[5 marks sum]

Question 15 Marks

Pramod wants to invest Rs 35,000 in shares such that the percentage return on his investment is $8 \frac{1}{7} \%$. He invested Rs 6,000 in $6 \%$ Rs 50 shares of 'Lakme' at Rs 40, Rs 15,000 in $8 \%$ Rs 100 shares of 'Volta' at Rs 125 and the remaining in $12 \%$ shares of 'BPL'. At what rate did he buy the 'BPL' shares?

Answer

Money invested $=$ Rs 35,000
For 'Lak me' shares:
Market value $=$ Rs 40
Amount invested $=$ Rs 6,000
Income from investment $=\frac{6}{40} \times 6000=$ Rs 900
For 'Volta' shares:
Market Value $=$ Rs 125
Amount invested $=$ Rs 15,000
Income from investment $=\frac{8}{125} \times \operatorname{Rs} 15000=$ Rs 960
For 'BPL' shares:
Market value $=$ Rs $x$
Amount invested $=$ Rs $(35,000-6,000-15,000)=$ Rs 14,000
Income from investment $=$ Rs $\frac{12}{x} \times 14000=$ Rs $\frac{168000}{x}$
Total investment from shares $=$ Rs $900+$ Rs $960+$ Rs $\frac{168000}{x}$
Pramod wants $8 \frac{1}{7} \%$ return on his investment $=\frac{57}{7} \%$
$\frac{57}{100 \times 7} \times \operatorname{Rs} 35000=$ Rs 2850
Therefore, Rs 2,850 - Rs $900+$ Rs $960+$ Rs $\frac{168000}{x}$
Rs $990 x$ - Rs 1,68, $000 x=$ Rs $169.69=$ Rs 170
Hence, Pramod bought BPL shares at Rs 170 per share.

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Question 25 Marks

Krithika wants to invest Rs 10,000 in shares of different companies such that the percentage return on her investment is 8%. She invested Rs 4,500 in 6% Rs 100 shares at Rs 75, Rs 2,500 in 8% Rs 100 shares at par and the rest in 16% Rs 100 shares. Find the rate at which she bought the 16% shares.

Answer

Money invested $=$ Rs 10,000
For $6 \%$ shares:
Market value $=$ Rs 75
Amount invested $=$ Rs 4,500
Income from investment $=$ Rs $\frac{6}{75} \times 4500=$ Rs 360
For $8 \%$ shares:
Market Value $=$ Rs 100
Amount invested $=$ Rs 2,500
Income from investment $=$ Rs $\frac{8}{100} \times 2500=$ Rs 200
For $16 \%$ shares:
Market value $=$ Rs $x$
Amount invested $=\operatorname{Rs}(10,000-4,500-2,500)=$ Rs 3,000
Income from investment $=$ Rs $\frac{16}{x} \times 3000=$ Rs $\frac{48000}{x}$
Total investment from shares $= Rs 360+ Rs 200+ Rs \frac{48000}{x}$
Krithika wants $8 \%$ return on his investment
$
\frac{8}{100} \times \text { Rs } 10000=\text { Rs } 800
$
Therefore,
$
\text { Rs } 800=\text { Rs } 360+\text { Rs } 200+\operatorname{Rs} \frac{48000}{x}
$
Rs $240 x=$ Rs 48,000
$
x=\text { Rs200 }
$
Hence, Krithika bought $16 \%$ shares at Rs 200 per share.

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Question 35 Marks

Ananth had Rs 50 shares of 'Esco' paying 6% dividend. He sold them at a market price of Rs 80 and invested the proceeds in buying Rs 100 shares of 'Y2K Software' at Rs 150 and paying 11% dividend. He thus increased his annual income by Rs 2,150. How many shares of 'Esco' did he sell?

Answer

For shares of 'Esoo':
Let $x$ be the no. of shares sold by Ananth.
Nominal value of each share $=$ Rs 50
Face value of $x$ shares $=$ Rs $50 x$
Market value of each share $=$ Rs 80
Market value of $x$ shares $=$ Rs $80 x=$ proceeds from selling
Dividend $=6 \%$ of Rs $50 x=\frac{6}{100} \times$ Rs $50 x=$ Rs $3 x \ldots . .$. (i)
For shares of 'Y2K Softvvare':
Market value of each share $=$ Rs 150
Number of shares bought= proceeds from selling 'Esco' / market value of 'Y2K Softvvare'
$
=\frac{80 x}{150}=\frac{8 x}{15}
$
Nominal value of each share $=$ Rs 100
Face value of $\frac{8 x}{15}$ shares $=$ Rs Rs $100 \times \frac{8 x}{15}=$ Rs $53.33 \times$
$
\text { Dividend }=11 \% \text { of Rs } 53.33 x =\operatorname{Rs} \frac{11 \times 53.33 x}{100}=\text { Rs } 5.86 x\ldots (ii)
$
Increase in annual income $=$ Rs 2, $150=$ subtraction of (i) from (ii)
Rs $(5.86 x-3 x)=$ Rs 2,150
$2.86 x=$ Rs 2,150
$\Rightarrow x=751$
Therefore, Ananth sold 751 shares

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Question 45 Marks

Payal had Rs 125 shares of 'Asian Chemicals' paying 12% dividend. She sold them at Rs 150 and invested the proceeds in Rs 50 shares of 'Saras Chemicals' at Rs 40 and paying 10% dividend. She thus increased her income by Rs 825. Find the number of shares of 'Asian chemicals' that Payal sold.

Answer

For shares of 'Asian Chemicals':
Let $x$ be the no. of shares sold by Pay al.
Nominal value of each share =Rs 125
Face value of $x$ shares $=$ Rs $125 x$
Market value of each share $=$ Rs 150
Market value of $x$ shares $=$ Rs $150 x=$ proceeds from selling
Dividend $=12 \%$ of Rs $125 x =\frac{12}{100}$ x Rs $125 x =$ Rs $15 x$$\ldots(i)$
For shares of 'Saras Chemicals':
Market value of each share $=$ Rs 40
Number of shares bought= proceeds from selling 'Asian Chemicals' /market value of 'Saras Chemicals'
$=\frac{150 x}{40}=\frac{15 x}{4}$
Nominal value of each share $=$ Rs 50
Face value of $\frac{15 x}{4}$ shares $=$ Rs $50 \times \frac{15 x}{4}=$ Rs $187.5 x$
$\text { Dividend }=10 \% \text { of Rs } 187.5 x =\text { Rs } \frac{10 \times 187.5 x}{100}=\text { Rs } 18.75 x \text {.$\ldots (ii)$ }$
Increase in annual income $=$ Rs $825=$ subtraction of (i) from (ii)
$\text { Rs }(18.75 x-15 x)=\text { Rs } 825$
$\Rightarrow 3.75 x=\text { Rs } 825$
$\Rightarrow x=220$
Therefore, Payal sold 220 shares

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Question 55 Marks

Ramesh had Rs $100$ shares of 'Bihar Steel' paying $8\%$ dividend. He sold them at a market price of Rs $130$ and invested the proceeds in buying Rs $50$ shares of 'Jindal steel' available at Rs $75$ and paying $12\%$ dividend. He thus increased the annual income by Rs $360.$ How many shares did Ramesh sell?

Answer

For shares of 'Bihar Steel':
Let $x$ be the no. of shares sold by Ramesh.
Nominal value of each share $=$ Rs $100$
Face value of $x$ shares $=$ Rs $100 x$
Market value of each share $=$ Rs $130$
Market value of $x$ shares $=$ Rs $130 x=$ proceeds from selling
$\text { Dividend }=8 \% \text { of Rs } 100 x =\frac{8}{100} \times \text { Rs } 100 x=\text { Rs } 8 \times\ldots (i)$
For shares of 'Jindal Steel':
Market value of each share $=$ Rs $75$
Number of shares bought $=$ proceeds from selling 'Bihar steel' I market value of 'Jindal steel'
$=\frac{130 x}{75}$
Nominal value of each share $=$ Rs $50$
Face value of $\frac{130 x}{75}$ shares $=$ Rs $50 \times \frac{130 x}{75}=$ Rs $86.667 \times$
$\text { Dividend }=12 \% \text { of Rs } 86.667 x=\text { Rs } \frac{12 \times 86.667 x}{100}=\text { Rs } 10.40 x\ldots (ii)$
Increase in annual income $=$ Rs $360=$ subtraction of (i) from (ii)
$\operatorname{Rs}(10.40 x-8 x)=\operatorname{Rs} 360 $
$\Rightarrow 2.4 x=\operatorname{Rs} 360$
$\Rightarrow x=150$
Therefore, Ramesh sold $150$ shares

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Question 65 Marks

Archana bought 250 shares of Rs 50 each of 'Indal' paying 12% of dividend. She bought them at such a price that she gets 15% return on her investment. At what share did she buy the shares?

Answer

Let Archana's investment be $x$.
Face value of 250 shares $=\operatorname{Rs}(50 \times 250)=\operatorname{Rs} 12,500$
Dividend for 250 shares $=12 \%$ of Rs $12500=$ Rs $\frac{12 \times 12500}{100}=$ Rs 1500
She gets Rs 1,500 as dividend which is equal to $15 \%$ of money invested
$\Rightarrow \frac{15 x}{100}=\operatorname{Rs} 1500$
$\Rightarrow x=\operatorname{Rs} 10000$
Hence, Archana invested Rs 10,000.
No. of shares bought by Archana $=250$
Value of a share $=$ Rs $\frac{10000}{250}=$ Rs 40
Archana bought a share for Rs 40 .

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Question 75 Marks

Vikram bought 200 shares of Rs 25 each of 'Calcutta Jute Co.' paying 8% of dividend. Vikram bought them at such a price that he gets 10% of his money. At what price did he buy the share?

Answer

Let Vikram's investment be $x$.
Face value of 200 shares $=\operatorname{Rs}(25 \times 200)=$ Rs 5,000
Dividend for 200 shares $=8 \%$ of Rs $5,000=$ Rs $\frac{8 \times 5000}{100}=$ Rs 400
He gets Rs 400 as dividend which is equal to $10 \%$ of money invested
$\Rightarrow \frac{10 x}{100}=\operatorname{Rs} 400$
$\Rightarrow x =\operatorname{Rs} 4000$
Hence, Vikram invested Rs 4,000.
No. of shares bought by Vikram $=200$
Value of a share $=$ Rs $\frac{4000}{200}=$ Rs 20
Vikram bought a share for Rs 20.

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Question 85 Marks

Karan buys 125 shares of Rs 100 each of 'Reliance Technologies Ltd.' which pays a dividend of 6%. He buys them at such a price that he gets 4% of his money. At what price did Karan buy the share?

Answer

Let Karan's investment be $x$.
Face value of 125 shares $=\operatorname{Rs}(100 \times 125)=\operatorname{Rs} 12,500$
Dividend for 125 shares $=6 \%$ of $12,500 J = Rs \frac{6 \times 12500}{100}=$ Rs 750
He gets Rs 750 as dividend which is equal to $4 \%$ of money invested
$
\Rightarrow \frac{4 x}{100}=\text { Rs } 750
$
$\Rightarrow 4 x=\operatorname{Rs} 75000$
$
\Rightarrow x=\operatorname{Rs} \frac{75000}{4}
$
$
\Rightarrow x=\operatorname{Rs} 18750
$
Hence, Karan invested Rs 18,750.
No. of shares bought by Karan $=125$
Value of a share $=$ Rs $\frac{18750}{125}=$ Rs 150
Karan bought a share for Rs 150.

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Question 95 Marks

Bhavana invested Rs 20,000 and Rs 25,000 in buying shares of 'Bharati Telecom' and 'Satyam Infoways' which later declared dividend of 10% and 12.5% respectively. After collecting the dividends Bhavana sells all her shares at a loss of 4% and 5% respectively on her investments. Find her total earnings.

Answer

Total investment $=\operatorname{Rs}(20,000+25,000)=\operatorname{Rs} 45,000$

Dividend given by 'Bharati Telecom' $=10 \%=$ Rs $\frac{10 \times 20000}{100}=$ Rs 2000

Dividend given by 'Satyam Infoways' = $12.5 \%=$

Rs $\frac{12.5 \times 25000}{100}=$ Rs $\frac{125 \times 25000}{10 \times 100}=$ Rs 3125

Total dividend earned $=\operatorname{Rs}(2,000+3,125)=\operatorname{Rs} 5,125$

Money earned by selling shares of 'Bharati Telecom'

$=\operatorname{Rs}(20,000-4 \%$ of Rs 20,000$)=\operatorname{Rs}(20,000-800)=\operatorname{Rs} 19,200$

Money earned by selling shares of 'Satyam Infoways'

$=\operatorname{Rs}(25,000-5 \%$ of Rs 25,000$)=\operatorname{Rs}(25,000-1250)=\operatorname{Rs} 23,750$

Total money earned by selling shares $=\operatorname{Rs}(19,200+23,750)=\operatorname{Rs} 42,950$

Total earnings $=$ money earned by selling shares + dividends earned $=\operatorname{Rs}(42,950+5,125)=\operatorname{Rs}$ 48,075

Bhavana's earnings from the transactions $=\operatorname{Rs}(48,075-45,000)$

$=$ Rs 3,075

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Question 105 Marks

Tarun invested Rs 24,000 and Rs 30,000 in buying Rs 100 at par shares of 'Vam Organics' and 'Hero Honda' which later declared dividend of 12% and 15% respectively. After collecting the dividends Tarun sold the shares as their prices had fallen by Rs 5 and Rs 10 respectively. Find Tarun's earnings from the above transactions.

Answer

Total investment $=\operatorname{Rs}(24,000+30,000)=\operatorname{Rs} 54,000$
No. of shares of 'Vam Organics' $=\frac{\text { money invested }}{\text { Cost of one share }}=\frac{24000}{100}=240$
No. of shares of 'Hero Honda' $=\frac{\text { money invested }}{\text { Cost of one share }}=\frac{30000}{100}=300$
Dividend given by 'Vam Organics' $=12 \%=$ Rs $\frac{12 \times 24000}{100}=$ Rs 2880
Dividend given by 'Hero Honda' $=15 \%=$ Rs $\frac{15 \times 30000}{100}=$ Rs 4500
Total dividend earned $=\operatorname{Rs}(2,880+4,500)=\operatorname{Rs} 7,380$
Money earned by selling shares of 'Varn Organics' = Rs ( 95 x 240)
$=$ Rs 22,800
Money earned by selling shares of 'Hero Honda' = Rs $(90 \times 300)$
$=$ Rs 27,000
Total money earned by selling shares $=\operatorname{Rs}(22,800+27,000)=\operatorname{Rs} 49,800$
Total earnings = money earned by selling shares + dividends earned
$=\operatorname{Rs}(49,800+7,380)=\operatorname{Rs} 57,180$
Tarun's earnings from the transactions $=$ Rs $(57,180-54,000)$
$=$ Rs 3,180

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Question 115 Marks

Akanksha invested 15%, 25% and 35% of her savings in buying shares of 'Infosys', 'Wipro' and 'Reliance' which declared dividends of 16%, 18% and 20% respectively. If her total income from dividends is Rs 52,125, find her savings and the amount invested in each company.

Answer

Let total savings be $x$.
Investment in 'Infosys' $=15 \%$ of $× =\frac{15}{100} \times x=\frac{3 x}{20}$
Investment in 'Wipro' $=25 \%$ of $× =\frac{25}{100} \times x=\frac{x}{4}$
Investment in 'Reliance' $=35 \%$ of $× =\frac{35}{100} \times x=\frac{7 x}{20}$
Dividend given by 'Infosys' $=16 \%$ of $\frac{3 x}{20}$
$=\frac{16 \times 3 x}{100 \times 20}=0.024 x\ldots (i)$
Dividend given by 'Wipro' $=18 \%$ of $\frac{x}{4}$
$=\frac{18 \times x}{100 \times 4}=0.045 x\ldots (ii)$
Dividend given by 'Reliance' $=20 \%$ of $\frac{7 x}{20}$
$=\frac{20 \times 7 x}{100 \times 20}=0.07 x\ldots (iii)$
$ \text { (i) }+ \text { (ii) }+ \text { (iii) }=\operatorname{Rs} 52,125 \ldots . . . . . . \text { (given) }$
$(0.024+0.045+0.07) x=\operatorname{Rs~52,~} 125$
$0.139 x=\operatorname{Rs~52,125}$
$x=\operatorname{Rs} \frac{52125}{0.139}=\text { Rs } 375000 $
Hence, Akanksha's savings $=$ Rs 3,75,000
Investment in 'Infosys' $=$ Rs $\frac{3 x}{20}=$ Rs $\frac{3 \times 375000}{20}=$ Rs $56250$
Investment in 'Wipro' $=$ Rs $\frac{x}{4}=$ Rs $\frac{375000}{4}=$ Rs $93750$
Investment in 'Reliance' $=$ Rs $\frac{7 x}{20}=$ Rs $\frac{7 \times 375000}{20}=$ Rs $131250$

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Question 125 Marks

Saurav invested 10%, 30% and 40% of his savings in buying shares of 3 different companies A, B and C which declared dividends of 12%, 15% and 16% respectively. If Saurav's total income from dividends is Rs 3,025, find his savings and the amount invested in each company.

Answer

Let total savings be $x$.
Investment in company A $=10 \%$ of $× =\frac{10}{100} \times x=\frac{x}{10}$
Investment in company $B =30 \%$ of $× =\frac{30}{100} \times x=\frac{3 x}{10}$
Investment in company C $=40 \%$ of $× =\frac{40}{100} \times x=\frac{4 x}{10}=\frac{2 x}{5}$
Dividend given by company A $=12 \%$ of $\frac{x}{10}$
$\frac{12 \times x}{100 \times 10}=0.012 x$$\ldots (i)$
Dividend given by company $B =15 \%$ of $\frac{3 x}{10}$
$=\frac{15 \times 3 x}{100 \times 10}=0.045 x\ldots (ii)$
Dividend given by company C $=16 \%$ of $\frac{2 x}{5}$
$\frac{16 \times 2 x}{100 \times 5}=0.064 x \ldots \ldots . . . . . \text { (iii) }$
$text { (i) }+(\text { ii) }+ \text { (iii) }=\operatorname{Rs} 3,025 \ldots \ldots . . . \text { (given) }$
$(0.012+0.045+0.064) x=\operatorname{Rs} 3,025$
$0.12 \text { I x }=\operatorname{Rs} 3,025$
$x=\operatorname{Rs} \frac{3025}{0.121}=\operatorname{Rs} 25000$
Hence, Saurav's savings $=$ Rs 25,000
Investment in company A $=$ Rs $\frac{x}{10}=$ Rs $\frac{25000}{10}=$ Rs 2500
Investment in company B $=$ Rs $\frac{3 x}{10}=$ Rs $\frac{75000}{10}=$ Rs 7500
Investment in company C $=$ Rs $\frac{2 x}{5}=$ Rs $\frac{50000}{5}=$ Rs 10000

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Mathematics [5 marks sum]

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