[4 marks sum] - Mathematics STD 10 Questions - Vidyadip

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18 questions · timed · auto-graded

Question 14 Marks

Usha sold 350 shares of Rs 150 each paying 6% dividend at Rs 120 and invested the proceeds in Rs 75 shares at par paying 8% dividend. Calculate the number of Rs 75 shares she bought and the change in her annual income.

Answer

In first case:
No. of shares sold $=350$
Face value of each share $=$ Rs 150
Face value of 350 shares $=\operatorname{Rs}(150 \times 350)=\operatorname{Rs} 52,500$
Market value of each share $=$ Rs 120
Market value of 350 shares $=\operatorname{Rs}(120 \times 350)=\operatorname{Rs} 42,000$
Dividend (income) for 350 shares $=6 \%$ of Rs $52,500=$
Rs $\frac{6 \times 52500}{100}=$ Rs 3150
In second case:
Proceeds from selling 350 shares $=$ Rs 42,000
Face value of each share $=$ Rs 75
Market value of each share $=$ Rs 75
No. of shares bought $=\frac{42000}{75}=560$
Usha bought 560 shares of Rs 75 each.
Face value of 560 shares $=\operatorname{Rs}(75 \times 560)=$ Rs 42,000
Dividend (income) for 560 shares $=8 \%$ of Rs $42,000=$
$
\text { Rs } \frac{8 \times 42000}{100}=\text { Rs } 3360
$
Change in annual income $=\operatorname{Rs}(3,360-3,150)=\operatorname{Rs} 210$

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Question 24 Marks

Gayathri wants to have a monthly income of Rs 500.For this she purchased Rs 75 shares of 'V.G.Electronics' paying 20% dividend. How many shares did Gayathri purchased and what is her investment if the market price of the share is Rs 62.50?

Answer

Let $x$ be the no. of shares purchased by Gayathri.
Value of $x$ shares $=$ Rs $75 x x=$ Rs $75 x$
Dividend for x no. of shares of V.G.Electronics $=20 \%$ of Rs 75 x
$=\operatorname{Rs} \frac{20 \times 75 x}{100}=\operatorname{Rs} 15 x$
Monthly income $=$ Rs $500=$ Dividend $/ 12$
$\Rightarrow \operatorname{Rs} \frac{15 x}{12}=\operatorname{Rs} 500$
$\Rightarrow \text { Rs } 15 x=\operatorname{Rs} 6000$
$\Rightarrow x=400$
Hence, Gayathri should purchase 400 shares.
The market price for shares $=$ Rs 62.50 Investment by
Gayathri at Rs $62.50=\operatorname{Rs}(62.50 \times 400)=\operatorname{Rs} 25,00$

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Question 34 Marks

Mr Lal wants to give a monthly scholarship of Rs 225 to a poor student. How many 15%, Rs 100 shares of 'Mercantile Co-operative Bank' should he purchase to realize his aim? What will be his investment if the market price of the share is Rs 120?

Answer

Let $x$ be the no. of shares purchased by Mr Lal.
Value of $x$ shares $=\operatorname{Rs}(100 \times X)=\operatorname{Rs} 100 x$
Dividend for $x$ no. of shares of Mercantile Co-operative Bank = $15 \%$ of Rs $100 x$
$
=\operatorname{Rs} \frac{15 \times 100 x}{100}=\operatorname{Rs} 15 x
$
Monthly scholarship $=$ Rs $225=$ Dividend/12
$
\Rightarrow \text { Rs } \frac{15 x}{12}=\text { Rs } 225
$
$
\Rightarrow \text { Rs } 15 x=\text { Rs } 2700
$
$
\Rightarrow x =180
$
Hence, Mr Lal should purchase 180 shares.
The market price for shares $=$ Rs 120 ,
Investment by Mr Lal at Rs $120=\operatorname{Rs}(120 \times 180)=\operatorname{Rs} 21,600$.

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Question 44 Marks

Rohit had 1000 shares of Rs 125 each of 'New Delhi Times' paying a dividend of 12%. He sold all of them at a market rate of Rs 150 and invested the proceeds in buying Rs 25 shares of BVL available at Rs 60 and paying 20% dividend. How many shares of BVL did Rohit buy and what is the change in his annual income?

Answer

In first case:
No. of shares sold $=1000$
Face value of each share $=$ Rs 125
Face value of 1000 shares $=$ Rs $(125 \times 1000)=\operatorname{Rs} 1,25,000$
Market value of each share $=$ Rs 150
Market value of 1000 shares $=\operatorname{Rs}(150 \times 1000)=\operatorname{Rs} 1,50,000$
Dividend (income) for 1000 shares $=12 \%$ of Rs 1,25,000 = Rs $\frac{12 \times 125000}{100}=$ Rs 15000
In second case:
Proceeds from selling 1000 shares $=$ Rs 1, 50, 000
Face value of each share $=$ Rs 25
Market value of each share $=$ Rs 60
No. of shares bought $=\frac{150000}{60}=2500$
Rohit bought 2,500 shares of Rs 60 each.
Face value of 2,500 shares $=\operatorname{Rs}(25 \times 2,500)=\operatorname{Rs} 62,500$
Dividend (income) for 2,500 shares $=20 \%$ of Rs $62,500=\frac{20 \times 62500}{100}=$ Rs 12500
Change in annual income $=\operatorname{Rs}(12,500-15,000)=-$ Rs 2,500 (less)

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Question 54 Marks

Mr Lele sold 250 shares of Rs 75 each of 'IOCL' paying 8% of dividend at Rs 112. He invested the proceeds in buying Rs 125 shares of HPCL paying 8% of dividend available at Rs 140. Calculate the number of shares of HPCL that Mr Lele bought and the change in his annual income.

Answer

In first case: No. of shares sold $=250$
Face value of each share $=$ Rs 75
Face value of 250 shares $=\operatorname{Rs}(75 \times 250)=\operatorname{Rs} 18,750$
Market value of each share $=$ Rs 112
Market value of 250 shares $=\operatorname{Rs}(112 \times 250)=\operatorname{Rs} 28,000$
Dividend (income) for 250 shares $=8 \%$ of Rs $18,750=$
Rs $\frac{8 \times 18750}{100}=$ Rs 1500
In second case:
Proceeds from selling 250 shares $=$ Rs 28,000
Face value of each share =Rs 125
Market value of each share $=$ Rs 140
No. of shares bought $=\frac{28000}{140}=200$
Mr Lele bought 200 shares of Rs 140 each.
Face value of 200 shares $=$ Rs $(125 \times 200)=R s 25,000$
Dividend (income) for 200 shares $=8 \%$ of Rs $25,000=$
Rs $\frac{8 \times 25000}{100}=$ Rs 2000
Change in annual income $=\operatorname{Rs}(2,000-1,500)=\operatorname{Rs} 500$

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Question 64 Marks

Amitesh had 400 shares of Rs 100 each of 'Telco' paying a dividend of 12.5%. He sold them at a market price of Rs 125 and invested the proceeds in Rs 50 shares of 'Adani Motors' available in the market at Rs 80 and paying a dividend of 16%. How many shares of Adani Motors did Amitesh buy and what is the change in his annual income?

Answer

In first case: No. of shares sold $=400$
Face value of each share $=$ Rs 100
Face value of 400 shares $=\operatorname{Rs}(100 \times 400)=\operatorname{Rs} 40,000$
Market value of each share $=$ Rs 125
Market value of 400 shares $=\operatorname{Rs}(125 \times 400)=$ Rs 50,000
Dividend (income) for 400 shares $=12.5 \%$ of Rs $40,000=\operatorname{Rs} \frac{12.5 \times 40000}{100}=$ Rs 5000
In second case:
Proceeds from selling 400 shares $=$ Rs 50,000
Face value of each share $=$ Rs 50
Market value of each share $=$ Rs 80
No. of shares bought $=\frac{50000}{80}=625$
Amitesh bought 625 shares of Rs 80 each.
Face value of 625 shares $=\operatorname{Rs}(50 \times 625)=$ Rs 31,250
Dividend (income) for 625 shares $=16 \%$ of Rs $31,250=\operatorname{Rs} \frac{16 \times 31250}{100}=$ Rs 5000
Change in annual income $=\operatorname{Rs}(5,000-5,000)=$ Rs $0= Nil$

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Question 74 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 84 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 94 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 104 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 Payal.
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 $= Rs. 50 \times \frac{15 x}{4} = Rs. 187.5 x$
$\text { Dividend }=10 \%$ 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 114 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 124 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 134 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 144 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 154 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 164 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 174 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. 13125$0

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Question 184 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 $\times =\frac{10}{100} \times x=\frac{x}{10}$
Investment in company $B =30 \%$ of $\times =\frac{30}{100} \times x=\frac{3 x}{10}$
Investment in company $C =40 \%$ of $\times =\frac{40}{100} \times x=\frac{4 x}{10}=\frac{2 x}{5}$
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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[4 marks sum] - Mathematics STD 10 Questions - Vidyadip