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Mathematics [4 marks sum]

Shares and Dividend · ICSE STD 10 (ICSE - English Medium). 37 questions.

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[4 marks sum]

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37 questions · timed · auto-graded

Question 14 Marks
Mr. Gupta has a choice to invest in ten-rupee shares of two firm at Rs. 13 or at Rs. 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 the difference between the returns from them is Rs. 30, find how much, in all, does he invest.
Answer
i) $1^{\text {st }}$ firm
Nominal value of 1 share $=$ Rs. 10
$
\begin{aligned}
& \text { Market value of } 1 \text { share }=\text { Rs. } 13 \\
& \text { Dividend } \%=5 \% \\
& \text { Dividend }=5 \% \text { of Rs. } 10=\text { Rs. } 0.50 \\
& \therefore \text { Income } \%=\frac{\text { Income }}{\text { Investment }} \times 100 \% \\
& =\frac{0.50}{13} \times 100 \%=3.846 \%
\end{aligned}
$
$2^{\text {nd }}$ firm
Nominal value of 1 share $=$ Rs. 10
$
\begin{aligned}
& \text { Market value of } 1 \text { share }=\text { Rs. } 16 \\
& \text { Dividend } \%=6 \% \\
& \text { Dividend }=6 \% \text { of Rs. } 10=\text { Rs. } 0.60 \\
& \therefore \text { Income } \%=\frac{\text { Income }}{\text { Investment }} \times 100 \% \\
& =\frac{0.60}{16} \times 100 \%=3.75 \%
\end{aligned}
$
Then first firm is paying better than second firm.
(ii)Let money invested in each firm= Rs y
For 1st firm
$
\begin{aligned}
& \therefore \text { No of shares purchased }=\frac{y}{13} \text { shares } \\
& \text { Total dividend }=\text { Rs. } 0.50 \times \frac{y}{13}=\text { Rs, } \frac{y}{26}
\end{aligned}
$
For 2nd firm:
$
\begin{aligned}
& \therefore \text { No of shares purchased }=\frac{y}{16} \text { shares } \\
& \text { Total dividend }=\text { Rs. } 0.60 \times \frac{y}{16}=\text { Rs } \frac{3 y}{80} \\
& \text { Given }- \text { difference of both dividend }=\text { Rs. } 30 \\
& \Rightarrow \frac{y}{26}-\frac{3 y}{80}=\text { Rs. } 30 \\
& \Rightarrow \text { Rs. } \frac{y}{1040}=30 \\
& \Rightarrow y=\text { Rs. } 30 \times 1040=\text { Rs. } 31,200 \\
& \text { Total money invested in both firms = Rs. } 31,200 \times 2 \\
& =\text { Rs. } 62,400
\end{aligned}
$
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Question 24 Marks
A man invests a certain sum of money in 6% hundred-rupee shares at Rs.12 premium. When the shares fell to Rs.96, he sold out all the shares bought and invested the proceed in 10%, ten-rupee shares at Rs.8. If the change in his income is Rs.540, Find the sum invested originally
Answer
Let the riginal sum invested $= x$
Then number of Rs 100 shares purchased at premium of Rs 12
$
\frac{ x }{100+12}=\frac{ x }{112}
$
The income per original share at $6 \%=R s ~ 6$
Total Income $=$ (Number of shares) $x$ (earning per share)
$
=\left(\text { Number of shares) } \times 6=\frac{ x }{112} \times 6=\frac{3 x }{56}\right.
$Proceeds from sale of original share at Rs 96 per share
$
=\left(\text { number of shares) } \times 96=\frac{x}{112} \times 96=\frac{6 x}{7}\right.
$Number of Rs 10 shares purchased at rs 8 per share from proceeds of oriiginal shares
$
=\frac{\text { Proceeds from sale of original shares }}{8}=\frac{\frac{6 x}{7}}{8}=\frac{3 x}{28}
$Income per new share Rs 10 at $10 \% \frac{10}{100} \times 10=$ Rs 1
Total income from new shares
$=($ Number of shares) $x$ (income per share)
$
=\frac{3 x }{28} \times 1=\frac{3 x }{28}
$
Given change in income $=540$Income from old shares - Income from new shares $=540$
$
\begin{aligned}
& \therefore 540=\frac{3 x}{28}-\frac{3 x}{56}=\frac{3 x}{56} \\
& \therefore x=\frac{540}{\frac{3}{56}}=10,080
\end{aligned}
$
Thus the original sum invested is Rs 10,080 .
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Question 34 Marks
Gopal  has some Rs.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 Rs.100 shares at Rs.60 of company B paying 20% dividend. If his income, from the shares sold, increases by Rs.18,000, find the number of shares sold by Gopal.
Answer
Let the number of share the man sold be $x$.
N.V of share $=$ Rs 100
Rate of Dividend $=10 \%$
Dividend on each share $=10 \%$ of Rs $100=$ Rs 10
So, the dividend on $x$ shares $=$ Rs $10 \times x=$ Rs $10 x$Selling price of each share $=$ Rs $100-20 \%$ of Rs $100=$ Rs 80
Amount obtained on selling $x$ shares $=$ Rs $80 \times x=$ Rs $80 x$The proceeds he invest in Rs 100 shares at Rs 60 of company B paying $20 \%$ dividend
N.V of share $=$ Rs 100
M.V of each share $=\operatorname{Rs} 60=\operatorname{Rs} 60$Number of shares bought by the man $=\frac{\text { Amount invested }}{\text { M.V of each share }}$
$
=\frac{80 x }{60}
$
$
=\frac{4 x }{3}
$
Dividend on each share $=20 \%$ of Rs $100=$ Rs 20Total dividend recieved = Dividend on each share $x$ Number of shares
$
\begin{aligned}
& =20 \times \frac{4 x }{3} \\
& =\frac{80 x }{3}
\end{aligned}
$
Increase in the income $=$ Rs 18000
$
\begin{aligned}
& \Rightarrow \frac{80 x}{3}-10 x=18000 \\
& \Rightarrow \frac{50 x}{3}=18000 \\
& x=\text { Rs } 1080
\end{aligned}
$
hence, the number of shares sold by Gopal is Rs 1080 .
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Question 44 Marks
Gagan invested Rs.80% of his savings in 10% Rs.100 shares at 20% premium and the rest of his savings in 20% Rs.50 shares at Rs.20% discount. If his incomes from these shares is Rs.5,600 calculate:
(i) His investment in shares on the whole
(ii) The number of shares of first kind that he bought
(iii) Percentage return, on the shares bought on the whole.
Answer
(i) Let the total savings be Rs $x$.
For 1st part:
N.V of each share $=$ Rs 100
M.V of each share $=100+\frac{20}{100}(100)=$ Rs 120 Number of shares bought $=0.8 \frac{x}{120} \ldots .($ Investment $=$ Rs $x)$
dividend on each share $=10 \%$ of $100=$ Rs $10 \ldots($ Rate $=10 \%)$
Total dividend $=10 \times 0.8 \frac{x}{120}=\operatorname{Rs} \frac{0.8 x}{12}$
For 2nd part:
N.V of each share $=$ Rs 50
M.V of each share $=50-\frac{20}{100}(50)=$ Rs 40
Number of shares bought $=\frac{0.2 x}{40}$ (investment $= Rs x$ )
Dividend on each share $=20 \%$ of $50= rs$ $10 \ldots \ldots \ldots($ rate $=20 \%)$
Total dividend $=10 \times \frac{0.2 x}{40}=\frac{0.2 x}{4}$ given that dividends (incomes) from both the investments are is Rs 5600
$
\Rightarrow \frac{0.8 x}{12}+\frac{0.2 x}{4}=5600
$
$\Rightarrow \frac{0.8 x+0.6 x}{12}=5600$
Thus, his investment in share on the whole is Rs
$
\begin{aligned}
& \Rightarrow x={ }^{\prime}(5600 \times 12) / 1.4 \\
& \Rightarrow x=48,000 \\
& 4800
\end{aligned}
$
(ii) So, number of shares bought $=\frac{0.8 x}{120}=\frac{0.8 \times 48,000}{120}= Rs 320$
(iii) The total dividend (return) $=\frac{0.8 x}{12}+\frac{0.2 x}{4}$
$
\begin{aligned}
& =\frac{0.8(48,000)}{12}+\frac{0.2(48000)}{4} \\
& =0.8 \times 4000+0.2 \times 12,000 \\
& =\operatorname{Rs} 5600
\end{aligned}
$
$
\text { Percentage return }=\frac{5600}{48,000} \times 100=11 \frac{2}{3} \%
$
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Question 54 Marks
A man invests a certain sum on buying 15% Rs.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, Rs.6480
(iii) Sum invested
Answer
(i) Dividend on one share $=15 \%$ of Rs 100
$
\begin{aligned}
& =\operatorname{Rs}\left(\frac{15}{100} \times 100\right) \\
& =\text { Rs } 15
\end{aligned}
$
So, the income from one share is Rs 15 .
(ii) Number of shares bought by the man
$
\begin{aligned}
& =\frac{\text { annual income }}{\text { dividend on one share }} \\
& =\frac{6480}{15} \\
& =\text { Rs } 432
\end{aligned}
$
(iii) Since the man bought shares of Rs 100 at $20 \%$ premium, the market value of one share
$
\begin{aligned}
& =\operatorname{Rs}\left(1+\frac{20}{100}\right) \times 100 \\
& =\operatorname{Rs}\left(\frac{120}{100} \times 100\right) \\
& =\operatorname{Rs} 120
\end{aligned}
$
His total investment $=$ number of shares $x$ market value of one share
$
\begin{aligned}
& =432 \times 120 \\
& =\text { Rs } 51,840
\end{aligned}
$
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Question 64 Marks
Mrs. Kulkarni invests Rs.1, 31,040 in buying Rs.100 shares at a discount of 9%. She sells shares worth Rs.72,000 at a premium of 10% and the rest at a discount of 5%. Find her total gain or loss on the whole.  
Answer
$
\text { Investment = Rs } 131040
$
N.V of 1 share $=$ Rs 100Discount $=9 \%$ of Rs $100=$ Rs 9
$\therefore M$.V of 1 share $=$ Rs $100-$ Rs $9=$ Rs 91
$\therefore$ Number of shares purchased $=\frac{\text { Investment }}{M \cdot V \text { of } 1 \text { share }}=\frac{131040}{91}=1440$
$\therefore$ Number of shares worth Rs $72000=\frac{72000}{100}=720$
$\therefore$ Mrs Kulkarni sells 720 shares at a premium of $10 \%$
M.V of 1 share $=\operatorname{Rs~} 100+\operatorname{Rs} 10=\operatorname{Rs} 110$
$\therefore$ Selling price of 720 shares $=720 \times$ Rs $110=$ Rs 79200
number of remaining shares $=1440-720=720$She sells 720 shares at a discount of $5 \%$
$M . V$ of 1 share $=\operatorname{Rs~} 100-\operatorname{Rs} 5=\operatorname{Rs} 95$
$\therefore$ Selling price of 720 shares $=720 \times$ Rs $95=$ Rs 68400
$\therefore$ Total selling price $=$ Rs $(79200+68400)=$ Rs 147600
$\therefore$ total gain $=$ Total selling price - Total investment
$
\begin{aligned}
& =\operatorname{Rs}(147600-131040) \\
& =\operatorname{Rs} 16560
\end{aligned}
$
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Question 74 Marks
Rohit invested Rs. 9,600 on Rs. 100 shares at Rs. 20 premium paying 8% dividend. Rohit sold the shares when the price rose to Rs. 160. He invested the proceeds (excluding dividend) in 10% Rs. 50 shares at Rs. 40. Find the :
(i) Original number of shares.
(ii) Sale proceeds.
(iii) New number of shares.
(iv) Change in the two dividends.
Answer
(i) 100 shares at Rs 20 premium means
Nominal value of the share is $Rs 100$
and its market value $=100+20=$ Rs 120
Number of shares $=\frac{\text { Money Invested }}{\text { Market value of } 1 \text { share }}=\frac{9600}{120}=80$
(ii) Each share is sold at Rs 160
$\therefore$ Sale proceeds $=80 \times$ Rs $160=$ Rs 12,800
(iii) Now, investment $=$ Rs 12800
Dividend $=10 \%$
Net value $=50$
Market value $=$ Rs 40
$\therefore$ Number of shares $=\frac{\text { Investment }}{\text { Market value }}=\frac{12800}{40}=320$
(iv) Now, dividend on 1 share $=10 \%$ of N.V $=10 \%$ of $50=5$
$\Rightarrow$ Dividend on 320 shares $=320 \times 5=1600$
Thus, change in two dividends $=1600-640=960$
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Question 84 Marks
Salman invests a sum of money in Rs.50 shares, paying 15% dividend quoted at 20% premium. If his annual dividend is Rs.600, calculate :
(i) The number of shares he bought.
(ii) His total investment.
(iii) The rate of return on his investment.
Answer
N.V of each share $=$ Rs 50
M.V of each share $=$ Rs $50+20 \%$ of Rs 50
$
\begin{aligned}
& =\% 0+\frac{20}{100} \times 50 \\
& =50+10 \\
& =\operatorname{Rs} 60\end{aligned}
$
Dividend on one share $=15 \%$ of Rs $50=\frac{15}{100} \times 50=7.5$
(i) Number of shares bought $=\frac{\text { Total dividend }}{\text { Dividend on one share }}=\frac{600}{7.5}=80$
(ii) His total investment $=$ Number of shares $x$ M.V of one share
$
\begin{aligned}
& =80 \times \operatorname{Rs} 60 \\
& =\operatorname{Rs} 4800
\end{aligned}
$
(iii) Rate of return $=\frac{\text { Total dividend }}{\text { Total investment }} \times 100 \%=\frac{600}{4800} \times 100 \%=12.5 \%$
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Question 94 Marks
Salman buys 50 shares of face value Rs.100 available at Rs.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 Rs.150, how many extra shares should he buy?
Answer
Number of shares bought $=50$
$N , V$ of one share $= Rs , 100$
M.V of each share $=$ Rs 132
(I) Investment $=$ M.V of each share $x$ Number of shares
$
\begin{aligned}
& =\operatorname{Rs} 132 \times 50 \\
& =\operatorname{Rs} 6600
\end{aligned}
$
(ii) Since dividend on 1 share $=7.5 \%$ of N.V $=\frac{7.5}{100} \times 100=$ Rs 7.50
His annual income $=$ Rs $7.50 \times 50=$ Rs 375
(iii) Extra shares to be bought $=\frac{\text { Increase in annual income }}{\text { Income in one share }}=\frac{150}{7.50}=20$
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Question 104 Marks
Vivek invests Rs 4,500 in 8%, Rs 10 shares at Rs 5. He sells the shares when the price rises to Rs 30, and invests the proceeds in 12% Rs 100 shares at Rs 125. Calculate :
(1) the sale proceeds
(2) the number of Rs 125 shares he buys.
(3) the change in his annual income from the dividend.
Answer
1 st case
Total investment $=$ Rs 4,500
Market value of 1 share $=$ Rs 15
$\therefore$ No of shares purchased $=\frac{4500}{15}=300$ shares
Nominal value of 1 share $=$ Rs 10
Nominal value of 300 shares $=$ Rs $10 \times 300=$ Rs 3,000
Dividend $=8 \%$ of Rs 3,000
$
=\frac{8}{100} \times 3000=\operatorname{Rs} 240
$Sale price of 1 share $=$ Rs 30Total sale price $=$ Rs $30 \times 300=$ Rs 9,000
2) new market price of 1 share $=$ Rs 125
$\therefore$ No of shares purchased $=\frac{9000}{125}=72$ shares
3) New nominal value of 1 share $=$ Rs 100
New nominal value of 72 shares $=\operatorname{Rs} 100 \times 72=\operatorname{Rs} 7,200$
Dividend $\%=12 \%$
New dividend $=12 \%$ of Rs 7,200
$=\frac{12}{100} \times \operatorname{Rs} 7200=$ Rs 864
Change in annual income $=$ Rs $864-$ Rs 240
$=$ Rs 624
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Question 114 Marks
Mr Shameem invested 33 1/3% of his savings in 20% Rs 50 shares quoted at Rs 60 and the remainder of the savings in 10% Rs 100 share quoted at ₹ 110. If his total income from these investments is Rs 9,200; find :
(1) his total savings
(2) the number of Rs 50 share
(3) the number of Rs 100 share
Answer
Let his total savings is Rs y
1 st case
His saving $=33 \frac{1}{3} \%$ of $y=\operatorname{Rs} \frac{y}{3}$
The market price of 1 share $=$ Rs 60
Then shares purchased $=\frac{y}{3 \times 60}=\frac{y}{180}$
Dividend on 1 share $=20 \%$ of Rs $50=\operatorname{Rs} 10$
Total dividend $=\frac{y}{180} \times 10=\operatorname{Rs} \frac{y}{18}$
2nd case
His saving $=66 \frac{2}{3} \%$ of $y=\operatorname{Rs} \frac{2 y}{3}$
Market price of 1 share $=$ Rs 110
Then shares purchased $=\frac{2 y }{3 \times 110}=\frac{ y }{165}$
Dividend on 1 share $=10 \%$ of Rs $100=$ Rs 10
Total dividend $=\frac{y}{165} \times 10=$ Rs $\frac{2 y}{33}$
Accoding to question
$
\begin{aligned}
& \text { Total income }=\text { Rs } 9200 \\
& \Rightarrow \frac{ y }{18}+\frac{2 y }{33}= Rs 9200 \\
& \Rightarrow \frac{23 y }{198}= Rs 9200 \\
& \Rightarrow y =\frac{9200 \times 198}{23}=\operatorname{Rs} 79200
\end{aligned}
$
The number of Rs 50 share $=\frac{79200}{180}=440$
The number of Rs 100 share $=\frac{79200}{165}=480$
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Question 124 Marks
Divide Rs 50,760 into two parts such that if one part is invested in 8% Rs 100 shares at 8% discount and the other in 9% Rs 100 shares at 8% premium, the annual incomes from both the investments are equal.
Answer
Total investment = Rs 50760
Let 1 st part $=$ Rs $y$
2nd part $=$ Rs $(50760-y)$
For 1st part
Nominal value of 1 share $=$ Rs 100
Market value of 1 share $=$ Rs $100-8 \%$ of Rs 100
= Rs 100 - Rs 8 = Rs 92
$\therefore$ No. shares purached $=\frac{ y }{92}$ shares
Dividend $\%=8 \%$
Dividend on 1 share $=8 \%$ of Rs $100=$ Rs 8
Total dividend $=\frac{ y }{92} \times \operatorname{Rs} 8=\operatorname{Rs} \frac{2 y }{23}$
For 2nd part
Nominal value of 1 share $=$ Rs 100
Market value of 1 share $=$ Rs $100+8 \%$ of Rs 100 $=$ Rs $100+$ Rs $8=$ Rs 108
$\therefore$ No of shares purchased $=\frac{50760- y }{108}$ share
Dividend $\%=9 \%$
Dividend on 1 share $=9 \%$ of Rs $100=$ Rs 9Total dividend $=\frac{50760- y }{108} \times \operatorname{Rs} 9=\operatorname{Rs} \frac{9(50760- y )}{108}$
Given that both dividend are equalThen Rs $\frac{2 y }{23}=\operatorname{Rs} \frac{9(50760- y )}{108}$
$
\begin{aligned}
& \Rightarrow 2 y \times 108=23(456840-9 y ) \\
& \Rightarrow 216 y =456840 \times 23-207 y \\
& \Rightarrow 423 y =456840 \times 23 \\
& \Rightarrow y =\frac{456840 \times 23}{423}=\operatorname{Rs} 24840
\end{aligned}
$
1 st part $=$ Rs 24840
2nd part $=$ Rs $50760-$ Rs $24840=$ Rs 25920
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Question 134 Marks
A man invested Rs 45,000 in 15% Rs100shares quoted at Rs 125. When the market value of these shares rose to Rs 140, he sold some shares, just enough to raise Rs 8,400. Calculate:
(1) the number of shares he still holds;
(2) the dividend due to him on these remaining shares.
Answer
1) Total investment $=$ Rs 45,000
Market value of 1 share $=$ Rs 125
$\therefore$ No of shares purchased $=\frac{45000}{125}=360$ shares
Nominal value of 360 shares $=$ Rs $100 \times 360=$ Rs 36,000
Let no. of shares sold $=n$
Then sale price of 1 share $=$ Rs 140
Total sale price of $n$ shares $=$ Rs 8,400
Then $n =\frac{8400}{140}=60$ shares
The no. of shares he still holds $=360-60=300$
2) Nominal value of 300 shares $=$ Rs $100 \times 300=$ Rs 30,000
Dividend $\%=15 \%$
Dividend $=15 \%$ of Rs 30,000
$=\frac{15}{100} \times 30000=\operatorname{Rs} 4500$
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Question 144 Marks
A man buys 400, twenty-rupee shares at a discount of 20% and receives a return of 12% on his money. Calculate:
(1) the amount invested by him.
(2) the rate of dividend paid by the company.
Answer
Nominal value of 1 share $=$ Rs 20
Market value of 1 share $=$ Rs $20-20 \%$ of Rs 20
$=$ Rs $20-$ Rs 4 = Rs 16
No. of shares purchased $=400$
Nominal value of 400 shares $=400 \times 20=$ Rs 8,000
(i) Market value of 400 shares $=400 \times 16=$ Rs 6,400
(ii) Return $\%=12 \%$Income $=12 \%$ of Rs 6,400
$=\frac{12}{100} \times \operatorname{Rs} 6400=$ Rs 768
Dividend $\%=\frac{\text { Income }}{\text { Nominal value }} \times 100 \%$
$=\frac{768}{8000} \times 100 \%=9.6 \%$
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Question 154 Marks
A man buys 400, twenty-rupee shares at a premium of Rs 4 each and receives a dividend of 12%. Find:
1) the amount invested by him.
2) his total income from the shares.
3) percentage return on his money.
Answer
Nominal value of 1 share $=$ Rs 20
Market value of 1 share $=$ Rs $20+\operatorname{Rs} 4=$ Rs 24
No. of shares purchased $=400$
Nominal value of 400 shares $=400 \times 20=$ Rs 8,000
1) Market value of 400 shares $=400 \times 24=\operatorname{Rs} 9,600$
2) Dividend $\%=12 \%$Dividend $=12 \%$ of Rs 8000
$
=\frac{12}{100} \times \operatorname{Rs} 8000=\operatorname{Rs} 960
$
3) Percentage return $=\frac{\text { income }}{\text { investment }} \times 100 \%$
$
=\frac{960}{9600} \times 100 \%=10 \%
$
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Question 164 Marks
A company declares a dividend of 11.2% to all its share-holders. If its Rs 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 Rs 1,680?
Answer
Nominal value of 1 share $=$ Rs 60
Market value of 1 share $=$ Rs $60+25 \%$ of Rs 60
$=$ Rs $60+\operatorname{Rs} 15=\operatorname{Rs} 75$
Let no. of shares purchased $=n$
Then nominal value of $n$ shares $=\operatorname{Rs}$ (60n)
Dividend $\%=11.2 \%$
Dividend $=$ Rs 1,680
$\therefore 11.2 \%$ of $60 n=$ Rs 1680
$\Rightarrow \frac{11.2}{100} \times 60 n = Rs 1680$
$\Rightarrow n =\frac{1680 \times 100}{11.2 \times 60}=250$
Then market value of 250 shares $=250 \times 75=$ Rs 18,750
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Question 174 Marks
How much should a man invest in Rs 100 shares selling at Rs 110 to obtain an annual income Rs 1,680, if the dividend declared is 12%?
Answer
Nominal value of 1 share $=$ Rs 100
Market value of 1 share $=$ Rs 110
Let no. of shares purchased $=n$
Then nominal value of $n$ shares $=R s(100 n)$Dividend $\%=12 \%$
Dividend $=$ Rs 1,680
$\therefore 12 \%$ of $100 n=$ Rs 1680
$\Rightarrow \frac{12}{100} \times 100 n = Rs 1680$
$\Rightarrow n =\frac{1680 \times 100}{12 \times 100}=140$
Then market value of 140 shares $=140 \times 110=$ Rs 15,400
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Question 184 Marks
A man invests Rs 20,020 in buying shares of nominal value Rs 26 at 10% premium. The dividend on the shares is 15% per annum. Calculate
1) the number of shares he buys
2) the dividend he receives annually.
3) the rate of interest he gets on his money.
Answer
Total investment $=$ Rs 20,020
Nominal value of 1 share $=$ Rs 26
Market value of 1 share $=$ Rs $26+10 \%$ of Rs 26
$=$ Rs $26+$ Rs $2.60=$ Rs 28.60
$\therefore$ No of shares purchased $=\frac{20.020}{28.60}=700$ shares
Nominal value of 700 shares $=$ Rs $26 \times 700=$ Rs 18,200
Dividend $\%=15 \%$
Dividend $=15 \%$ of Rs 18,200
$=\frac{15}{100} \times 18200=$ Rs 2730
$\therefore$ Income $\%=\frac{\text { Income }}{\text { Investment }} \times 100 \%$
$=\frac{2730}{20020} \times 100 \%=\frac{150}{11} \%=13 \frac{7}{11} \%$
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Question 194 Marks
A man buys 75, Rs 100 shares of a company which pays 9 per cent dividend. He buys shares at such a price that he gets 12 per cent of his money. At what price did he buy the shares?
Answer
Nominal value of 1 share $=$ Rs. 100
Nominal value of 75 shares $=100 \times 75=$ Rs. 7500
Dividend $\%=9 \%$
$\therefore$ Dividend $=9 \%$ of Rs. 7500
$
\begin{aligned}
& =\frac{9}{100} \times 7500 \\
& =\text { Rs. } 675
\end{aligned}
$
Let market price of 1 share $=$ Rs. $y$
Then market price of 75 shares $=$ Rs. $y$
Profit $\%$ on investment $=12 \%$
$12 \%$ of $75 y=$ Rs. 675
$=\frac{12}{100} \times 75 y$
$=$ Rs. 675
$y=$ Rs. 75
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Question 204 Marks
Two brothers A and B invest Rs 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 per cent of the dividend received by B
Answer
For $A$
Total investment $=$ Rs 16,000
Nominal value of 1 share $=$ Rs 100
Market value of 1 share $=$ Rs 80
$\therefore$ No of shares purchased $=\frac{16000}{80}=200$ shares
Nominal value of 200 shares $=100 \times 200=$ Rs 20,000Dividend $\%=3 \%$Dividend $=3 \%$ of $Rs 20,000$
$\frac{3}{100} \times \operatorname{Rs} 20,000=\operatorname{Rs} 600$
For BTotal investment $=$ Rs 16,000
Nominal value of 1 share $=$ Rs 10
Market value of 1 share $=$ Rs 10
$\therefore$ No of shares purchased $=\frac{16000}{10}=1600$ shares
Nominal value of 1600 shares $=10 \times 1600=$ Rs 16,000Dividend received by $B=$ Dividend received by $A=R s 600$
Dividend $\%=\frac{\text { Dividend }}{\text { Nominal Value }} \times 100 \%$
$=\frac{600}{16000} \times 100 \%$
$=3.75 \%$
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Question 214 Marks
A man sold 400 (Rs 20) shares of a company, paying 5% at Rs 18 and invested the proceeds in (Rs 10) shares of another company paying 7% at Rs 12. How many (Rs 10) shares did he buy and what was the change in his income?
Answer
1st case
Nominal value of 1 share $=\operatorname{Rs} 20$
Nominal value of 400 shares $=$ Rs $20 \times 400= 8,000$
Market value of 1 share $=\text{₹}  18$
Market value of 400 shares $=\text{₹}  18 \times 400=\text{₹}  7,200$Dividend $\%=5 \%$
Dividend $=5 \%$ of Rs 8,000
$
\frac{5}{100} \times 8000=\text { Rs } 400
$
2nd case
Nominal value of 1 share $=\operatorname{Rs} 10$
Market value of 1 share $=$ Rs 12
$\therefore$ No of shares purchased $=\frac{7200}{12}=600$ shares
Nominal value of 600 shares $=\operatorname{Rs} 10 \times 600=\operatorname{Rs} 6,000$
Dividend $\%=7 \%$
Dividend $=7 \%$ of Rs 6,000
$
=\frac{7}{100} \times 6000=\text { Rs } 420
$
Annual change in income $=$ Rs $420-$ Rs 400
= Rs 20 increase
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Question 224 Marks
A man bought 360, ten-rupee shares of a company, paying 12% per annum. He sold the shares when their price rose to Rs 21 per share and invested the proceeds in five-rupee shares paying 4.5 per cent per annum at Rs 3.50 per share. Find the annual change in his income.
Answer
1st case
Nominal value of 1 share $=$ Rs 10
Nominal value of 360 shares $=$ Rs $10 \times 360=$ Rs 3,600
Market value of 1 share $=$ Rs 21
Market value of 360 shares $=$ Rs $21 \times 360=$ Rs 7,560
Dividend $\%=12 \%$
Dividend $=12 \%$ of Rs 3,600
$
=\frac{12}{100} \times 3600=\operatorname{Rs} 432
$
2nd case
Nominal value of 1 share $=$ Rs 5
Market value of 1 share $=$ Rs 3.50
$\therefore$ No of shares purchased $=\frac{7560}{3.50}= Rs 2160$ shares
Nominal value of 2160 shares $=$ Rs $5 \times 2160=$ Rs 10,800
Dividend $\%=4.5 \%$
Dividend $=4.5 \%$ of Rs 10,800
$
=\frac{4.5}{132} \times 10800=\operatorname{Rs} 486
$
Annual change in income = Rs 486 - Rs 432
$=$ Rs 54 increase
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Question 234 Marks
A man has a choice to invest in hundred-rupee shares of two firms at Rs 120 or at Rs 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 Rs 26,400 with each firm, how much will be the difference between the annual returns from the two firms.
Answer
1) $1 st$ firm
Market value of 1 share $=$ Rs 120
Nominal value of 1 share $=$ Rs 100
Dividend $=5 \%$
Income on Rs $120=5 \%$ of Rs $100=$ Rs 5
Income on Rs $1=\frac{5}{120}=$ Rs 0.041
2 nd firm
Market value of 1 share $=$ Rs 132
Nominal value of 1 share $=$ Rs 100
Dividend $=6 \%$
Income on Rs $132=6 \%$ of Rs $100=$ Rs 6
Income on Rs $1=\frac{6}{132}=$ Rs 0.045
Then investment in second company is giving better return.
2) Income on investment of Rs 26,400 in each firm
$
=\frac{5}{120} \times 26400=\text { Rs } 1100
$
Income on investment of Rs 26,400 in second firm
$
=\frac{6}{132} \times 26400=\text { Rs } 1200
$
$\therefore$ Difference between both return $=$ Rs $1200-$ Rs $1100=$ Rs 100
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Question 244 Marks
Which is the better investment: 16% Rs 100 shares at 80 or 20% Rs 100 shares at 120?
Answer
1 st case
$16 \%$ of Rs 100 shares at 80 means;
Market value of 1 share $=$ Rs 80
Nominal value of 1 share $=$ Rs 100
Dividend $=16 \%$
Income on Rs $80=16 \%$ of Rs $100=$ Rs 16
income on Rs $1=\frac{16}{80}=$ Rs 0.20
2nd case
$20 \%$ of Rs 100 shares at 120 means
Market value of 1 share $=$ Rs 120
Nominal value of 1 share $=$ Rs 100
Dividend $=20 \%$
Income on Rs $120=20 \%$ of Rs $100=$ Rs 20
Income on Rs $1=\frac{20}{120}=$ Rs 0.17
Then $16 \%$ Rs 100 shares at 80 is better investment
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Question 254 Marks
A company with 10,000 shares of nominal value Rs 100 declares an annual dividend of 8% to the shareholders
1) Calculate the total amount of dividend paid by the company.
2) Ramesh had bought 90 shares of the company at Rs 150 per share. Calculate the dividend he receives and the percentage of return on his investment.
Answer
1) Nominal value of 1 share $=$ Rs 100
Nominal value of 10,000 shares $=\operatorname{Rs} 100 \times 10,000=\operatorname{Rs} 10,00,000$
Dividend $\%=8 \%$
Dividend $=8 \%$ of Rs $10,00,000$
$
=\frac{8}{100} \times 10,00,000=\operatorname{Rs} 80,000
$
2) Market value of 90 shares $=$ Rs $150 \times 90=$ Rs 13,500
Nominal value of 90 shares $=\operatorname{Rs~} 100 \times 90=\operatorname{Rs} 9,000$
Dividend $=8 \%$ of Rs 9,000
$
=\frac{8}{100} \times 9000=\operatorname{Rs} 720
$
Return $\%=\frac{\text { Income }}{\text { Investment }} \times 1000 \%$
$
=\frac{720}{13}, 500 \times 100 \%
$
$
=5 \frac{1}{3} \%
$
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Question 264 Marks
Mr Sharma has 60 shares of nominal value Rs 100 and decides to sell them when they are at a premium of 60%. He invests the proceeds in shares of nominal value Rs 50, quoted at 4% discount, and paying 18% dividend annually. Calculate :
1) the sale proceeds
2) the number of shares he buys and
3) his annual dividend from the shares.
Answer
1st case
Nominal value of 1 share $=$ Rs 100
Nominal value of 60 shares $=$ Rs $100 \times 60=$ Rs 6,000
Market value of 1 share $=$ Rs $100+60 \%$ of Rs 100
$=$ Rs $100+$ Rs $60=$ Rs 160
Market value of 60 shares $=\operatorname{Rs} 160 \times 60=\operatorname{Rs} 9,600$
2)
Nominal value of 1 share $=$ Rs 50
Market value of 1 share $=$ Rs $50-4 \%$ of Rs 50
$=\operatorname{Rs} 50-$ Rs $2=$ Rs 48No of shares purchased $=\frac{9600}{48}=200$ shares
3) Nominal value of 200 shares $=\operatorname{Rs} 50 \times 200=\operatorname{Rs} 10,000$ Dividend $\%=18 \%$Dividend $=18 \%$ of Rs 10,000
$=\frac{18}{100} \times 10000=\operatorname{Rs} 1800$
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Question 274 Marks
A man invests Rs 11,200 in a company paying 6 per cent per annum when its Rs 100 shares can be bought for ₹ 140. Find:
1) his annual dividend
2) his percentage return on his investment.
Answer
Nominal value of 1 share $=$ Rs 100
Market value of 1 share $=$ Rs 140
Total investment $=$ Rs 11,200
No of shares purchased $=\frac{11200}{140}=80$ shares
Then nominal value of 80 shares $=80 \times 100=\operatorname{Rs} 8,000$
1)
Dividend $\%=6 \%$
Dividend $=6 \%$ of Rs 8,000
$
=\frac{6}{100} \times \operatorname{Rs} 8000=\text { Rs } 480
$
2) Return $\%=\frac{\text { Income }}{\text { Investment }} \times 100 \%$
$
\begin{aligned}
& =\frac{480}{11200} \times 100 \% \\
& =4.29 \%
\end{aligned}
$
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Question 284 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 is the return she gets as per cent on her investment? Give your answer to the nearest integer.
Answer
Nominal value of 1 share $=\operatorname{Rs} 100$
Market value of 1 share $=$ Rs $100+40 \%$ of Rs 100
$=\operatorname{Rs} 100+\operatorname{Rs} 40=\operatorname{Rs} 140$
No. of shares purchased $=1800$
Nominal value of 1800 shares $=1800 \times 100=\text{₹}  1,80,000$
Market value of 1800 shares $=1800 \times 140=\text{₹}  2,52,000$
(1) Dividend $\%=15 \%$Dividend $=15 \%$ of Rs $1,80,000$
$=\frac{15}{100} \times$ Rs $1,80,000=$ Rs 27000
(2) $\therefore$ Return $\%=\frac{\text { Income }}{\text { Investment }} \times 100 \%$
$=\frac{27,000}{2,52,000} \times 100 \%=10.7 \%=11 \%$
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Question 294 Marks
A company, with 10,000 shares of Rs 100 each, declares an annual dividend of 5%.
(1) What is the total amount of dividend paid by the company?
(2) What should be the annual income of a man who has 72 shares in the company?
(3) If he received only 4% of his investment, find the price he paid for each share
Answer
Nominal value of 1 share $=$ Rs 100
Nominal value of 10,000 shares $=10,000 \times$ Rs $100=$ Rs $10,00,000$
1) Dividend $\%=5 \%$
$
=\frac{5}{100} \times 10,00,000=\operatorname{Rs} 50,000
$
2) Nominal value of 72 shares $=\operatorname{Rs} 100 \times 72=\operatorname{Rs} 7,200$
$
\begin{aligned}
& \text { Dividend }=5 \% \text { of Rs } 7,200 \\
& =\frac{5}{100} \times 7200=\operatorname{Rs} 360
\end{aligned}
$
3) Let market value of 1 share $=$ Rs $y$
Then market value of 10000 shares $=$ Rs $10000 y$
Return $\%=4 \%$
then $4 \%$ of Rs $10000 y=$ Rs 50000
$
\begin{aligned}
& \Rightarrow \frac{4}{100} \times 10,000 y =\operatorname{Rs} 50,000 \\
& \Rightarrow y =\operatorname{Rs} 125
\end{aligned}
$
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Question 304 Marks
A man buys Rs 50 shares of a company, paying 12% dividend, at a premium of Rs 10. Find:
(1) the market value of 320 shares;
(2) his annual income;
(3) his profit per cent.
Answer
Nominal value of 1 share $=$ Rs 50
Market value of 1 share $=\operatorname{Rs} 50+\operatorname{Rs} 10=\text{₹}  60$
Market value of 320 shares $=320 \times 60=$ Rs 19,200
Nominal value of 320 shares $=320 \times 5=\operatorname{Rs} 16,000$
Annual income $=12 \%$ of Rs 16000
$
\begin{aligned}
& =\frac{12}{100} \times 16000 \\
& =\text { Rs } 1920
\end{aligned}
$
Profit $\%=\frac{1920}{19200} \times 100 \%=10 \%$
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Question 314 Marks
A man invests Rs 7,770 in a company paying 5% dividend when a share of nominal value of Rs 100 sells at a premium of Rs 5. Find:
1) the number of shares bought;
2) annual income;
3) percentage income.
Answer
Total money invested $=$ Rs 7,770
Nominal value of 1 share $=$ Rs 100
Market value of 1 share $=\operatorname{Rs} 100+\operatorname{Rs} 5=\operatorname{Rs} 105$
$\therefore$ No. of shares purchased $=\frac{7770}{105}=74$
Nominal value of 74 shares $=74 \times 100=\operatorname{Rs} 7400$Annual income $=5 \%$ of Rs 7400
$
\begin{aligned}
& =\frac{5}{100} \times 74000 \\
& =\text { Rs } 370
\end{aligned}
$
$
\text { Income } \%=\frac{370}{7770} \times 100 \%=4.76 \%
$
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Question 324 Marks
A man invests Rs 3,072 in a company paying 5% per annum when its Rs 10 shares can be bought for Rs 16 each. Find :
(1) his annual income
(2) his percentage income on his investment.
Answer
Market value of 1 share $=$ Rs 16
A nominal value of 1 share $=$ Rs 10
Money invested $=$ Rs 3,072
$\therefore$ No. of shares purchased $=\frac{3072}{16}=192$
Nominal value of 192 Shares $=10 \times 192=$ Rs 1920
Annual income $=5 \%$ of Rs 1920
$
\begin{aligned}
& =\frac{5}{100} \times 1920 \\
& =\text { Rs } 96
\end{aligned}
$
Income $\%=\frac{96}{3072} \times 100 \%=3.125 \%=3 \frac{1}{8} \%$
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Question 334 Marks
A man invests Rs 800 in buying Rs 5 shares and when they are selling at a premium of Rs 1.15, he sells all the shares. Find his profit and profit per cent.
Answer
Nominal value of 1 share $=$ Rs 5
Market value 1 share = Rs $5+\operatorname{Rs} 1.15=\operatorname{Rs} 6.15$
Total money invested $=$ Rs 800
No of shares purchased $=\frac{800}{5}=160$
Market value of 160 shares $=160 \times 6.15=$ Rs 984
His profit =Rs $984-$ Rs $800=$ Rs 184 profit
$
=\frac{184}{800} \times 100 \%=23 \%
$
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Question 344 Marks
By investing Rs 7,500 in a company paying 10 per cent dividend, an annual income of Rs 500 is received. What price is paid for each of Rs 100 share?
Answer
Total investment $=\text{₹}  7,500$
Nominal value of 1 share $=\text{₹}  100$
No. of shares purchased $=y$
Nominal value of $y$ shares $=100 x y=\text{₹} (100 y)$
Dividend $\%=10 \%$
Dividend $=$ Rs 500
$\therefore 10 \%$ of $100 y=$ Rs 500
$\Rightarrow \frac{10}{100} \times 100 y =$ Rs 500
$\Rightarrow y =\frac{500}{10}=50$ shares
$\therefore$ market Value of 1 shares $=\frac{7500}{50}=$ Rs 150
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Question 354 Marks
A man invests Rs 8,800 in buying shares of a company of face value of rupees hundred each at a premium of 10%. If he earns Rs 1,200 at the end of the year as the dividend, find:
(1) the number of shares he has in the company.
(2) the dividend per cent per share.
Answer
Total investment $=$ Rs 8,800
Nominal value of 1 share $=$ Rs 100
Market value of 1 share $=$ Rs 110
$\therefore$ No of shares purchased $=\frac{8800}{110}=80$
Nominal value of 80 shares $=80 \times 100=\text{₹}  8,000$Let dividend $\%= y \%$
then $y \%$ of Rs $8,000=$ Rs 1,200
$
\Rightarrow \frac{ y }{100} \times 8000=1200
$
$
\Rightarrow y =15 \%
$
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Question 364 Marks
A company pays a dividend of 15% on its ten-rupee shares from which it deducts income tax at the rate of 22%. Find the annual income of a man who owns one thousand shares of this company.
Answer
Nominal value of 1 share $=\operatorname{Rs} 10$
Nominal value of 1000 shares $=1000 \times 10=\operatorname{Rs} 10,000$
$\therefore$ Dividend $=15 \%$ of Rs 10000
$
=\frac{15}{100} \times 10000=\operatorname{Rs} 1500
$
$\therefore$ Income tax paid $=22 \%$ of Rs 1500
$
=\frac{22}{100} \times 1500=\text { Rs } 330
$
His net income $=$ Rs $1,500-$ Rs $330=$ Rs 1,170
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Question 374 Marks
A man buys Rs 75 shares at a discount of Rs 15 of a company paying 20% dividend. Find:
(1) the market value of 120 shares;
(2) his annual income;
(3) his profit per cent.
Answer
Nominal value of 1 share $=\operatorname{Rs} 75$
Market value of 1 share $=\operatorname{Rs} 75-\operatorname{Rs} 15=\operatorname{Rs} 60$Market value of 120 shares $=120 \times 60=$ Rs 7,200
Nominal value of 120 shares $=120 \times 75=$ Rs 9,000
Annual income $=20 \%$ of Rs 9000
$=\frac{20}{100} \times 9000$
$=$ Rs 1800Profit $\%=\frac{1800}{7200} \times 100 \%=25 \%$
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[4 marks sum] - Mathematics STD 10 Questions - Vidyadip