[2 Mark Question Answer] - Mathematics STD 10 Questions - Vidyadip

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18 questions · timed · auto-graded

Question 12 Marks

Amit Kumar invests Rs 36,000 in buying Rs 100 shares at Rs 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.
Give your answer correct to the nearest whole number.

Answer

$
\begin{aligned}
& \text { Investment = Rs. } 36000 \\
& \text { Face value }=\text { Rs. } 100 \\
& \text { Premium = Rs. } 20 \text {, dividend }=15 \% \\
& \text { (i) No. of shares } \\
& =\frac{36000}{120} \\
& =300
\end{aligned}
$
(ii) Dlvidend
$
\begin{aligned}
& =15 \% \text { of }(100 \times 300) \\
& =\text { ₹ } 4500
\end{aligned}
$
(iii) $\%$ Return
$
\begin{aligned}
& =\frac{4500}{36000} \times 100 \\
& =\frac{450}{36} \\
& =12.5 \% \\
& =13 \% .
\end{aligned}
$

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Question 22 Marks

Ashok invests Rs.26400 on 12% Rs.25 shares of a company. If he receives a dividend of Rs 2475, find:
(i) the number of shares he bought.
(ii) the market value of each share.

Answer

Investment $=$ Rs. 26400
Face value of each share $=$ Rs. 25
Rate of dividend $=12 \%$
and total dividend = Rs. 2475
We know,
Dlvidend earned
$=$ M.P. of share $x$ No. of share $\times \frac{r}{100}$
(i) $\therefore$ Number of share
$=\frac{2475}{12} \times \frac{100}{25}$
$=825$ shares
(ii) Market value of each other
$=\frac{26400}{825}$
$=\text { ₹ }32$.

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Question 32 Marks

What sum should a person invest in Rs 25 shares, selling at Rs 36, to obtain an income of Rs 720, if the dividend declared is 12%? Also find the percentage return on his income.
(i) The number of shares bought by him.
(ii) The percentage return on his income.

Answer

$
\begin{aligned}
& \text { Nominal value of each share }=\text { Rs. } 25 \\
& \text { Market value of each share }=\text { Rs. } 36 \\
& \text { Total income }=\text { ₹ }720 \\
& \text { Rate of dividend }=12 \% \\
& \text { Total nominal value } \\
& =\frac{100}{12} \times 720 \\
& =\text { ₹ } 6000 \\
& \text { (i) } \therefore \text { Number of shares } \\
& =\frac{6000}{25} \\
& =240
\end{aligned}
$
(i) $\therefore$ Number of shares
$
\begin{aligned}
& =\frac{6000}{25} \\
& =240
\end{aligned}
$Total investment
$
\begin{aligned}
& =240 x \text { ₹ } 36 \\
& =\text { ₹ }8640
\end{aligned}
$
(ii) Percentage return
$
\begin{aligned}
& =\frac{720 \times 100}{8640} \\
& =8 \frac{1}{3} \%
\end{aligned}
$

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Question 42 Marks

A lady holds 1800, Rs. 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? Give your answer to the nearest integer.

Answer

Total number of shares $=1800$
Nominal value of each share $=$ Rs. 100
Rate of dividend $=15 \%$
(i) Total face value of 1800 shares
$
\begin{aligned}
& =\text { Rs }, 100 \times 1800 \\
& =\text { Rs. } 180000
\end{aligned}
$
$\therefore$ Total dividend
$
\begin{aligned}
& =\text { Rs. } 180000 \times \frac{15}{100} \\
& =\text { Rs. } 27000
\end{aligned}
$
(ii) Market value of each share
$
\begin{aligned}
& =\text { Rs. } 100+\text { Rs. } 40 \\
& =\text { Rs. } 140
\end{aligned}
$
$\therefore$ Total investment
$=$ Rs. $140 \times 1800$
$=$ Rs. 252000
$\therefore$ Percentage on his return
$
=\frac{27000 \times 100}{252000}
$
$
\begin{aligned}
& =10.7 \\
& =11 \% \ldots \text { (in integers). }
\end{aligned}
$

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Question 52 Marks

Find the market price of 5% share when a person gets a dividend of Rs 65 by investing Rs. 1430.

Answer

$
\begin{aligned}
& \text { Amount of dividend }=\text { Rs. } 65 \\
& \text { Rate of dividend }=5 \% \\
& \therefore \text { Total face value } \\
& =\frac{65 \times 100}{5} \\
& =\text { Rs. } 1300
\end{aligned}
$
$
\begin{aligned}
& \text { If face value is Rs. } 1300 \text {, then market value } \\
& =\text { Rs. } 1430
\end{aligned}
$
and if face value is Rs. 100 , then market value
$
\begin{aligned}
& =\frac{1430 \times 100}{1300} \\
& =\text { Rs. } 110 .
\end{aligned}
$

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Question 62 Marks

A company with 10000 shares of Rs. 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.

Answer

No. of shares $=10000$
Face value of each share $=$ Rs. 100
Rate of dividend $=5 \%$
(i) Total face value of 10000 shares
$=$ Rs. $100 \times 10000$
$=$ Rs. 1000000
$\therefore$ Total amount of dividends
$=\frac{1000000 \times 5}{100}$
$=$ Rs. 50000
(ii) Income of 722 shares $=72 \times 5=$ Rs. 360
(iii) Rate of interest on investment $=4 \%$
$\therefore$ Market value of each share
$=\frac{100}{4} \times 5$
$=$ Rs. 125.

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Question 72 Marks

A man buys 200 ten-rupee shares at Rs 12.50 each and receives a dividend of 8%. Find the amount invested by him and the dividend received by him in cash.

Answer

Face value of 200 shares
$
\begin{aligned}
& =\text { Rs. } 10 \times 200 \\
& =\text { Rs. } 2000
\end{aligned}
$
(i) Amount invested for the purchase of 200 shares at the rate of Rs. 12.50 each
$
\begin{aligned}
& =\text { Rs. } 12.50 \times 200 \\
& =\text { Rs. } 2500
\end{aligned}
$
(ii) Rate of dividend $=8 \%$
$\therefore$ Total amount of dividend
$
\begin{aligned}
& =\text { Rs. } \frac{2000 \times 8}{100} \\
& =\text { Rs. } 160 .
\end{aligned}
$

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Question 82 Marks

By purchasing Rs. 50 gas shares for Rs. 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?

Answer

Market value of each share $=\operatorname{Rs} 80$
Face value of each share $=$ Rs. 50
Interest on investment $=4 \%$
Dividend on Rs. $80=\frac{80 \times 4}{100}=\frac{32}{10}$
Now dividend on face value Rs. $50=\frac{32}{10}$
$\therefore$ Percent dividend $=\frac{32}{10} \times \frac{100}{50}=\frac{64}{10}=6.4 \%$
No. of shares purchased $=200$
$\therefore$ Face value of 200 shares
$=$ Rs. $200 \times 50$
$=$ Rs. 10000
Dlvidend = Rs. $10000 \times \frac{6.4}{100}$
$=$ Rs. 640 .

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Question 92 Marks

Which is better investment : 6% Rs. 100 shares at Rs. 120 or 8% Rs. 10 shares at Rs. 15

Answer

Let the investment in each case $=$ Rs. 120 In the first case,
Dividend on Rs. $120=$ Rs. 6
In second case, Dividend on Rs. 10
$
=\frac{8 \times 10}{100}=0.8
$
Now dividend on Rs. $15=0.8$
then dividend on Rs. $120=\frac{0.8 \times 120}{15}=$ Rs. 6.4
It is clear that, second investment i.e. $8 \%$
Rs. 10 shares at 15 is more profitable.

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Question 102 Marks

Two companies have shares of 7% at Rs. 116 and 9% at Rs. 145 respectively. In which of the shares would the investment be more profitable?

Answer

Let the investment in each case $=$ Rs. $116 \times 145$
Dividend in first case
$\therefore$ Dividend in first case
$=$ Rs. $\frac{116 \times 145 \times 7}{116}=$ Rs. 1015
ans dividend in second case
$=$ Rs. $\frac{116 \times 145 \times 9}{145}=$ Rs. 1044
From the above it is clear that the second type of share i.e. $9 \%$ at Rs. 145 are more profitable.

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Question 112 Marks

A man invests Rs. 10400 in 6% shares at Rs. 104 and Rs. 11440 in 10.4% shares at Rs. 143. How much income would he get in all?

Answer

In first case; Total investment = Rs. 10400
Rate of dividend $=6 \%$
Market value of each share $=$ Rs. 104
$\therefore$ Total dividend $=\frac{10400 \times 6}{104}$
$=$ Rs. 600
In second case, Investment = Rs. 11440
Rate of dividend $=10.4 \%$
Market value of each share $=$ Rs. 143
$\therefore$ Total dividend $=$ Rs. $\frac{11440 \times 10.4}{143}$
$=$ Rs. 832
Total dividend from both cases $=$ Rs. $600+$ Rs. 832
$
=\text { Rs. } 1432 .
$

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Question 122 Marks

By investing Rs. 7500 in a company paying 10 percent dividend, an income of Rs. 500 is received. What price is paid for each Rs.100 share

Answer

$\begin{aligned} & \text { Investment = Rs. } 7500 \\ & \text { Rate of dividend }=10 \% \\ & \text { Total income }=\text { Rs. } 500 . \\ & \text { Face value of each share = Rs. } 100 \\ & \text { Total face value } \\ & =\frac{100 \times 500}{10} \\ & =\text { Rs. } 5000\end{aligned}$
$\begin{aligned} & \text { If face value is Rs. } 5000 \text {, then investment }=\text { Rs. } 7500 \\ & \text { and if face value is Rs. } 100 \text { then market value of each share } \\ & =\frac{7500 \times 100}{5000} \\ & =\text { Rs. } 150 \text {. }\end{aligned}$

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Question 132 Marks

Ajay owns 560 shares of a company. The face value of each share is Rs. 25. The company declares a dividend of 9%. Calculate.
(i) the dividend that Ajay will get.
(ii) the rate of interest, on his investment if Ajay has paid Rs. 30 for each share.

Answer

$\begin{aligned} & \text { No. of shares }=560 \\ & \text { Face value of each share }=\text { Rs. } 25 \\ & \text { Rate of dividend }=9 \% \text { p.a. } \\ & \text { Total face value of } 560 \text { shares } \\ & =\text { Rs. } 25 \times 560 \\ & =\text { Rs. } 14000 \\ & \text { (i) } \therefore \text { Amount of dividend } \\ & =\text { Rs. } 14000 \times \frac{9}{100} \\ & =\text { Rs. } 1260 \\ & \text { (ii) Market value of each other }=\text { Rs. } 30 \\ & \therefore \text { Total investment } \\ & =\text { Rs. } 30 \times 560 \\ & =\text { Rs. } 16800 \\ & \therefore \text { Percentage of interest on his investment } \\ & =\frac{1260 \times 100}{16800} \\ & =7.5 \% .\end{aligned}$

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Question 142 Marks

A company pays a dividend of 15% on its ten-rupee shares from which it deducts tax at the rate of 22%. Find the annual income of a man, who owns one thousand shares of this company.

Answer

No. of shares $=1000$
Face value of each are $=$ Rs. 10
Rate of dividend $=15 \%$,
Rate of tax deducted $=22 \%$
Total face value of 1000 shares
$
=\text { Rs. } 10 \times 1000
$
$
=\text { Rs. } 10000
$
Total dividend
$
\begin{aligned}
& =\text { Rs. } 10000 \times \frac{15}{100} \\
& =\text { Rs. } 1500
\end{aligned}
$
Tax deducted at the rate of $22 \%$
$
\begin{aligned}
& =\text { Rs. } 1500 \times \frac{22}{100} \\
& =\text { Rs. } 330
\end{aligned}
$
Net annual income
$
\begin{aligned}
& =\text { Rs. } 1500-\text { Rs. } 330 \\
& =\text { Rs. } 1170 .
\end{aligned}
$

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Question 152 Marks

A man invests Rs 8800 on buying shares of face value of rupees hundred each at a premium of 10%. If he earns Rs 1200 at the end of year as dividend, find :
(i) the number of shares he has in the company.
(ii) the dividend percentage per share.

Answer

$
\text { Investment = Rs. } 8800
$
Face value of each share $=$ Rs. 100
and market value of each share
$
\begin{aligned}
& =\text { Rs. } 100+\text { Rs. } 10 \\
& =\text { Rs. } 110
\end{aligned}
$
Total income $=$ Rs. 1200
Total face value
$
\begin{aligned}
& =\text { Rs. } \frac{8800 \times 100}{110} \\
& =\text { Rs. } 8000
\end{aligned}
$
(i) No. of shares
$
\begin{aligned}
& =\frac{8000}{100} \\
& =80
\end{aligned}
$
(ii) Rate of dividend
$
\begin{aligned}
& =\frac{1200 \times 100}{8000} \\
& =15 \% .
\end{aligned}
$

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Question 162 Marks

Mr. Tiwari invested Rs 29,040 in 15% Rs 100 shares at a premium of 20%. Calculate:
(i) The number of shares bought by Mr. Tiwari.
(ii) Mr. Tiwari’s income from the investment.
(iii) The percentage return on his investment.

Answer

$\begin{aligned} & \text { (i) M.V. of one share }=\left[\frac{20}{100} \times 100+100\right] \\ & =\text { Rs. } 120 \\ & \text { No. of shares } \\ & =\frac{\text { Investment }}{\text { M.V. of } 1 \text { share }} \\ & =\text { ₹ } \frac{29040}{120} \\ & =\text { ₹ }242 \\ & \text { (ii) Income } \\ & =242 \times 15 \\ & =\text { ₹ }3,630 \\ & \text { (iii) } \because \text { rate } \% \\ & =\frac{\text { dividend }}{\text { M.V. }} \times 100 \\ & =\frac{15}{120} \times 100 \\ & =12.5 \% .\end{aligned}$

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Question 172 Marks

A man buys Rs. 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?

Answer

$
\begin{aligned}
& \text { Face value of each share }=\text { Rs. } 40 \\
& \text { Dividend }=10 \% \\
& \text { Gain on investment }=10 \% \\
& \therefore \text { Dividend on Rs. } 40=\frac{40 \times 10}{100}=\text { Rs. } 4
\end{aligned}
$
Now Rs. 16 is interset on the market value = Rs. 100
$\therefore$ Market value if interset is Rs. 4
$
=\frac{100 \times 4}{16}=\text { Rs. } 25 \text {. }
$

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Question 182 Marks

Rohit Kulkami invests Rs 10000 in 10% Rs 100 shares of a company. If his annual dividend is Rs 800, find :
(i) The market value of each share.
(ii) The rate percent which he earns on his investment.

Answer

$
\text { Investment = Rs } 10000
$Face value of each share $=$ Rs 100
Rate of dividend $=10 \%$
Annual dividend $=$ Rs 800
$
\text { (i) } \therefore \text { Market value }=\frac{10000 \times 10}{800}=\text { ₹ }125
$
(ii) Rate percent on investment
$
=\frac{800 \times 100}{10000}=8 \%
$

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[2 Mark Question Answer] - Mathematics STD 10 Questions - Vidyadip