ICSE Class 10 Mathematics · Selina Concise Mathematics · 62 solved questions
The money required to buy 50, ₹ 20 shares at 10% premium is :
Given,
N.V. of share = ₹ 20
M.V. of share = N.V. + Premium = ₹ 20 + $\frac{10}{100} \times 20$ = ₹ 20 + ₹ 2 = ₹ 22.
By formula,
Money required to buy shares = No. of shares × M.V. of each share
= 50 × ₹ 22
= ₹ 1,100.
Hence, Option 2 is the correct option.
The money required to buy 50, ₹ 20 shares at ₹ 10 discount is :
Given,
N.V. of share = ₹ 20
M.V. of share = N.V. - Discount = ₹ 20 - ₹ 10 = ₹ 10.
By formula,
Money required to buy shares = No. of shares × M.V. of each share
= 50 × ₹ 10
= ₹ 500.
Hence, Option 3 is the correct option.
The money required to buy 50, ₹ 20 shares quoted at ₹ 22 is :
Given,
M.V. of share = ₹ 22
By formula,
Money required to buy shares = No. of shares × M.V. of each share
= 50 × ₹ 22
= ₹ 1100.
Hence, Option 1 is the correct option.
₹ 200 shares are available at a discount of 20%. The market price of 50 shares is :
Given,
N.V. of each share = ₹ 200
Discount % = 20%
M.V. of each share = N.V. - Discount = ₹ 200 - $\frac{20}{100} \times 200$ = ₹ 200 - ₹ 40 = ₹ 160.
Market price of 50 shares = 50 × Market price of each share
= 50 × ₹ 160
= ₹ 8000.
Hence, Option 2 is the correct option.
500, ₹ 50 shares at par earn a dividend of ₹ 1250 in one year. The rate of dividend is :
Given,
N.V. = ₹ 50
No. of shares = 500
Dividend = ₹ 1250
By formula,
Dividend = No. of shares × Rate of dividend × N.V. of share
Let rate of dividend be x%.
Substituting values we get :
$$\begin{aligned}\Rightarrow 1250 = 500 \times x% \times 50 \\[1em] \Rightarrow 1250 = 500 \times \frac{x}{100} \times 50 \\[1em] \Rightarrow x = \frac{1250 \times 100}{500 \times 50} \\[1em] \Rightarrow x = \frac{125000}{25000} \\[1em] \Rightarrow x = 5.\end{aligned}$$
Rate of dividend = 5%.
Hence, Option 4 is the correct option.
A man invested in a company paying 12% dividend on its share. If the percentage return on his investment is 10%, then the shares are :
Given,
Dividend rate = 12% of face value.
So, if face value = ₹100, dividend = ₹12.
Return = 10%
By formula,
Return % = $\frac{\text{Dividend on one share}}{\text{Investment on one share}} \times 100$
Investment on one share equals to the market value of the share.
Substituting values we get :
⇒ 10 = $\frac{12}{\text{Market value}}$ × 100
⇒ Market value = $\frac{12}{10}$ × 100
⇒ Market value = ₹ 120.
Since market value > face value, the shares are said to be above par.
Hence, Option 3 is the correct option.
How much money will be required to buy 400, ₹ 12.50 shares at a premium of ₹ 1?
No. of shares to be bought = 400.
₹ 12.50 shares at a premium of ₹ 1 means; nominal value of the share is ₹ 12.50 and its market value = ₹ 12.50 + ₹ 1 = ₹ 13.50
∴ Money required to buy 400 shares = 400 × ₹ 13.50 = ₹ 5,400.
Hence, money required to buy 400 shares = ₹ 5,400.
How much money will be required to buy 250, ₹ 15 shares at a discount of ₹ 1.50 ?
No. of shares to be bought = 250.
₹ 15 shares at a discount of ₹ 1.50 means; nominal value of the share is ₹ 15 and its market value = ₹ 15 - ₹ 1.50 = ₹ 13.50
∴ Money required to buy 250 shares = 250 × ₹ 13.50 = ₹ 3,375.
Hence, money required to buy 250 shares = ₹ 3,375.
Find the annual income derived from 125, ₹ 120 shares paying 5% dividend.
Annual income = No. of shares × Rate of div. × N.V. of 1 share
= $125 × \frac{5}{100} \times 120$
= ₹ 750.
Hence, annual income = ₹ 750.
A man invests ₹ 3,072 in a company paying 5% per annum, when its ₹ 10 share can be bought for ₹ 16 each. Find :
(i) his annual income
(ii) his percentage income on his investment.
(i) Man invests ₹ 3,072 and M.V. of each share = ₹ 16
No. of shares bought = $\frac{3072}{16}$ = 192.
Annual income = No. of shares × Rate of div. × N.V. of 1 share
= $192 × \frac{5}{100} \times 10$
= ₹ 96.
His total annual income = ₹ 96.
(ii) Percentage income = $\frac{96}{3072} \times 100 = \frac{9600}{3072}$ = 3.125%.
Hence, percentage income = 3.125%.
A man invests ₹ 7,770 in a company paying 5 percent dividend when a share of nominal value of ₹ 100 sells at a premium of ₹ 5. Find :
(i) the number of shares bought;
(ii) annual income;
(iii) percentage income.
Total money invested = ₹ 7,770
Market value = ₹ 100 + ₹ 5 = ₹ 105
(i) No. of shares bought = $\frac{7770}{105}$ = 74.
Hence, no. of shares bought = 74.
(ii) Annual income = No. of shares × Rate of div. × N.V. of 1 share
= $74 × \frac{5}{100} \times 100$
= ₹ 370.
His total annual income = ₹ 370.
(iii) Percentage income = $\frac{370}{7770} \times 100 = \frac{37000}{7770}$ = 4.76%.
Hence, percentage income = 4.76%.
A man buys ₹ 50 shares of a company, paying 12 percent dividend, at a premium of ₹ 10. Find :
(i) the market value of 320 shares;
(ii) his annual income;
(iii) his profit percent.
(i) Market value of 1 share = ₹ 50 + ₹ 10 = ₹ 60.
∴ Market value of 320 shares = 320 × ₹ 60 = ₹ 19,200.
Hence, market value of 320 shares = ₹ 19,200.
(ii) Annual income = No. of shares × Rate of div. × N.V. of 1 share
= $320 × \frac{12}{100} \times 50$
= ₹ 1,920.
His total annual income = ₹ 1,920.
(iii) Profit % = $\frac{1920}{19200} \times 100 = \frac{192000}{1920}$ = 10%.
Hence, profit % = 10%.
A man invests ₹ 8,800 in buying shares of a company of face value of rupees hundred each at a premium of 10 %. If he earns ₹ 1,200 at the end of the year as dividend, find :
(i) the number of shares he has in the company.
(ii) the dividend percent per share.
(i) F.V. = ₹ 100
Premium = 10 % = $\frac{10}{100} \times 100$ = ₹ 10.
Market value = ₹ 100 + ₹ 10 = ₹ 110.
Investment = ₹ 8,800
No. of shares = $\frac{8800}{110}$ = 80.
Hence, the no. of shares = 80.
(ii) Annual income = No. of shares × Rate of div. × N.V. of 1 share
Let dividend percent = x%,
1200 = $80 × \frac{x}{100} \times 100$
1200 = 80x
x = $\frac{1200}{80} = 15$%.
Hence, dividend percent per share = 15%.
A man invests ₹ 3,360 in buying shares of nominal value ₹ 24 and selling at 12% premium. The dividend on the shares is 15% per annum. Calculate:
(i) the number of shares he buys;
(ii) the dividend he receives annually.
(i) F.V. = ₹ 24
Premium = 12% = $\frac{12}{100} \times 24$ = ₹ 2.88.
Market value = ₹ 24 + ₹ 2.88 = ₹ 26.88
Investment = ₹ 3,360
No. of shares = $\frac{3,360}{26.88}$ = 125.
Hence, the no. of shares = 125.
(ii) By formula,
Annual income = No. of shares × Rate of div. × N.V. of 1 share
= $125 × \frac{15}{100} \times 24$
= ₹ 450.
Hence, dividend received annually = ₹ 450.
By investing ₹ 7,500 in a company paying 10 percent dividend, an annual income of ₹ 500 is received. What price is paid for each of ₹ 100 share ?
Let x be price paid for each share.
No. of shares = $\frac{7500}{x}$
Annual income = No. of shares × Rate of div. × N.V. of 1 share
$$\begin{aligned}\Rightarrow 500 = \frac{7500}{x} × \frac{10}{100} \times 100 \\[1em] \Rightarrow x = \frac{75000}{500} = 150.\end{aligned}$$
Hence, price paid for ₹ 100 share = ₹ 150.
The number of ₹ 25 shares, paying 24% dividend, with total dividend ₹ 1,350 is :
Given,
Dividend = ₹ 1350
N.V. of share = ₹ 25
Rate of dividend = 24%
Let no. of shares be n.
By formula,
Dividend = No. of shares × Rate of dividend × N.V. of share
Substituting values we get :
$$\begin{aligned}\Rightarrow 1350 = n \times 24% \times 25 \\[1em] \Rightarrow 1350 = n \times \frac{24}{100} \times 25 \\[1em] \Rightarrow n = \frac{1350 \times 100}{24 \times 25} \\[1em] \Rightarrow n = \frac{1350}{6} = 225.\end{aligned}$$
Hence, Option 3 is the correct option.
₹ 600 shares of a company are available at a discount of 20%. If the company pays a dividend of 20%, the rate of return is :
Given,
N.V. of share = ₹ 600
Discount = 20%
M.V. = N.V. - Discount
= ₹ 600 - 20%
= ₹ 600 - $\frac{20}{100} \times 600$
= ₹ 600 - ₹ 120 = ₹ 480.
Dividend = 20%
Let rate of return be r%.
We know that,
Interest on M.V. = Dividend on N.V.
r% of ₹ 480 = 20% of ₹ 600
$$\begin{aligned}\Rightarrow \frac{r}{100} \times 480 = \frac{20}{100} \times 600 \\[1em] \Rightarrow 4.8r = 120 \\[1em] \Rightarrow r = \frac{120}{4.8} \\[1em] \Rightarrow r = 25%.\end{aligned}$$
Hence, Option 2 is the correct option.
100 shares at par value of ₹ 120 each, give 10% half-yearly dividend. The annual dividend from these shares is :
Given,
Dividend % = 10% half-yearly or 20% yearly.
N.V. = ₹ 120
No. of shares = 100
By formula,
Dividend = No. of shares × Rate of dividend × N.V. of share
Substituting values we get :
$$\begin{aligned}\text{Dividend} = 100 \times 20% \times 120 \\[1em] = 100 \times \frac{20}{100} \times 120 \\[1em] = ₹ 2400.\end{aligned}$$
Hence, Option 2 is the correct option.
Amit invested a certain amount of money in ₹ 100 shares, paying a 7.5% dividend. The rate of return on his investment is 10%. The money invested by Amit to purchase 10 shares is :
Let ₹ P be the price per share.
Amit brought 10 shares, so total investment = ₹ 10P
Dividend = 7.5%
Dividend per share = $\frac{7.5}{100} \times 100$ = ₹ 7.5
Total dividend = ₹ 7.5 × 10 = ₹ 75.
Rate of return = 10%
By formula,
Rate of return × Investment = Dividend
$$\begin{aligned}\Rightarrow 10% \times 10P = 75 \\[1em] \Rightarrow \frac{10}{100} \times 10P = 75 \\[1em] \Rightarrow \frac{100P}{100} = 75 \\[1em] \Rightarrow P = ₹ 75.\end{aligned}$$
Total investment = 10P = 10 × ₹75 = ₹750.
Hence, Option 2 is the correct option.
200 ₹ 20 shares, each available at a discount of 20%, give 10% dividend. The rate of return is :
Given,
Dividend = 10%
N.V. = ₹ 20
Discount = 20%
M.V. = N.V. - Discount
= ₹ 20 - 20%
= ₹ 20 - $\frac{20}{100} \times 20$
= ₹ 20 - ₹ 4 = ₹ 16.
Dividend = 10%
Let rate of return/interest be r%.
We know that,
Interest on M.V. = Dividend on N.V.
r% of 16 = 10% of 20
$$\begin{aligned}\Rightarrow \frac{r}{100} \times 16 = \frac{10}{100} \times 20 \\[1em] \Rightarrow r = \frac{10 \times 20}{16} \\[1em] \Rightarrow r = \frac{200}{16} \\[1em] \Rightarrow r = 12.5%\end{aligned}$$
Hence, Option 1 is the correct option.
By purchasing ₹ 25 gas shares for ₹ 40 each, a man gets 4 percent profit on his investment. What rate percent is the company paying ? What is his dividend if he buys 60 shares?
Profit = 4% = $\frac{4}{100} \times 40 = 1.6$
Let company be paying x% dividend.
As,
Annual income = No. of shares × Rate of div. × N.V. of 1 share
⇒ 1.6 = 1 × $\frac{x}{100}$ × 25
⇒ x = $\frac{160}{25}$ = 6.4%.
For 60 shares dividend = 60 $\times \frac{6.4}{100} \times 25$ = ₹ 96.
Hence, rate paid by company = 6.4% and dividend = ₹ 96.
Hundred rupee shares of a company are available in the market at a premium of ₹ 20. Find the rate of dividend given by the company when a man's return on his investment is 15 percent.
We know that,
Rate of dividend × N.V. = Profit (return) % × M.V.
Market value = ₹ 100 + ₹ 20 = ₹ 120.
Let rate of dividend be x%
$$\begin{aligned}\Rightarrow \frac{x}{100} \times 100 = \frac{15}{100} \times 120 \\[1em] \Rightarrow x = 18%.\end{aligned}$$
Hence, rate of dividend = 18%.
₹ 50 shares of a company are quoted at a discount of 10%. Find the rate of dividend given by the company, the return on the investment on these shares being 20 percent.
We know that,
Rate of dividend × N.V. = Profit (return) % × M.V.
Market value = ₹ 50 - ₹ $\frac{10}{100} \times 50$ = ₹ 50 - ₹ 5 = ₹ 45.
Let rate of dividend be x%
$$\begin{aligned}\Rightarrow \frac{x}{100} \times 50 = \frac{20}{100} \times 45 \\[1em] \Rightarrow x = \frac{20 \times 45}{50} \\[1em] \Rightarrow x = 18%\end{aligned}$$
Hence, rate of dividend = 18%.
How much should a man invest in ₹ 100 shares selling at ₹ 110 to obtain an annual income of ₹ 1,680, if the dividend declared is 12% ?
Let man invest ₹ x
∴ No. of shares = $\frac{x}{110}$
We know that,
Annual income = No. of shares × Rate of div. × N.V. of 1 share
$$\begin{aligned}\Rightarrow 1680 = \frac{x}{110} \times \frac{12}{100} \times 100 \\[1em] \Rightarrow x = \frac{1680 \times 110}{12} \\[1em] \Rightarrow x = 15,400\end{aligned}$$
Hence, investment = ₹ 15,400.
A company declares a dividend of 11.2% to all its share-holders. If its ₹ 60 share is available in the market at a premium of 25%, how much should Rakesh invest, in buying the shares of this company, in order to have an annual income of ₹ 1,680?
Let man invest ₹ x
Market value = ₹ 60 + $\frac{25}{100} \times 60$ = ₹ 60 + ₹ 15 = ₹ 75
∴ No. of shares = $\frac{x}{75}$
We know that,
Annual income = No. of shares × Rate of div. × N.V. of 1 share
$$\begin{aligned}\Rightarrow 1680 = \frac{x}{75} \times \frac{11.2}{100} \times 60 \\[1em] \Rightarrow x = \frac{1680 \times 100 \times 75}{11.2 \times 60} \\[1em] \Rightarrow x = 18,750\end{aligned}$$
Hence, investment = ₹ 18,750.
A man buys 400, twenty-rupee shares at a premium of ₹ 4 each and receives a dividend of 12%. Find :
(i) the amount invested by him
(ii) his total income from the shares
(iii) percentage return on his money.
(i) Market value = ₹ 20 + ₹ 4 = ₹ 24.
Amount invested = 400 × ₹ 24 = ₹ 9,600
Hence, amount invested = ₹ 9,600.
(ii) Annual income = No. of shares × Rate of div. × N.V. of 1 share
= 400 × $\frac{12}{100} \times 20$
= ₹ 960.
Hence, annual income = ₹ 960.
(iii) Percentage return = $\frac{\text{Income}}{\text{Investment}} \times 100 = \frac{960}{9600} \times 100$ = 10%.
Hence, percentage return = 10%.
A company with 10,000 shares of ₹ 100 each, declares an annual dividend of 5%.
(i) What is the total amount of dividend paid by the company ?
(ii) What should be the annual income of a man who has 72 shares in the company ?
(iii) If he received only 4% of his investment, find the price he paid for each share.
(i) Dividend = No. of shares × Rate of div. × N.V. of 1 share
= 10,000 × $\frac{5}{100} \times 100$
= ₹ 50,000.
Hence, total dividend = ₹ 50,000.
(ii) Annual income = No. of shares × Rate of div. × N.V. of 1 share
= 72 × $\frac{5}{100} \times 100$
= ₹ 360.
Hence, annual income of man = ₹ 360.
(iii) Let investment be ₹ x.
Given return % = 4%.
$$\begin{aligned}\therefore 4 = \frac{360}{x} \times 100 \\[1em] \Rightarrow x = \frac{36000}{4} = 9,000.\end{aligned}$$
Price paid for each share = $\frac{\text{Investment}}{\text{No. of shares}} = \frac{9000}{72} = 125.$
Hence, price of each share = ₹ 125.
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 is the return she gets as percent on her investment?
Give your answer to nearest integer.
Market value = ₹ 100 + ₹ $\frac{40}{100} \times 100$ = ₹ 100 + ₹ 40 = ₹ 140.
Annual Dividend = No. of shares × Rate of div. × N.V. of 1 share
= 1800 × $\frac{15}{100} \times 100$
= ₹ 27,000.
Investment = No. of shares × M.V. = 1800 × ₹ 140 = ₹ 2,52,000.
Return % = $\frac{\text{Dividend}}{\text{Investment}} \times 100 = \frac{27000}{252000} \times 100 =$ 10.71% ≈ 11%.
Hence, annual dividend = ₹ 27,000 and return % = 11%.
Mr. Sharma has 60 shares of N.V. ₹ 100 and sells them when they are at a premium of 60%. He invests the proceeds in shares of nominal value ₹ 50, quoted at 4% discount, and paying 18% dividend annually. Calculate :
(i) the sale proceeds
(ii) the number of shares he buys; and
(iii) his annual dividend from the shares.
(i) Market value of initial shares = ₹ 100 + $\frac{60}{100} \times 100$ = ₹ 100 + ₹ 60 = ₹ 160.
Sale proceeds = 60 × ₹ 160 = ₹ 9,600.
Hence, sale proceeds = ₹ 9,600.
(ii) M.V. of second shares = ₹ 50 - $\frac{4}{100} \times 50$ = ₹ 50 - ₹ 2 = ₹ 48.
No. of shares = $\frac{9600}{48}$ = 200.
Hence, no. of shares = 200.
(iii) Annual dividend = No. of shares × Rate of div. × N.V. of 1 share
= 200 × $\frac{18}{100} \times 50$
= ₹ 1,800.
Hence, annual dividend = ₹ 1,800.
A company with 10,000 shares of nominal value ₹ 100 declares an annual dividend of 8% to the share-holders.
(i) Calculate the total amount of dividend paid by the company.
(ii) Ramesh had bought 90 shares of the company at ₹ 150 per share. Calculate dividend he receives and percentage return on his investment.
(i) Annual dividend = No. of shares × Rate of div. × N.V. of 1 share
= 10,000 × $\frac{8}{100} \times 100$
= ₹ 80,000.
Hence, annual dividend paid by company = ₹ 80,000.
(ii) Investment = 90 × ₹ 150 = ₹ 12,500
Annual dividend = No. of shares × Rate of div. × N.V. of 1 share
= 90 × $\frac{8}{100} \times 100$
= ₹ 720.
Return% = $\frac{\text{Annual dividend}}{\text{Investment}} \times 100 = \frac{720}{12500} \times 100 = 5\frac{1}{3}$%
Hence, dividend received by Ramesh = ₹ 720 and return % = $5\frac{1}{3}$%.
Which is better investment : 16% of ₹ 100 shares at 80 or 20% ₹ 100 shares at 120?
Since, Profit% on M.V. = Dividend% on N.V.
In first case :
P% on ₹ 80 = 16% on ₹ 100
$$\begin{aligned}\Rightarrow \frac{P}{100} \times 80 = \frac{16}{100} \times 100 \\[1em] \Rightarrow P = \frac{16}{80} \times 100 = 20%.\end{aligned}$$
In second case :
P% on ₹ 120 = 20% on ₹ 100
$$\begin{aligned}\Rightarrow \frac{P}{100} \times 120 = \frac{20}{100} \times 100 \\[1em] \Rightarrow P = \frac{20}{120} \times 100 = 16\frac{4}{6}%.\end{aligned}$$
Hence, 16% of ₹ 100 shares at 80 is the better investment.
A man has a choice to invest in hundred-rupee shares of two firms at ₹ 120 or at ₹ 132. The first firm pays a dividend of 5% per annum and the second firm pays a dividend of 6% per annum. Find :
(i) which company is giving a better return.
(ii) if a man invests ₹26,400 with each firm, how much will be the difference between the annual returns from the two firms ?
(i) First company's dividend = 5% and second company's = 6%.
∴ Second company is giving a better return.
(ii) No. of shares of first company = $\frac{26400}{120} = 220$
Annual income = No. of shares × Rate of div. × N.V. of 1 share
= 220 × $\frac{5}{100} \times 100$
= ₹ 1,100.
No. of shares of second company = $\frac{26400}{132} = 200$
Annual income = No. of shares × Rate of div. × N.V. of 1 share
= 200 × $\frac{6}{100} \times 100$
= ₹ 1,200.
Difference between annual returns = ₹ 1200 - ₹ 1100 = ₹ 100.
Hence, difference between annual returns of two firms = ₹ 100.
A man bought 360, ten-rupee shares of a company, paying 12 percent per annum. He sold shares when their price rose to ₹ 21 per share and invested the proceeds in five-rupee shares paying 4.5 percent per annum at ₹ 3.50 per share. Find annual change in his income.
In first case :
Annual income = No. of shares × Rate of div. × N.V. of 1 share
= 360 × $\frac{12}{100} \times 10$
= ₹ 432
S.P. of shares = 360 × ₹ 21 = ₹ 7,560
M.V. of second shares = ₹ 3.50
No. of shares purchased = $\frac{\text{Investment}}{\text{M.V. of share}} = \frac{7560}{3.5}$ = 2160.
Annual income = No. of shares × Rate of div. × N.V. of 1 share
= 2160 × $\frac{4.5}{100} \times 5$
= ₹ 486.
Change in income = ₹ 486 - ₹ 432 = ₹ 54.
Hence, the change in income = ₹ 54 (increase).
Two brothers A and B invest ₹ 16,000 each in buying shares of two companies. A buys 3% hundred rupee shares at 80 and B buys ten-rupee shares at par. If they both receive equal dividend at the end of the year, find the rate percent of the dividend received by B.
For A,
M.V. of shares = 80
Investment = ₹ 16,000
No. of shares = $\frac{16000}{80}$ = 200.
Annual income = No. of shares × Rate of div. × N.V. of 1 share
= 200 × $\frac{3}{100} \times 100$
= ₹ 600.
For B,
M.V. of shares = 10
Investment = ₹ 16,000
No. of shares = $\frac{16000}{10}$ = 1600.
Let rate of dividend be x%
Annual income = No. of shares × Rate of div. × N.V. of 1 share
$$\begin{aligned}\Rightarrow 600 = 1600 \times \frac{x}{100} \times 10 \\[1em] \Rightarrow x = \frac{600 \times 100}{1600 \times 10} \\[1em] \Rightarrow x = \frac{60000}{16000} = 3.75%\end{aligned}$$
Hence, the rate percent of the dividend received by B = 3.75%.
A company pays 18% dividend and its ₹ 100 share is available at a premium of 20%. The number of shares bought for ₹ 7,200 is :
N.V. of share = ₹ 100
Premium = 20%
M.V. of share = N.V. + premium
= ₹ 100 + 20%
= ₹ 100 + $\frac{20}{100} \times 100$
= ₹ 100 + ₹ 20 = ₹ 120.
No. of shares bought = $\frac{\text{Sum invested}}{\text{M.V.}} = \frac{7200}{120}$ = 60.
Hence, Option 3 is the correct option.
100, ₹ 100 shares (paying 10% dividend) are brought at a discount of ₹ 20 and another 100, ₹ 100 shares (paying 10% dividend) are brought at ₹ 120. The total dividend earned is :
For 1st share :
N.V. = ₹ 100
Dividend % = 10%
No. of shares = 100
Dividend = No. of shares × Dividend % × N.V.
= 100 × 10% × 100
= 100 × $\frac{10}{100} \times$ 100
= ₹ 1000.
For 2nd share :
N.V. = ₹ 100
Dividend % = 10%
No. of shares = 100
Dividend = No. of shares × Dividend % × N.V.
= 100 × 10% × 100
= 100 × $\frac{10}{100} \times$ 100
= ₹ 1000.
Total dividend = ₹ 1000 + ₹ 1000 = ₹ 2000.
Hence, Option 2 is the correct option.
The money required, to buy 80 shares, each of ₹ 60 and quoted at ₹ 70, is :
Given,
M.V. of share = ₹ 70
No. of shares = 80
Sum required = No. of shares × M.V.
= 80 × ₹ 70 = ₹ 5600.
Hence, Option 1 is the correct option.
₹ 20,000 is spent in buying ₹ 50 shares with dividend 5%. The dividend earned is :
Given,
N.V. of each share = ₹ 50
Sum invested = ₹ 20,000
No. of shares bought = $\frac{\text{Sum invested}}{\text{N.V. of each share}} = \frac{20,000}{50}$ = 400.
By formula,
Dividend = No. of shares × Dividend % × N.V.
= 400 × 5% × 50
= $400 \times \frac{5}{100} \times 50$
= ₹ 1000.
Hence, Option 1 is the correct option.
Each of ₹ 500 shares is available at a discount of ₹ 100. If the dividend on these shares is 8%, the income percent is :
Given,
N.V. of each share = ₹ 500
Discount = ₹ 100
M.V. = N.V. - Discount
= ₹ 500 - ₹ 100 = ₹ 400.
Dividend = 8%
Let income percent be r%.
By formula,
Income percent on M.V. = Dividend on N.V.
Substituting values we get :
r% of 400 = 8% of 500
$$\begin{aligned}\Rightarrow \frac{r}{100} \times 400 = \frac{8}{100} \times 500 \\[1em] \Rightarrow 4r = 40 \\[1em] \Rightarrow r = \frac{40}{4} = 10%.\end{aligned}$$
Hence, Option 4 is the correct option.
Investing in 16% ₹ 100 shares at ₹ 80 or in 20% ₹100 shares at ₹120.
Assertion (A): It is better to invest in 16% ₹ 100 shares at ₹ 80.
Reason (R): Return % from the shares = $\frac{\text{Income}}{\text{Investment}} \times 100%$.
Both A and R are true and R is correct reason for A.
Reason
Face value of the 1st share = ₹ 100
Dividend rate = 16%
Market value = ₹ 80
Dividend (or income) per share = Dividend rate x face value of each share
= 16% of 100 = $\frac{16}{100}$ x 100 = ₹ 16
Rate of return = $\frac{\text{Annual income on 1 share}}{\text{Investment on 1 share}}$ x 100
= $\frac{16}{80}$ x 100 = 20%
Face value of second share = ₹ 100
Dividend rate = 20%
Market value = ₹ 120
Dividend (or income) per share = Dividend rate x face value of each share
= 20% of 100 = $\frac{20}{100}$ x 100 = ₹ 20
Rate of return = $\frac{\text{Annual income on 1 share}}{\text{Investment on 1 share}}$ x 100
= $\frac{20}{120}$ x 100 = 16.66%
The scheme that offers a higher rate of return is considered better. And, rate of return in first scheme is 20% and that of second scheme is 16.66%.
So, Assertion (A) is true.
Rate of return = $\frac{\text{Annual income on 1 share}}{\text{Investment on 1 share}}$ x 100
= $\frac{\text{Income}}{\text{Investment}}$ x 100
The given formula for rate of return is true.
So, Reason (R) is true.
Hence, option 3 is correct.
₹ 50 shares of a company are bought by John at 20% discount and sold at the gain of 25%.
Assertion (A): The net gain on each share is 5%.
Reason (R): The selling price of each share = $₹ 50 \times \frac{80}{100} \times \frac{125}{100}$.
A is false, R is true.
Reason
Face value of share = ₹ 50
Discount = 20%
Discounted value = 20% of ₹ 50 = $\frac{20}{100} \times 50$ = ₹ 10
Discounted price = ₹ 50 - ₹ 10 = ₹ 40
Gain = 25%
Selling price = ₹ 40 + 25% of ₹ 40
= ₹ 40 + $\frac{25}{100} \times 40$ = ₹ (40 + 10) = ₹ 50
Gain = ₹ 50 - ₹ 40 = ₹ 10
Gain % = $\frac{\text{Gain}}{\text{CP}} \times 100$
= $\frac{10}{40} \times 100$ = 25%
So, Assertion (A) is false.
As per the Reason (R),
The selling price of each share = $₹ 50 \times \frac{80}{100} \times \frac{125}{100}$
$$\begin{aligned}= ₹ (50 \times 0.8 \times 1.25) \\[1em] = ₹ 50\end{aligned}$$
This is equal to the selling price computed above.
So, Reason (R) is true.
Hence, option 2 is correct.
₹ 2,250 is invested in buying ₹ 50 shares available at 10% discount and the dividend paid by the company is 12%.
Statement (1) : Number of shares bought = $\frac{2,250}{45}$ = 50
Statement (2) : Total dividend paid by the company = (12% of ₹ 50) x 50
Both the statements are true.
Reason
Total investment = ₹ 2,250
Discount on shares = 10%
Dividend rate = 12%
Face value of each share = ₹50
Discounted value = 10% of ₹50
= $\frac{10}{100} \times 50$ = ₹ 5
Discounted price = ₹ 50 - 5 = ₹ 45
And, number of shares = $\frac{\text{Total Investment}}{\text{Market Value of 1 share}}$
= $\frac{2,250}{45}$ = 50
So, statement 1 is true.
The annual dividend = number of shares x rate of dividend x face value of one share
= 50 x 12% x 50
= (12% of ₹ 50) x 50
So, statement 2 is true.
Hence, option 1 is correct.
100 shares are bought at ₹ 60 per share and the dividend received is ₹ 600.
Statement (1) : Rate of return x ₹ 60 x 100 = ₹ 600
Statement (2) : Rate of return x Market value = Dividend received on each share
Both the statements are true.
Reason
Number of shares bought = 100
Price per share = ₹60
Total dividend received = ₹600
Rate of return = $\frac{\text{Annual income}}{\text{Investment}}$
= $\frac{\text{Annual income}}{\text{No. of shares} \times \text{price per share}}$
⇒ Rate of return = $\frac{600}{100 \times 60}$
⇒ Rate of return x 60 x 100 = 600
So, statement 1 is true.
Rate of return = $\frac{\text{Annual income}}{\text{No. of shares} \times \text{price per share}}$
⇒ Rate of return x Price per share = $\frac{\text{Annual income}}{\text{No. of shares}}$
⇒ Rate of return x Market value = Dividend received on each share
So, statement 2 is true.
Hence, option 1 is correct.
Ankit had the option of investing in company A, where 7% ₹ 100 shares are available at ₹ 120 or in company B, where 8%, ₹ 1000 shares are available at ₹ 1620.
Statement (1) : Investment in company B is better than company A.
Statement (2) : Yield % of company B is better than in company A.
For company A :
Dividend = 7%
N.V. = ₹ 100
M.V = ₹ 120
Dividend per share = 7% of N.V.
= $\frac{7}{100} \times 100$ = ₹ 7
⇒ Rate of return = $\frac{\text{Dividend earned on 1 share}}{\text{Market Value of one share}} \times 100$
= $\frac{7}{120} \times 100$ = 5.83%
For company B :
Dividend = 8%
N.V. = ₹ 1000
M.V = ₹ 1620
Dividend per share = 8% of N.V.
= $\frac{8}{100} \times 1000$ = ₹ 80
⇒ Rate of return = $\frac{\text{Dividend earned on 1 share}}{\text{Market Value of one share}} \times 100$
= $\frac{80}{1620} \times 100$ = 4.94%
Investment in company B is better than A. This is false, because A gives higher yield.
So, statement 1 is false.
Yield of company B is better than A.
Company A gives better return that is 5.83%.
So, statement 2 is false.
Hence, option 2 is correct.
By investing ₹ 45,000 in 10% ₹ 100 shares, Sharad gets ₹ 3,000 as dividend. Find the market value of share.
Let market value of share be x.
∴ No. of share = $\frac{45000}{x}$
Annual dividend = No. of shares × Rate of div. × N.V. of 1 share
$$\begin{aligned}\therefore 3000 = \frac{45000}{x} \times \frac{10}{100} \times 100 \\[1em] \Rightarrow x = \frac{450000}{3000} \\[1em] \Rightarrow x = 150\end{aligned}$$
Hence, M.V. of share = ₹ 150.
Mrs. Kulkarni invests ₹ 1,31,040 in buying ₹ 100 shares at a discount of 9%. She sells shares worth ₹ 72,000 at a premium of 10% and the rest at a discount of 5%. Find her total gain or loss on the whole.
Investment = ₹ 1,31,040
N.V. of 1 share = ₹ 100
Discount = 9% of ₹ 100 = ₹ 9
∴ M.V. of 1 share = ₹ 100 - ₹ 9 = ₹ 91
∴ No. of shares purchased = $\frac{\text{Investment}}{\text{M.V. of 1 share}} = \frac{131040}{91}$ = 1440
No. of shares worth ₹ 72,000 = $\frac{72000}{100} = 720$
∴ Mrs. Kulkarni sells 720 shares at a premium of 10%
M.V. of 1 share = ₹ 100 + ₹ 10 = ₹ 110
∴ Selling price of 720 shares = 720 × ₹ 110 = ₹ 79,200
No. of remaining shares = 1440 - 720 = 720.
She sells 720 shares at a discount of 5%
M.V. of 1 share = ₹ 100 - ₹ 5 = ₹ 95
∴ Selling price of 720 shares = 720 × ₹ 95 = ₹ 68,400
∴ Total selling price = ₹ 79,200 + ₹ 68,400 = ₹ 1,47,600
∴ Total gain = Total selling price - Total investment = ₹ 1,47,600 - ₹ 1,31,040 = ₹ 16,560.
Hence, total gain = ₹ 16,560.
A man invests a certain sum in buying 15% ₹ 100 shares at 20% premium. Find :
(i) his income from one share
(ii) the number of shares bought to have an income, from the dividend, ₹ 6,480.
(iii) sum invested.
(i) Dividend on 1 share = $\frac{15}{100} \times 100$ = ₹ 15.
Hence, the income from one share is ₹ 15.
(ii) Number of shares bought = $\frac{\text{Annual income}}{\text{Div. on 1 share}} = \frac{6480}{15} =$ 432.
Hence, the number of shares bought = 432.
(iii) M.V. = ₹ 100 + ₹ $\frac{20}{100} \times 100$ = ₹ 100 + ₹ 20 = ₹ 120.
Total investment = No. of shares × M.V. = 432 × ₹ 120 = ₹ 51,840.
Hence, sum invested = ₹ 51,840.
Ashwarya bought 496, ₹ 100 shares at ₹ 132 each. Find :
(i) investment made by her.
(ii) income of Ashwarya from these shares, if rate of dividend is 7.5%
(iii) how much extra must Ashwarya invest in order to increase her income by ₹ 7,200?
(i) M.V. = ₹ 132
Investment = 496 × ₹ 132 = ₹ 65,472
Hence, investment made by Ashwarya = ₹ 65,472.
(ii) Dividend = No. of shares × Rate of div. × N.V. of 1 share
= 496 × $\frac{7.5}{100} \times 100$
= ₹ 3,720.
Hence, income of Ashwarya = ₹ 3,720.
(iii) Dividend on 1 share = 1 × $\frac{7.5}{100} \times 100$ = 7.5
No. of shares to buy in order to increase income by 7200 = $\frac{7200}{7.5} = 960$
Investment = 960 × 132 = ₹ 1,26,720.
Hence, investment required = ₹ 1,26,720.
Gopal has some ₹ 100 shares of company A, paying 10% dividend. He sells a certain number of these shares at a discount of 20% and invests the proceeds in ₹ 100 shares at ₹ 60 of company B paying 20% dividend. If his income, from the shares sold, increases by ₹ 18,000, find the number of shares sold by Gopal.
Let the number of shares Gopal sold be x.
N.V. = ₹ 100
Rate of dividend = 10%
Dividend = No. of shares × Rate of div. × N.V. of 1 share
= x $\times \frac{10}{100} \times 100$
= 10x.
S.P. = ₹ 100 - 20% of ₹ 100
= ₹ 100 - $\frac{20}{100} \times 100$
= ₹ 100 - ₹ 20
= ₹ 80.
Amount obtained on selling x shares = ₹ 80x.
The proceeds he invested in ₹ 100 shares at ₹ 60 of company B paying 20% dividend.
N.V. = ₹ 100
M.V. = ₹ 60
No. of shares bought by man = $\frac{\text{Amount invested}}{\text{M.V.}} = \frac{80x}{60} = \frac{4x}{3}.$
Dividend = No. of shares × Rate of div. × N.V. of 1 share
= $\frac{4x}{3} \times \frac{20}{100} \times 100$
= $\frac{80x}{3}$.
Given, increase in income = ₹ 18000
$$\begin{aligned}\therefore \frac{80x}{3} - 10x = 18000 \\[1em] \Rightarrow \frac{80x - 30x}{3} = 18000 \\[1em] \Rightarrow \frac{50x}{3} = 18000 \\[1em] \Rightarrow x = \frac{18000 \times 3}{50} \\[1em] \Rightarrow x = 1080.\end{aligned}$$
Hence, no.of shares sold by Gopal is 1080.
A man invests a certain sum of money in 6% hundred-rupee shares at ₹ 12 premium. When the shares fell to ₹ 96, he sold out all the shares bought and invested the proceed in 10%, ten-rupee shares at ₹ 8. If the change in his income is ₹ 540, find the sum invested originally.
Let sum originally invested be ₹ x,
M.V. of first type of shares = ₹ 100 + ₹ 12 = ₹ 112.
No. of shares = $\frac{x}{112}$
Annual income = No. of shares × Rate of div. × N.V. of 1 share
$$\begin{aligned}= \frac{x}{112} \times \frac{6}{100} \times 100 \\[1em] = \frac{3x}{56}.\end{aligned}$$
S.P. of shares = ₹ 96 × $\frac{x}{112} = \frac{96x}{112}$
M.V. of second type of shares = ₹ 8
No. of second type of shares = $\frac{\frac{96x}{112}}{8} = \frac{12x}{112}$
Annual income = No. of shares × Rate of div. × N.V. of 1 share
$$\begin{aligned}= \frac{12x}{112} \times \frac{10}{100} \times 10 \\[1em] = \frac{6x}{56}.\end{aligned}$$
Given, change in income = ₹ 540
$$\begin{aligned}\therefore \frac{6x}{56} - \frac{3x}{56} = 540 \\[1em] \Rightarrow \frac{3x}{56} = 540 \\[1em] \Rightarrow x = \frac{540 \times 56}{3} = 10,080.\end{aligned}$$
Hence, sum invested originally = ₹ 10,080.
Mr. Gupta has a choice to invest in ten-rupee shares of two firms at ₹ 13 or at ₹ 16. If the first firm pays 5% dividend and the second firm pays 6% dividend per annum, find :
(i) which firm is paying better.
(ii) if Mr. Gupta invests equally in both the firms and difference between the returns from them is ₹ 30, find how much, in all, does he invest?
(i) First firm :
Nominal value of 1 share = ₹ 10
M.V. = ₹ 13
Dividend = 5%
Dividend = 1 × $\frac{5}{100} \times 10$ = 0.50
Income% = $\frac{\text{Income}}{\text{Investment}} \times 100 = \frac{0.5}{13} \times 100$ = 3.846%
Second firm :
Nominal value of 1 share = ₹ 10
M.V. = ₹ 16
Dividend = 6%
Dividend = 1 × $\frac{6}{100} \times 10$ = 0.60
Income% = $\frac{\text{Income}}{\text{Investment}} \times 100 = \frac{0.6}{16} \times 100$ = 3.75%
Hence, first firm pays better.
(ii) Let investment on both firms be ₹ x each.
In first case :
M.V. = ₹ 13
No. of shares = $\frac{x}{13}$
Annual income = No. of shares × Rate of div. × N.V. of 1 share
$$\begin{aligned}= \frac{x}{13} \times \frac{5}{100} \times 10 \\[1em] = \frac{x}{26}.\end{aligned}$$
In second case :
M.V. = ₹ 16
No. of shares = $\frac{x}{16}$
Annual income = No. of shares × Rate of div. × N.V. of 1 share
$$\begin{aligned}= \frac{x}{16} \times \frac{6}{100} \times 10 \\[1em] = \frac{3x}{80}.\end{aligned}$$
Given, difference between returns = ₹ 30
$$\begin{aligned}\Rightarrow \frac{x}{26} - \frac{3x}{80} = 30 \\[1em] \Rightarrow \frac{40x - 39x}{1040} = 30 \\[1em] \Rightarrow \frac{x}{1040} = 30 \\[1em] \Rightarrow x = 30 \times 1040 = 31,200.\end{aligned}$$
Total investment = x + x = 2x = 2 x 31200 = ₹ 62,400.
Hence, total investment = ₹ 62,400.
A man invested ₹ 45,000 in 15% ₹ 100 shares quoted at ₹ 125. When the M.V. of these shares rose to ₹ 140, he sold some shares, just enough to raise ₹ 8,400. Calculate :
(i) the number of shares he still holds;
(ii) the dividend due to him on these remaining shares.
(i) No. of shares = $\frac{\text{Investment}}{\text{M.V.}} = \frac{45000}{125}$ = 360.
S.P. of one share = ₹ 140,
Hence, shares required to raise ₹ 8400,
= $\frac{\text{Money required}}{\text{S.P. of each share}} = \frac{8400}{140} = 60.$
Shares left = 360 - 60 = 300.
Hence. no. of shares left = 300.
(ii) Annual dividend = No. of shares × Rate of div. × N.V. of 1 share
= 300 × $\frac{15}{100} \times 100$
= ₹ 4,500.
Hence, dividend due = ₹ 4,500.
A dividend of 12% was declared on ₹ 150 shares selling at a certain price. If the rate of return is 10%, calculate :
(i) the market value of the shares.
(ii) the amount to be invested to obtain an annual dividend of ₹ 1,350.
(i) Let M.V. be ₹ x.
We know that,
Rate of dividend × N.V. = Profit (return) % × M.V.
$$\begin{aligned}\Rightarrow \frac{12}{100} \times 150 = \frac{10}{100} \times x \\[1em] \Rightarrow x = 180.\end{aligned}$$
Hence, market value of shares = ₹ 180.
(ii) Let amount to be invested be ₹ y.
No. of shares = $\frac{y}{180}$
Annual income = No. of shares × Rate of div. × N.V. of 1 share
$$\begin{aligned}\therefore 1350 = \frac{y}{180} \times \frac{12}{100} \times 150 \\[1em] \Rightarrow y = 13,500\end{aligned}$$
Hence, amount to be invested = ₹ 13,500.
Divide ₹50,760 into two parts such that if one part is invested in 8% ₹ 100 shares at 8% discount and the other in 9% ₹ 100 shares at 8% premium, the annual incomes from both the investments are equal.
Let money invested be ₹ x and ₹ (50760 - x)
In first case :
M.V. = ₹ 100 - $\frac{8}{100}$ x 100 = ₹ 100 - ₹ 8 = ₹ 92.
No. of shares = $\frac{x}{92}$
Annual income = No. of shares × Rate of div. × N.V. of 1 share
= $\frac{x}{92} \times \frac{8}{100} \times 100 = \frac{2x}{23}$
In second case :
M.V. = ₹ 100 + $\frac{8}{100}$ x 100 = ₹ 100 + ₹ 8 = ₹ 108.
No. of shares = $\frac{50760 - x}{108}$
Annual income = No. of shares × Rate of div. × N.V. of 1 share
= $\frac{50760 - x}{108} \times \frac{9}{100} \times 100 = \frac{50760 - x}{12}$
Given, annual income are same,
$$\begin{aligned}\therefore \frac{2x}{23} = \frac{50760 - x}{12} \\[1em] \Rightarrow 24x = 23(50760 - x) \\[1em] \Rightarrow 24x = 1167480 - 23x \\[1em] \Rightarrow 47x = 1167480 \\[1em] \Rightarrow x = \frac{1167480}{47} \\[1em] \Rightarrow x = 24,840\end{aligned}$$
50760 - x = ₹ 50760 - ₹ 24840 = ₹ 25,920.
Hence, money invested in first firm = ₹ 24,840 and in second firm = ₹ 25,920.
Vivek invests ₹ 4,500 in 8%, ₹ 10 shares at ₹ 15. He sells the shares when the price rises to ₹ 30, and invests the proceeds in 12% ₹ 100 shares at ₹ 125. Calculate :
(i) the sale proceeds
(ii) the number of ₹ 125 shares he buys
(iii) the change in his annual income from dividend.
(i) Investment = ₹ 4,500
M.V. = ₹ 15
No. of shares = $\frac{4500}{15}$ = 300.
Given, shares are sold when price rises to ₹ 30,
Sale proceeds = 300 × 30 = ₹ 9,000.
Hence, sale proceeds = ₹ 9,000.
(ii) M.V. of second type of shares = ₹ 125
Investment = ₹ 9,000
No. of shares = $\frac{9000}{125}$ = 72.
Hence, no. of ₹ 125 shares = 72.
(iii) Annual income = No. of shares × Rate of div. × N.V. of 1 share
In first case :
Annual income = 300 × $\frac{8}{100} \times 10$ = ₹ 240.
In second case :
Annual income = 72 × $\frac{12}{100} \times 100$ = ₹ 864.
Difference = ₹ 864 - ₹ 240 = ₹ 624.
Hence, difference in annual income = ₹ 624.
Mr. Parekh invested ₹52,000 on ₹ 100 shares at a discount of ₹ 20 paying 8% dividend. At the end of one year he sells the shares at a premium of ₹ 20. Find :
(i) the annual dividend.
(ii) the profit earned including his dividend.
(i) M.V. = ₹ 100 - ₹ 20 = ₹ 80.
Investment = ₹52,000
No. of shares = $\frac{52000}{80} = 650$
Annual dividend = No. of shares × Rate of div. × N.V. of 1 share
= 650 × $\frac{8}{100} \times 100$
= ₹ 5,200.
Hence, annual dividend = ₹ 5,200.
(ii) S.P. = ₹ 100 + ₹ 20 = ₹ 120.
S.P. of 650 shares = 650 × ₹ 120 = ₹ 78,000
Profit = S.P. - C.P. = ₹ 78,000 - ₹ 52,000 = ₹ 26,000.
Profit + dividend = ₹ 26,000 + ₹ 5,200 = ₹ 31,200.
Hence, profit earned including dividend = ₹ 31,200.
Salman buys 50 shares of face value ₹ 100 available at ₹ 132.
(i) What is his investment?
(ii) If the dividend is 7.5%, what will be his annual income ?
(iii) If he wants to increase his annual income by ₹ 150, how many extra shares should he buy?
(i) Investment = ₹ 132 × 50 = ₹ 6,600
Hence, Salman's investment = ₹ 6,600.
(ii) Annual income = No. of shares × Rate of div. × N.V. of 1 share
= 50 × $\frac{7.5}{100} \times 100$
= ₹ 375.
Hence, annual income = ₹ 375.
(iii) Let no. of shares needed to get income of ₹ 525 (₹ 375 + ₹ 150) be x
Annual income = No. of shares × Rate of div. × N.V. of 1 share
525 = x $\times \frac{7.5}{100} \times 100$
x = $\frac{525}{7.5}$ = 70.
Extra shares = 70 - 50 = 20.
Hence, Salman should buy 20 extra shares.
Anaya invests a sum of money in ₹ 50 shares, paying 15% dividend quoted at 20% premium. If her annual dividend is ₹ 600, calculate :
(i) the number of shares she bought.
(ii) her total investment.
(iii) the rate of return on her investment.
(i) Let no. of shares be x.
By formula,
Annual income (or dividend) = No. of shares × Rate of div. × N.V. of 1 share
600 = $x \times \frac{15}{100} \times 50$
x = $\frac{1200}{15}$ = 80.
Hence, no. of shares = 80.
(ii) M.V. = ₹ 50 + $\frac{20}{100} \times 50$ = ₹ 50 + ₹ 10 = ₹ 60
Total investment = No. of shares × M.V. of each share
= 80 × ₹ 60 = ₹ 4,800.
Hence, total investment = ₹ 4,800.
(iii) Annual income = ₹ 600.
Return % = $\frac{\text{Income}}{\text{Investment}} \times 100 = \frac{600}{4800} \times 100 = 12.5%$
Hence, return % = 12.5%.
₹ 100 shares of a company giving 10% dividend, are available at ₹ 150. Mr. Saha invests ₹18,000 to buy these shares. He sells 80% of his shares after one year. Find :
(i) the number of shares he purchased.
(ii) the number of shares he sold
(iii) his annual income from the remaining 20% shares he still holds.
(i) Given,
Total investment = ₹ 18,000
Market value = ₹ 150
N.V = ₹ 100
By formula,
⇒ Total investment = Number of shares × Market value of one share
⇒ 18000 = Number of shares × 150
⇒ Number of shares = $\frac{18000}{150}$
⇒ Number of shares = 120.
Hence, the number of shares Mr.Saha purchased = 120.
(ii) Number of shares sold by Mr Saha = 80% of 120
= $\frac{80}{100} \times 120$
= 0.8 × 120
= 96.
Hence, the number of shares Mr.Saha sold = 96.
(iii) Number of shares remaining = Total no. of shares - No. of shares sold = 120 - 96 = 24.
By formula,
Annual income = Number of shares × Rate of dividend × N.V. of 1 share
= 24 × $\frac{10}{100} \times 100$
= ₹ 240.
Hence, annual income from remaining shares = ₹ 240.
Mr. Gautam sold a certain number of ₹ 20 shares paying 8% dividend at ₹ 18 and invested the proceed in ₹ 10 shares paying 12% dividend at 50% premium. If the change in his annual income is ₹ 120, find the number of shares sold by Mr. Gautam.
Let the number of shares Mr. Gautam sold be x.
For initial shares,
N.V. = ₹ 20
Rate of dividend = 8%
By formula,
Annual income (from first investment) = No. of shares × Rate of div. × N.V. of 1 share
= x × $\frac{8}{100}$ × 20
= $\frac{8x}{5}$
S.P. of each share = ₹ 18.
Amount obtained on selling shares = S.P × No. of shares = ₹ 18x.
The proceeds he invested in ₹ 10 shares at ₹ 15, paying 12% dividend.
N.V. = ₹ 10
Premium = 50% of ₹ 10 = $\frac{50}{100} \times 10$ = 5
M.V. = N.V. + Premium = ₹ 10 + 5 = ₹ 15
Number of shares = $\frac{\text{Total investment}}{\text{Market value of each share}}$
$= \frac{18x}{15} = \frac{6x}{5}$
The change in Mr. Gautam's annual income = ₹ 120
By formula,
Annual income (from second investment) = No. of shares × Rate of div. × N.V. of 1 share
= $\frac{6x}{5} \times \frac{12}{100} \times 10$
= $\frac{720x}{500} = \frac{36x}{25}$
Given, change in income = ₹ 120
$$\begin{aligned}\therefore \frac{8x}{5} - \frac{36x}{25} = 120 \\[1em] \Rightarrow \frac{40x - 36x}{25} = 120 \\[1em] \Rightarrow \frac{4x}{25} = 120 \\[1em] \Rightarrow x = \frac{120 \times 25}{4} \\[1em] \Rightarrow x = 750.\end{aligned}$$
Hence, Mr. Gautam sold 750 shares.
A man invests ₹ 50,000 of his savings in 12%, ₹ 100 shares at ₹ 125 another ₹ 60,000 in 15%, ₹ 100 shares at ₹ 120 and remainder 18% ₹ 100 shares at ₹ 140. If his annual income is ₹ 21,300 find :
(i) the rate of return on the whole.
(ii) the investment in third company.
(i) Given,
1st Company = 12%, ₹100 shares at ₹125
Investment = ₹50,000
2nd Company = 15%, ₹100 shares at ₹120
Investment = ₹60,000
3rd Company = 18%, ₹100 shares at ₹ 140
Investment = Remaining
Total annual income = ₹ 21,300
For 1st Company :
Number of shares = $\frac{\text{Total investment}}{\text{Market value of each share}} = \frac{50000}{125} = 400$
Annual income = No. of shares × Rate of div. × N.V. of 1 share
= 400 × $\frac{12}{100}$ × 100
= 400 × 12
= ₹ 4,800
For 2nd company :
Number of shares = $\frac{\text{Total investment}}{\text{Market value of each share}} = \frac{60000}{120} = 500$
Annual income = No. of shares × Rate of div. × N.V. of 1 share
= 500 × $\frac{15}{100}$ × 100
= 500 × 15
= ₹ 7,500
Income from first two companies = ₹ 4,800 + ₹ 7,500 = ₹ 12,300
Total annual income = ₹ 21,300
Income from 3rd Company = ₹ 21,300 - ₹ 12,300 = ₹ 9,000
Annual income = No. of shares × Rate of div. × N.V. of 1 share
9000 = No. of shares × $\frac{18}{100}$ × 100
9000 = No. of shares × 18
No. of shares = $\frac{9000}{18}$ = 500
Investment in 3rd company = Number of shares × Market price = 500 × 140 = ₹ 70,000
Total Investment = ₹ 50,000 + ₹ 60,000 + ₹ 70,000 = ₹ 1,80,000
Rate of Return = $\frac{\text{Total income}}{\text{Total investment}} \times 100$
= $\frac{21300}{180000} \times 100$
= 11.83%
Hence, rate of return = 11.83%.
(ii) Investment in 3rd company = Number of shares × Market price = 500 × 140 = ₹ 70,000
Hence, investment in third company = ₹ 70,000.
Case study:
Share market is a place where investors trade different instruments like stocks, mutual funds, etc.
It is a place where companies sell parts (called shares) of their companies and investors buy them in expectation of greater returns.
Mr. Reddy wants to invest his money in company which gives a better return. He has following options:
Company X : ₹ 100 shares are available at ₹ 120 with a dividend of 8% p.a.
Company Y : ₹ 10 shares are available at ₹ 8 with a dividend of 6% p.a.
Based on the above information, answer the following questions :
(i) If Mr. Reddy wants to invest ₹ 15,000 in company X, then what will be his Annual Income ?
(ii) If Mr. Reddy wants to invest ₹ 15,000 in company Y, then what will be his Annual Income ?
(iii) Which company is a better option for Mr. Reddy to invest in ?
(i) Given,
For company X :
N.V = ₹ 100
M.V. = ₹ 120
Dividend = 8%
Investment = ₹ 15,000
Number of shares = $\frac{\text{Total investment}}{\text{Market value of each share}} = \frac{15000}{120} = 125$
Annual Income from Company X = No. of shares × Rate of div. × N.V. of 1 share
= 125 × $\frac{8}{100}$ × 100
= 125 × 8
= ₹ 1,000.
Hence, annual income from Company X = ₹ 1,000.
(ii) Given,
For company Y :
N.V = ₹ 10
M.V. = ₹ 8
Dividend = 6%
Investment = ₹ 15,000
Number of shares = $\frac{\text{Total investment}}{\text{Market value of each share}} = \frac{15000}{8} = 1875$
Annual Income from Company Y = No. of shares × Rate of div. × N.V. of 1 share
= 1875 × $\frac{6}{100}$ × 10
= 1875 × 0.6
= ₹ 1,125
Hence, annual income from Company Y = ₹ 1,125.
(iii) Annual income from Company X = ₹ 1,000
Annual income from Company Y = ₹ 1,125
Since, ₹ 1,125 > ₹ 1,000
Thus, company Y gives better return than company X.
Hence, it is a better option to invest in company Y.
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