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Mathematics [3 marks sum]

Shares and Dividend · ICSE STD 10 (ICSE - English Medium). 16 questions.

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16 questions · timed · auto-graded

Question 13 Marks
Ashok invested Rs.26,400 in 12%, Rs.25 shares of a company. If he receives a dividend of Rs.2,475, find the:
(i) number of shares he bought.
(ii) market value of each share.
Answer
(i) Total dividend = Rs. 2,475
And, dividend on each share $=12 \%$ of Rs $25=\frac{12}{100} \times$ Rs $25=$ Rs 3
$\therefore$ Number of shares bought $=\frac{\text { Total dividend }}{\text { Dividend on } 1 \text { share }}=\frac{2475}{3}=825$
(ii) Market value of 825 shares $=$ Rs. 26,400
$\therefore$ Market value of each share $=\frac{\text { Total investment }}{\text { No. of shares }}=\frac{26400}{825}=$ Rs 32
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Question 23 Marks
Ashwarya bought 496, Rs.100 shares at Rs.132 each, find :
(i) Investment made by her
(ii) Income of Ashwarya from these shares, if the rate of dividend is 7.5%.
(iii) How much extra must ashwarya invest in order to increase her income by Rs.7,200
Answer
(i) N.V of each share $=$ Rs 100
M.V of each share $=$ Rs 132
Investment made by her $=496 \times 132=$ rs 65,472
(ii) Dividend on 1 share $=7.5 \%$ of Rs $100=$ Rs 7.5So, income of Aishwarya from these shares $=496 \times 7.5=$ Rs 3,720
(iii) If she wants to increase her income by RS 7200
the number of shares she should buy $=\frac{\text { increase in the income }}{\text { income of one share }}=\frac{7200}{7.5}=$ Rs 960
So, she should invest $=960 \times 7.5=\operatorname{Rs} 1,26,720$
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Question 33 Marks
How much should a man invest in Rs. 50 shares selling at Rs. 60 to obtain an income of Rs. 450, if the rate of dividend declared is 10%. Also find his yield percent, to the nearest whole number.
Answer
Face value of each share $=$ Rs. 50
Dividend $(\%)=10 \%$
Dividend on 1 share $=\frac{10}{100} \times 50=$ Rs. 5
$\therefore$ Number of shares bought $=\frac{\text { Total dividend }}{\text { Dividend per share }}=\frac{450}{5}=90$
market value of each share $=$ Rs 60
$\therefore$ Total investment $=90 \times 60=$ rs 5400
Percentage return $=\frac{\text { Total dividend }}{\text { Total investment }} \times 100=\frac{450}{5400} \times 100=8.33 \approx 8 \%$
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Question 43 Marks
By investing Rs.45,000 in 10% Rs.100 shares, Sharad gets Rs.3,000 as dividend. Find the market value of each share.
Answer
Annual income from 1 share $=10 \%$ of Rs $100=$ Rs 10Total annual income $=$ Rs 3000Number of shares bought $=$
$
\frac{\text { total annual income }}{\text { Annual income from } 1 \text { share }}=\frac{3000}{10}=300
$
$\Rightarrow$ Market value of one share $=\frac{\text { Total investment }}{\text { Number of shares }}=\frac{45000}{300}$
$=\operatorname{Rs} 150$
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Question 53 Marks
Mr. Parekh invested Rs. 52,000 on Rs. 100 shares at a discount of Rs. 20 paying 8% dividend. At the end of one year, he sells the shares at a premium of Rs. 20. find
1) The annual dividend
2) The profit earned including his dividend.
Answer
$
\begin{aligned}
& \text { Rate of dividend }=8 \% \\
& \text { Amount invested }=\text { Rs. } 52,000 \\
& \text { Market price }=\text { Rs. } 100-\text { Rs. } 20=\text { Rs. } 80 \\
& \text { Number of shares purchased }=\text { Rs. } \frac{52,000}{80}=650
\end{aligned}
$Number of shares purchased $=$ Rs. $\frac{52,000}{80}=650$
(1) Annual dividend $=650 \times 8=$ Rs. 5200
(2) On selling market rate $=$ Rs $100+20=$ Rs 120
$\Rightarrow$ sale price $=$ Rs. $120 \times 650=$ Rs. 78,000
Profit $=$ Rs. $(78,000-52,000)=$ Rs 26000
$\Rightarrow$ Total gain $=26000+5200=$ Rs 31200
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Question 63 Marks
A dividend of 12% was declared on Rs 150 shares selling at a certain price. If the rate of return is 10%, calculate:
(1) the market value of the shares.
(2) the amount to be invested to obtain an annual dividend of Rs 1,350.
Answer
1) Nominal value of 1 share $=$ Rs 150
Dividend $\%=12 \%$
Dividend on 1 share $=12 \%$ of Rs 150
$
\frac{12}{100} \times \text { Rs } 150=\text { Rs } 18
$
Let market value of 1 share= Rs $y$
Return $\%=10 \%$
$10 \%$ of $\operatorname{Rs}( y )=\operatorname{Rs} 18$
$
\Rightarrow \frac{10}{100} \times y=\operatorname{Rs} 18
$
$
= y =\operatorname{Rs} 180
$
2) When dividend is Rs 18 then investment is Rs 180
When dividend is Rs 1350 then investment
$
\begin{aligned}
& \frac{180}{18} \times \operatorname{Rs} 1350 \\
& =\text { Rs } 13500
\end{aligned}
$
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Question 73 Marks
Mr.Tiwari. invested Rs 29,040 in 15% Rs 100 shares quoted at a premium of 20%. Calculate:
(1) the number of shares bought by Mr Tiwari.
(2) Mr. Tiwari’s income from the investment.
(3) the percentage return on his investment.
Answer
Total investment $=$ Rs 29,040
Nominal value of 1 share $=$ Rs 100
Market value of 1 share $=$ Rs $100+20 \%$ of Rs 100
$=\operatorname{Rs} 100+\operatorname{Rs} 20=\operatorname{Rs} 120$
$\therefore$ No of shares purchsed $=\frac{29040}{120}=242$ shares
Nominal value of 242 shares $=$ Rs $100 \times 242=$ Rs 24,200
Dividend $\%=15 \%$
Dividend $=15 \%$ of Rs 24,200
$=\frac{15}{100} \times 24200=$ Rs 3630
income $\%=\frac{\text { income }}{\text { investment }} \times 100 \%$
$=\frac{3630}{29040} \times 100 \%$
$=12.5 \%$
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Question 83 Marks
A company declares 8 per cent dividend to the shareholders. If a man receives Rs 2,840 as his dividend, find the nominal value of his shares.
Answer
Given: Rate of dividend $=8 \%$
Dividend $=2840$
Let Nominal value of his share $=x$
We know:
Dividend $=$ Rate of dividend $\times \times$ Nominal value of a share
So,
$
\begin{aligned}
& 2840=\frac{8}{100} \times x \\
& x=\frac{2840 \times 100}{8}=355 \times 100=35500
\end{aligned}
$
Nominal value of his share $=$ Rs. 35500
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Question 93 Marks
Rs 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 per cent.
Answer
Nominal value of 1 share $=$ Rs 50
Market value of 1 share $=$ Rs $50-10 \%$ of Rs 50
$
=\operatorname{Rs} 50-\operatorname{Rs} 5=\operatorname{Rs} 45
$
Profit $\%$ on investment $=20 \%$
Then profit on 1 share $=20 \%$ of Rs $45=$ Rs 9
$\therefore$ Dividend $\%=\frac{9}{50} \times 100 \%=18 \%$
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Question 103 Marks
Hundred rupee shares of a company are available in the market at a premium of Rs 20. Find the rate of dividend given by the company, when a man’s return on his investment is 15%.
Answer
Nominal value of 1 share $=\operatorname{Rs} 100$
Market value of 1 share $=$ Rs $100+$ Rs $20=$ Rs 120
Profit $\%$ on investment of 1 share $=15 \%$
Then profit $=15 \%$ of Rs $120=$ Rs 18
$\therefore$ Dividend $\%=\frac{18}{100} \times 100 \%=18 \%$
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Question 113 Marks
By purchasing Rs 25 shares for Rs 40 each, a man gets a 4 percent profit on his investment. What rate percent is the company paying? What is his dividend if he buys 60 shares?
Answer
Nominal value of 1 share $=$ Rs 25
Market value of 1 share $=$ Rs 40
Profit $\%$ on investment $=4 \%$
Then profit on 1 share $=4 \%$ of Rs $40=$ Rs 1.60
$\therefore$ Dividend $\%=\frac{1.60}{25} \times 100 \%=6.4 \%$
No. of shares purchased $=60$
Then dividend on 60 shares $=60 \times$ Rs $1.60=$ Rs 96
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Question 123 Marks
A person buys 120 shares at a nominal value of Rs 40 each, which he sells at Rs 42.50 each. Find his profit and profit per cent.
Answer
Nominal value of 120 shares $=$ Rs $40 \times 120=$ Rs 4,800
Market value of 120 shares $=$ Rs $42.50 \times 120=$ Rs 5,100
His profit $=$ Rs 5,100- Rs 4,800 = Rs 300
profit $=\frac{300}{4800} \times 100 \%=6.25 \%$
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Question 133 Marks
How much money will be required to buy 250, Rs.15 shares at a discount of Rs.1.50?
Answer
Number of shares to be bought = 250
Rs 15 shares at a discount of Rs 1.50 means;
Nominal value of the share is Rs 15 and
its market value = Rs 15 - rs 1.50 = Rs 13.50
∴ Money required to buy 1 share = Rs 13.50
⇒ Money required to buy 250 shares = 250 x Rs 13.50 = Rs 3375
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Question 143 Marks
How much money will be required to buy 400, Rs.12.50 shares at a premium of Rs.1?
Answer
Number of shares to be bought = 400
Rs, 12,50 shares at a premium of Re, 1 means
nominal value of the share is Rs, 12.50 and
its market value = Rs, 12,50 + Re, 1 = Rs, 13.50
Money required to buy 1 share = Rs, 13.50
Money required to buU 400 shares = 400 x Rs,13.50= Rs, 5400
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Question 153 Marks
A man invests Rs 1,680 in buying shares of nominal value ₹ 24 and selling at 12% premium. The dividend on the shares is 15% per annum. Calculate:
1) the number of shares he buys;
2) the dividend he receives annually.
Answer
Nominal value of 1 share $=$ Rs 24
Market value of 1 share $=$ Rs $24+12 \%$ of Rs 24
$
=\text{₹}  24+\text { Rs } 2.88=\text { Rs } 26.88
$
Total investment $=$ Rs 1,680
$\therefore$ No of shares purchase $=\frac{1680}{26.88}=62.5$
Nominal value of 62.5 shares $=62.5 \times 24=$ Rs 1,500
Dividend $=15 \%$ of Rs 1500
$
=\text { Rs } 225
$
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Question 163 Marks
A man has 300, Rs 50 shares of a company paying 20% dividend. Find his net income after paying 3% income tax.
Answer
Nominal value of 1 share $=$ Rs 50
Nominal value of 300 shares $=300 \times 50=\operatorname{Rs} 15,000$
$\therefore$ Dividend $=20 \%$ of Rs 15000
$=\frac{20}{100} \times 15000=$ Rs 3000
$\therefore$ Income tax paid $=3 \%$ of Rs 3000
$=\frac{3}{100} \times 3000=\operatorname{Rs} 90$
His net income $=$ Rs $3,000-$ Rs $90=$ Rs 2,910
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[3 marks sum] - Mathematics STD 10 Questions - Vidyadip