Find the number of shares sold by him.
Let the number of shares sold by the man be x
The man sold the shares at a discount of 25%,
∴ Selling price of the shares = ₹100 - 25% of ₹100 = ₹100 - ₹25 = ₹75
Sales proceeds = ₹75x
Number of ₹100 16% shares purchased by the man
$$\begin{aligned}= \frac{75x}{80} \\[0.5em] = \frac{15x}{16}\end{aligned}$$
Annual Income from previous shares = No. of shares x Rate of Dividend x Nominal Value per share
$$\begin{aligned}= x \times \frac{10}{100} \times 100 \\[0.5em] = \bold{₹10x}\end{aligned}$$
Annual Income from new shares = No. of shares x Rate of Dividend x Nominal Value per share
$$\begin{aligned}= \frac{15x}{16} \times \frac{16}{100} \times 100 \\[0.5em] = \bold{₹15x}\end{aligned}$$
As per the given,
$$\begin{aligned}15x - 10x = 2000 \\ 5x = 2000 \\ x = 400\end{aligned}$$
∴ Number of shares sold by the man = 400
A man invests ₹6750, partly in shares of 6% at ₹140 and partly in shares of 5% at ₹125. If his total income is ₹280, how much has he invested in each ?
Let the investment of the man in shares of 6% at ₹140 be ₹x, then his investment in shares of 5% at ₹125 = ₹(6750 - x)
$\text{Income on 1 share of ₹140} = 6$% $\text{ of ₹100} = ₹6$
$\text{Income on ₹x} = ₹\frac{6}{140}x = ₹\frac{3}{70}x$
$\text{Income on 1 share of ₹125} = 5$% $\text{ of ₹100} = ₹5$
$\text{Income on ₹(6750 - x)} = ₹\frac{5}{125}(6750 - x) = ₹\frac{1}{25}(6750 - x)$
But the total income of the man is ₹280,
$$\begin{aligned}\therefore \frac{3}{70}x + \frac{1}{25}(6750 - x) = 280 \\[0.5em] \Rightarrow \frac{3}{70}x + \frac{1}{25}(6750 - x) = 280 \\[0.5em] \Rightarrow \frac{15x + 94500 - 14x}{350} = 280 \\[0.5em] \Rightarrow x + 94500 = 280 \times 350 \\[0.5em] \Rightarrow x = 98000 - 94500 \\[0.5em] \Rightarrow x = 3500 \\[0.5em] \therefore 6750 - x = 6750 - 3500 = 3250\end{aligned}$$
∴ Investment in 6% shares at ₹140 = ₹3500
and Investment in 5% shares at ₹125 = ₹3250
Divide ₹20304 into two parts such that if one part is invested in 9% ₹50 shares at 8% premium and the other part is invested in 8% ₹25 shares at 8% discount, then the annual incomes from both the investment are equal.
Let the investment in 9% ₹50 shares be ₹x, then the investment in 8% ₹25 shares = ₹(20304 - x)
9% ₹50 shares are at 8% premium
∴ Market Value of one 9% ₹50 share = ₹50 + 8% of ₹50 = ₹54
8% ₹25 shares are at 8% discount
∴ Market Value of one 8% ₹25 share = ₹25 - 8% of ₹25 = ₹23
$$\begin{aligned}\text{Income on 1 share of ₹54} = 9% \text{ of ₹50} = ₹4.50 \\[0.5em] \text{Income on ₹x} = ₹\frac{4.5}{54}x = ₹\frac{x}{12} \\[0.5em] \text{Income on 1 share of ₹23} = 8% \text{ of ₹25} = ₹2 \\[0.5em] \text{Income on ₹(20304 -x)} = ₹\frac{2}{23}(20304 - x) \\[0.5em]\end{aligned}$$
But the annual incomes from both the investments should be equal
$$\begin{aligned}\therefore \frac{x}{12} = \frac{2}{23}(20304 - x) \\[0.5em] \Rightarrow 23x = 487296 - 24x \\[0.5em] \Rightarrow 47x = 487296 \\[0.5em] \Rightarrow x = \frac{487296}{47} \\[0.5em] \Rightarrow x = 10368 \\[0.5em] \therefore (20304 -x) = 20304 - 10368 = 9936\end{aligned}$$
∴ Investment in 9% ₹50 shares at ₹54 = ₹10368
and Investment in 8% ₹25 shares at ₹23 = ₹9936
The sum of money required to buy 50, ₹ 40 shares at ₹ 38.50 is :
M.V. of share = ₹ 38.50
No of shares bought = 50
Money required = ₹ 38.50 × 50 = ₹ 1925.
Hence, Option 3 is the correct option.
If Jagbeer invest ₹10320 on ₹100 shares at a discount of ₹14, then the number of shares he buys is
Nominal Value per share = ₹100
As Jagbeer buys the shares at a discount of ₹14,
∴ Market Value per share = ₹100 - ₹14 = ₹86
Jagbeer's Total Investment = ₹10320
$$\begin{aligned}\therefore \text{No. of shares} = \frac{\text{Investment}}{\text{M.V.}} \\[0.5em] = \frac{10320}{86} = 120\end{aligned}$$
∴ Option 2 is the correct option.
If Nisha invests ₹19200 on ₹50 shares at a premium of 20%, then the number of shares she buys is
Nominal Value per share = ₹50
As Nisha buys the shares at a premium of 20%,
∴ Market Value per share = ₹50 + 20% of ₹50 = ₹50 + ₹10 = ₹60
Nisha's Total Investment = ₹19200
$$\begin{aligned}\therefore \text{No. of shares} = \frac{\text{Investment}}{\text{M.V.}} \\[0.5em] = \frac{19200}{60} = 320\end{aligned}$$
∴ Option 3 is the correct option.
₹40 shares of a company are selling at 25% premium. If Mr. Jacob wants to buy 280 shares of the company, then the investment required by him is
Nominal Value per share = ₹40
As the shares are selling at 25% premium,
∴ Market Value per share = ₹40 + 25% of ₹40 = ₹40 + ₹10 = ₹50
No of shares Mr. Jacob wants to buy = 280
∴ Total Investment of Mr. Jacob = 280 x 50 = ₹14000
∴ Option 2 is the correct option.
Arun possesses 600 shares of ₹25 of a company. If the company announces a dividend of 8%, then Arun's annual income is
No. of shares = 600
Nominal Value per share = ₹25
Rate of Dividend = 8%
Annual Dividend = No. of shares x Rate of Dividend x Nominal Value per share
$$\begin{aligned}= 600 \times \frac{8}{100} \times 25 \\[0.5em] = ₹1200\end{aligned}$$
∴ Option 4 is the correct option.
A man invests ₹24000 on ₹60 shares at a discount of 20%. If the dividend declared by the company is 10%, then his annual income is
Nominal Value per share = ₹60
As the shares are bought at a discount of 20%,
∴ Market Value per share = ₹60 - 20% of ₹60 = ₹60 - ₹12 = ₹48
Total Investment = ₹24000
$$\begin{aligned}\therefore \text{No. of shares} = \frac{\text{Investment}}{\text{M.V.}} \\[0.5em] = \frac{24000}{48} = 500\end{aligned}$$
Rate of Dividend = 10%
Annual Dividend = No. of shares x Rate of Dividend x Nominal Value per share
$$\begin{aligned}= 500 \times \frac{10}{100} \times 60 \\[0.5em] = ₹3000\end{aligned}$$
∴ Option 1 is the correct option.
Salman has some shares of ₹50 of a company paying 15% dividend. If his annual income is ₹3000, then the number of shares he possesses is
Let the number of shares Salman owns be x
Nominal Value per share = ₹50
Rate of Dividend = 15%
Annual Dividend = ₹3000
Annual Dividend = No. of shares x Rate of Dividend x Nominal Value per share
According to the given,
$$\begin{aligned}3000 = x \times \frac{15}{100} \times 50 \\[0.5em] 3000 = \frac{15x}{2} \\[0.5em] x = \frac{3000 \times 2}{15} \\[0.5em] x = 400\end{aligned}$$
∴ Option 2 is the correct option.
(i) Shares of company A, paying 12%, ₹ 100 shares are at ₹ 80.
(ii) Shares of company B, paying 12%, ₹ 100 shares are at ₹ 100.
(iii) Shares of company C, paying 12%, ₹ 100 shares are at ₹ 120.
Shares of which company are at premium ?
Companies in which Market value is greater than nominal value, there shares are at premium.
∴ Shares of company C are at premium.
Hence, Option 3 is the correct option.
The sum invested to purchase 15 shares of a company of nominal value ₹ 75 available at a discount of 20% is:
N.V. = ₹ 75
Discount = 20%
M.V. = ₹ 75 - $\frac{20}{100} \times 75$
= ₹ 75 - ₹ 15
= ₹ 60.
Cost of 15 shares = 15 × ₹ 60 = ₹ 900.
Hence, Option 4 is the correct option.
Assertion (A): Dividend, the profit a shareholder receive from the company, depends on the market value.
Reason (R): Dividend is always calculated as the percentage of face value of the share.
Dividends are paid based on the face value (nominal value) of the share, not the market value.
The percentage declared as dividend is applied to the face value, regardless of what the share is currently worth on the stock market.
So, assertion (A) is false.
If a company declares a 10% dividend, that means the shareholder gets 10% of the face value per share not the market value.
So, reason (R) is true.
Thus, Assertion (A) is false, but Reason (R) is true.
Hence, option 2 is the correct option.
Quotation of the share of a company is as follows "10% ₹ 120 shares at ₹ 1200".
Assertion (A): The company is in profit.
Reason (R): The above share is at premium.
"10% ₹ 120 shares at ₹ 1,200"
Here's what this means:
Face value of share = ₹ 120
Dividend rate = 10% of face value = ₹ 12 dividend per share
Market price = ₹ 1,200 (i.e., each share is being sold at ₹ 1,200)
So the share is selling at a premium of ₹ 1,200 − ₹ 120 = ₹ 1,080.
So, reason (R) is true.
The company is in profit if it distributes dividends, which is indicated by the 10% dividend rate in the share quotation.
So, assertion (A) is true.
Thus, both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).
Hence, option 4 is the correct option.
A man purchases 1200 shares of a company of face value ₹ 50 at a discount of ₹ 10.
Assertion (A): His total investment is ₹ 60,000.
Reason (R): The market value of each share is ₹ 40.
Given,
Number of shares = 1200
Face value per share = ₹ 50
Discount = ₹ 10
Market value (purchase price) per share = ₹ 50 − ₹ 10 = ₹ 40
So, reason (R) is true.
By formula,
Investment = Number of shares x Market value per share
= 1200 x 40
= ₹ 48,000.
So, assertion (A) is false.
Thus, Assertion (A) is false, but Reason (R) is true.
Hence, option 2 is the correct option.
If a man received ₹1080 as dividend from 9% ₹20 shares, find the number of shares purchased by him.
Let the number of shares purchased by the man be x
Nominal Value per share = ₹20
Rate of Dividend = 9%
Annual Dividend = ₹1080
Annual Dividend = No. of shares x Rate of Dividend x Nominal Value per share
According to the given,
$$\begin{aligned}1080 = x \times \frac{9}{100} \times 20 \\[0.5em] 1080 = \frac{9x}{5} \\[0.5em] x = \frac{1080 \times 5}{9} \\[0.5em] x = 600\end{aligned}$$
∴ Number of shares purchased by the man = 600
Find the percentage interest on capital invested in 18% shares when a ₹10 share costs ₹12.
Nominal Value per share = ₹10
Market Value per share = ₹12
Rate of Dividend = 18%
Dividend on 1 share
$= 18$% $\text{ of ₹10}$
$$\begin{aligned}= \frac{18}{100} \times 10 \\[0.5em] = ₹\frac{9}{5}\end{aligned}$$
% $\text{Return} = \Big(\frac{\text{Inc. per share}}{\text{M.V. per share}} \times 100\Big)$ %
$= \Big(\frac{\frac{9}{5}}{12} \times 100\Big)$ %
$= \Big(\frac{9}{5} \times \frac{1}{12} \times 100 \Big)$ %
$= \bold{15}$ %
Mahesh Kulkarni invests ₹10000 in 10% ₹100 shares of a company. If his annual dividend is ₹800, find :
(i) the market value of each share.
(ii) the rate percent which he earns on his investment.
(i)
Let the market value of each share be ₹x
Total Investment of Mahesh Kulkarni = ₹10000
$\therefore \text{No. of shares} = \frac{10000}{x}$
Nominal Value per share = ₹100
Rate of Dividend = 10%
Annual Dividend = ₹800
Annual Dividend = No. of shares x Rate of Dividend x Nominal Value per share
According to the given,
$$\begin{aligned}800 = \frac{10000}{x} \times \frac{10}{100} \times 100 \\[0.5em] 800 = \frac{100000}{x} \\[0.5em] x = \frac{100000}{800} \\[0.5em] x = 125\end{aligned}$$
∴ Market Value of each share = ₹125
(ii)
% $\text{Return} = \Big(\frac{\text{Annual Inc.}}{\text{Investment}} \times 100\Big)$ %
$= \Big(\frac{800}{10000} \times 100\Big)$ %
$= \bold{8}$ %
∴ Rate percent Mahesh Kulkarni earns on his investment = 8%
At what price should a 9% ₹100 share be quoted when the money is worth 6%?
Let the market value of 1 share be ₹x
Dividend on 1 share of ₹100 = 9% of ₹100 = ₹9
% $\text{Return} = \Big(\frac{\text{Annual Inc.}}{\text{Investment}} \times 100\Big)$ %
As per the given,
$$\begin{aligned}6 = \frac{9}{x} \times 100 \\[0.5em] x = \frac{9 \times 100}{6} \\[0.5em] x = 150\end{aligned}$$
∴ 9% ₹100 share should be quoted at ₹150
By selling at ₹92, some 2.5% ₹100 shares and investing the proceeds in 5% ₹100 shares at ₹115, a person increased his annual income by ₹90. Find:
(i) the number of shares sold.
(ii) the number of shares purchased.
(iii) the new income.
(iv) the rate percent which he earns on his investment.
(i)
Let the number of shares sold by the man be x
Selling price of one share = ₹92
∴ Sales proceeds = ₹92x
Number of ₹100 5% shares purchased by the man
$$\begin{aligned}= \frac{92x}{115} \\[0.5em] = \frac{4x}{5}\end{aligned}$$
Annual Income from previous shares = No. of shares x Rate of Dividend x Nominal Value per share
$$\begin{aligned}= x \times \frac{2.5}{100} \times 100 \\[0.5em] = \frac{25x}{10} \\[0.5em] = \bold{₹\frac{5x}{2}}\end{aligned}$$
Annual Income from new shares = No. of shares x Rate of Dividend x Nominal Value per share
$$\begin{aligned}= \frac{4x}{5} \times \frac{5}{100} \times 100 \\[0.5em] = \bold{₹4x}\end{aligned}$$
As per the given,
$$\begin{aligned}4x - \frac{5x}{2} = 90 \\[0.5em] \Rightarrow \frac{8x - 5x}{2} = 90 \\[0.5em] \Rightarrow \frac{3x}{2} = 90 \\[0.5em] \Rightarrow x = \frac{90 \times 2}{3} \\[0.5em] \Rightarrow x = 60 \\[0.5em]\end{aligned}$$
∴ Number of shares sold = 60
(ii)
$$\begin{aligned}\text{No. of shares purchased} = \frac{4x}{5} \\[0.5em] = \frac{4 \times 60}{5} \\[0.5em] = 48\end{aligned}$$
∴ Number of shares purchased = 48
(iii)
Annual Income from new shares = ₹4x [From part (i) above]
= ₹(4 x 60)
= ₹240
(iv)
Total Investment = ₹(48 x 115) = ₹5520
% $\text{Return} = \Big(\frac{\text{Annual Inc.}}{\text{Investment}} \times 100\Big)$ %
$= \Big(\frac{240}{5520} \times 100\Big)$ %
$= \Big(\frac{2400}{552} \Big)$ %
$= \Big(\frac{100}{23} \Big)$ %
$= \bold{4\frac{8}{23}}$ %
A man has some shares of ₹100 par value paying 6% dividend. He sells half of these at a discount of 10% and invests the proceeds in 7% ₹50 shares at a premium of ₹10. This transaction decreases his income from dividends by ₹120.
Calculate:
(i) the number of shares before the transaction.
(ii) the number of shares he sold.
(iii) his initial annual income from shares.
Let the number of 6% ₹100 shares held by the man be x
Number of shares sold by the man = x/2
As the 6% ₹100 shares were at par,
∴ Nominal Value = Market Value = ₹100
As the shares were sold at a discount of 10%,
∴ Selling price of one share = ₹100 - 10% of ₹100 = ₹100 - ₹10 = ₹90
$$\begin{aligned}\therefore \text{Sales proceeds} = 90 \times \frac{x}{2} \\[0.5em] = ₹45x\end{aligned}$$
Market Value of 7% ₹50 shares at a premium of ₹10 = ₹50 + ₹10 = ₹60
Number of 7% ₹50 shares purchased by the man
$$\begin{aligned}= \frac{45x}{60} \\[0.5em] = \frac{3x}{4}\end{aligned}$$
Annual Income from previous shares = No. of shares x Rate of Dividend x Nominal Value per share
$$\begin{aligned}= x \times \frac{6}{100} \times 100 \\[0.5em] = \bold{₹6x}\end{aligned}$$
Annual Income from new shares = No. of shares x Rate of Dividend x Nominal Value per share
$$\begin{aligned}= \frac{3x}{4} \times \frac{7}{100} \times 50 \\[0.5em] = \bold{₹\frac{21x}{8}}\end{aligned}$$
New Annual Income = Annual income from (x/2) 6% ₹100 shares + Annual income from (3x/4) 7% ₹50 shares
$$\begin{aligned}= \frac{6x}{2} + \frac{21x}{8} \\[0.5em] = 3x + \frac{21x}{8} \\[0.5em] = \frac{24x + 21x}{8} \\[0.5em] = \frac{45x}{8}\end{aligned}$$
As per the given,
$$\begin{aligned}6x - \frac{45x}{8} = 120 \\[0.5em] \Rightarrow \frac{48x - 45x}{8} = 120 \\[0.5em] \Rightarrow \frac{3x}{8} = 120 \\[0.5em] \Rightarrow x = \frac{120 \times 8}{3} \\[0.5em] \Rightarrow x = 320 \\[0.5em]\end{aligned}$$
(i) Number of shares before the transaction = x = 320
(ii) Number of shares sold = x / 2 = 160
(iii) Initial Income = 6x = 6 x 320 = 1920
Divide ₹101520 into two parts such that if one part is invested in 8% ₹100 shares at 8% discount and the other in 9% ₹50 shares at 8% premium, the annual incomes are equal.
Let the investment in 8% ₹100 shares be ₹x, then the investment in 9% ₹50 shares = ₹(101520 - x)
8% ₹100 shares are at 8% discount
∴ Market Value of one 8% ₹100 share = ₹100 - 8% of ₹100 = ₹92
9% ₹50 shares are at 8% premium
∴ Market Value of one 9% ₹50 share = ₹50 + 8% of ₹50 = ₹54
$$\begin{aligned}\text{Income on 1 share of ₹92} = 8% \text{ of ₹100} = ₹8 \\[0.5em] \text{Income on ₹x} = ₹\frac{8}{92}x == ₹\frac{2}{23}x \\[0.5em] \text{Income on 1 share of ₹54} = 9% \text{ of ₹50} = ₹4.50 \\[0.5em] \text{Income on ₹(101520 - x)} = ₹\frac{4.5}{54}(101520 - x) = ₹\frac{101520 - x}{12} \\[0.5em]\end{aligned}$$
But the annual incomes from both the investments should be equal
$$\begin{aligned}\therefore \frac{2x}{23} = \frac{101520 - x}{12} \\[0.5em] \Rightarrow 24x = 2334960 - 23x \\[0.5em] \Rightarrow 47x = 2334960 \\[0.5em] \Rightarrow x = \frac{2334960}{47} \\[0.5em] \Rightarrow x = 49680 \\[0.5em] \therefore (101520 -x) = 101520 - 49680 = 51840\end{aligned}$$
∴ Investment in 8% ₹100 shares at ₹92 = ₹49680
and Investment in 9% ₹50 shares at ₹54 = ₹51840
A man buys ₹40 shares of a company which pays 10% dividend. He buys the shares at such a price that his profit is 16% on his investment. At what price did he buy each share?
Let the market value of 1 share be ₹x
Dividend on 1 share of ₹40 = 10% of ₹40 = ₹4
$$\begin{aligned}% \text{Return} = \Big(\frac{\text{Annual Inc.}}{\text{Investment}} \times 100\Big)% \\[0.5em]\end{aligned}$$
As per the given,
$$\begin{aligned}16 = \frac{4}{x} \times 100 \\[0.5em] x = \frac{4 \times 100}{16} \\[0.5em] x = 25\end{aligned}$$
∴ The man bought each share at ₹25
A person invested 20%, 30% and 25% of his savings in buying shares at par values of three different companies A, B and C which declare dividends of 10%, 12% and 15% respectively. If his total income on account of dividends be ₹4675, find his savings and the amount which he invested in buying shares of each company.
Let the savings of the person be ₹x.
Amount invested in company A
$$\begin{aligned}= \frac{20}{100}x \\[0.5em] = \frac{x}{5}\end{aligned}$$
Amount invested in company B
$$\begin{aligned}= \frac{30}{100}x \\[0.5em] = \frac{3x}{10}\end{aligned}$$
Amount invested in company C
$$\begin{aligned}= \frac{25}{100}x \\[0.5em] = \frac{x}{4}\end{aligned}$$
As shares are at par so Nominal Value and Market Value of shares are equal.
Dividend from company A
$$\begin{aligned}= \frac{10}{100} \times \frac{x}{5} \\[0.5em] = \frac{x}{50}\end{aligned}$$
Dividend from company B
$$\begin{aligned}= \frac{12}{100} \times \frac{3x}{10} \\[0.5em] = \frac{9x}{250}\end{aligned}$$
Dividend from company C
$$\begin{aligned}= \frac{15}{100} \times \frac{x}{4} \\[0.5em] = \frac{3x}{80}\end{aligned}$$
As per the given,
$$\begin{aligned}\frac{x}{50} + \frac{9x}{250} + \frac{3x}{80} = 4675 \\[0.5em] \Rightarrow \frac{40x + 72x + 75x}{2000} = 4675 \\[0.5em] \Rightarrow \frac{187x}{2000} = 4675 \\[0.5em] \Rightarrow x = \frac{2000 \times 4675}{187}\\[0.5em] \Rightarrow x = 50000 \\[1.5em] \text{Savings of the person} = \bold{₹50000} \\[0.5em] \text{Investment in company A shares} = \frac{x}{5} = \frac{50000}{5} = \bold{₹10000} \\[0.5em] \text{Investment in company B shares} = \frac{3x}{10} = \frac{3 \times 50000}{10} = \bold{₹15000} \\[0.5em] \text{Investment in company C shares} = \frac{x}{4} = \frac{50000}{4} = \bold{₹12500} \\[0.5em]\end{aligned}$$
Virat and Dhoni invest ₹36000 each in buying shares of two companies. Virat buys 15% ₹40 shares at a discount of 20%, while Dhoni buys ₹75 shares at a premium of 20%. If both receive equal dividends at the end of the year, find the rate percent of the dividend declared by Dhoni's company.
Total Investment of Virat = ₹36000
Nominal Value of Virat's shares = ₹40
As, Virat buys shares at 20% discount, Market Value of Virat's shares
$$\begin{aligned}= ₹40 - 20% \text{ of } ₹40 \\[0.5em] = ₹40 - ₹\Big(\frac{20}{100} \times 40 \Big) \\[0.5em] = ₹40 - ₹8 \\[0.5em] = ₹32\end{aligned}$$
No. of shares purchased by Virat
$$\begin{aligned}= \frac{36000}{32} \\[0.5em] = 1125\end{aligned}$$
Rate of Dividend of Virat's shares = 15%
Annual Dividend = No. of shares x Rate of Dividend x Nominal Value per share
Annual Dividend of Virat
$$\begin{aligned}= 1125 \times \frac{15}{100} \times 40 \\[0.5em] = ₹6750\end{aligned}$$
Let rate percent of the dividend declared by Dhoni's company be r%
Total Investment of Dhoni = ₹36000
Nominal Value of Dhoni's shares = ₹75
As, Dhoni buys shares at 20% premium, Market Value of Dhoni's shares
$$\begin{aligned}= ₹75 + 20% \text{ of } ₹75 \\[0.5em] = ₹75 + ₹\Big(\frac{20}{100} \times 75 \Big) \\[0.5em] = ₹75 + ₹15 \\[0.5em] = ₹90\end{aligned}$$
No. of shares purchased by Dhoni
$$\begin{aligned}= \frac{36000}{90} \\[0.5em] = 400\end{aligned}$$
Annual Dividend of Dhoni
$$\begin{aligned}= 400 \times \frac{r}{100} \times 75 \\[0.5em] = ₹300r\end{aligned}$$
As both Dhoni and Virat receive equal dividends,
$$\begin{aligned}\therefore 300r = 6750 \\[0.5em] \Rightarrow r = \frac{6750}{300} \\[0.5em] \Rightarrow r = 22.5\end{aligned}$$
∴ Rate percent of the dividend declared by Dhoni's company = 22.5%
A man invests ₹ 36,000 in 15% ₹ 100 shares at ₹ 120, when the market value of this shares rose to ₹ 200, he sold some shares to purchase a laptop worth ₹ 40,000. Calculate :
(i) the number of shares he still holds
(ii) the dividend he will get on these remaining shares.
(i) Given,
Investment amount = ₹ 36,000
Face value per share = ₹ 100
Market value per share = ₹ 120
Dividend = 15%
By formula,
Number of shares = $\frac{\text{Total investment}}{\text{Market value per share}} = \frac{36000}{120}$ = 300
Given,
The man sold some shares to purchase a laptop worth ₹ 40,000, when the shares price rose to ₹ 200. Let no. of shares sold be x.
⇒ x × 200 = 40000
⇒ x = $\frac{40000}{200}$ = 200.
Remaining shares = Total shares - sold shares
= 300 - 200 = 100.
Hence, the number of shares he still holds = 100.
(ii) By formula,
Annual dividend = Number of shares x Dividend rate x face value of share
= 100 x $\frac{15}{100}$ x 100
= ₹ 1,500
Hence, the dividend the man will get on the remaining shares = ₹ 1,500.
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