[3 marks sum]

Question 13 Marks

Ashutosh invested Rs 58,500 in buying shares of Rs 150 each of 'Van Chemicals', when it was available in the market at a premium of 30%. He sells one third of them at a market rate of Rs 215, one third of them at a market rate of Rs 195 and the rest at Rs 175. Find his loss or gain from the transaction.

Answer

Investment by Ashutosh $=$ Rs 58,500

Price at which Ashutosh purchased one share =

$\operatorname{Rs}(150+30 \%$ of Rs 150$)=\operatorname{Rs}(150+45)=\operatorname{Rs} 195$

No. of shares purchased by Ashutosh $=\frac{58500}{195}=300$

Shares sold at Rs $215=1 / 3 \times 300=100$

Selling price of 100 shares at Rs 215

$=\operatorname{Rs}(100 \times 215)=\operatorname{Rs} 21,500$$\ldots (i)$

Shares sold at Rs $195=1 / 3 \times 300=100$

Selling price of 100 shares at Rs 175
$
=\operatorname{Rs}(100 \times 175)=\operatorname{Rs} 17,500\ldots(ii)
$
Adding (i), (ii) and (iii), gives total money Ashutosh received by selling his shares
$
=\operatorname{Rs}(21,500+19,500+17,500)=\operatorname{Rs} 58,500
$
Difference in selling price and cost price $=\operatorname{Rs}(58,500-58,500)$

$=$ Rs 0 .

Hence, Ashutosh sold his shares at no loss or no gain.

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Question 23 Marks

Divya invested Rs 50,000 in buying shares of Rs 125 each of 'Hitech Technologies'. She sold half of them when they were at a premium of 24% and the remaining half when they were at a discount of 20%. Find her gain or loss in the transaction.

Answer

Investment by Divya $=$ Rs 50,000
Nominal value of a share =Rs 125
No. of shares purchased by Divya $=\frac{50000}{125}=400$
Shares sold at premium $=200$
Market value of a share with Premium
$=\operatorname{Rs}(125+24 \%$ of Rs 125$)$
$=\operatorname{Rs}(125+30)=\operatorname{Rs} 155$
Value of 200 shares $=\operatorname{Rs}(155 \times 200)=\operatorname{Rs} 31,000$$\ldots (i)$
Shares sold at discount $=200$
Market value of a share with discount $=$ Rs ( $125-20 \%$ of Rs 125 )
$
=\operatorname{Rs}(125-25)=\operatorname{Rs} 100
$
Value of 200 shares $=\operatorname{Rs}(100 \times 200)=$ Rs 20,000$\ldots(ii)$
Adding (i) and (ii), gives total money Divya received by selling her shares
$
=\operatorname{Rs}(31,000+20,000)=\operatorname{Rs} 51,000
$
Hence, Divya gained Rs 1,000

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Question 33 Marks

Mahesh bought 600 shares of Rs 50 each of 'Excel Computers'. He sold one third of them when they were at a premium of Rs 20 and the remaining when they were at a discount of Rs 5. Find his gain or loss in the transaction.

Answer

No. of shares $=600$
Nominal value of a share $=$ Rs 50
Investment by Mahesh $=$ Rs $(50 \times 600)=$ Rs 30,000
Shares sold at premium $=\frac{1}{3} \times 600=200$
Market value ofa share with Premium $= Rs (50+20)= Rs 70$
Value of 200 shares $=$ Rs $(70 \times 200)=$ Rs 14,000$\ldots (i)$
Shares sold at discount $=600-200=400$
Market value of a share with discount $=$ Rs $(50-5)=$ Rs 45
Value of 400 shares $=\operatorname{Rs}(45 \times 400)=\operatorname{Rs} 18,000$$\ldots(ii)$
Adding ( i) and (ii), gives total money Mahesh received by selling his shares $= Rs (14,000+18,000)$ $=$ Rs 32,000
Difference in selling price and cost price $=\operatorname{Rs}(32,000-30,000)=\operatorname{Rs} 2,000$
Hence, Mahesh gained Rs 2,000

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Question 43 Marks

Anu has 750 shares of Rs 60 each of 'Tata Infotech' paying 15% dividend. Find her net income after paying 6% income tax.

Answer

No. of shares $=750$
Nominal value of each share $=$ Rs 60
Face value of 750 shares $=\operatorname{Rs}(60 \times 750)=\operatorname{Rs} 45,000$
Rate of dividend $=15 \%$
Total dividend $=\frac{45000 \times 15}{100}=$ Rs 6750
Rate of income tax $=6 \%$
Total tax $=\frac{6 \times 6750}{100}=$ Rs 405
Net income $=$ Rs $(6,750-405)=$ Rs 6,345

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Question 53 Marks

Yash has 1200 shares of Rs 150 each of 'Honeywell Corporation' paying 18% dividend. Find his net income after paying.

Answer

No. of shares $=1200$
Nominal value of each share $=$ Rs 150
Face value of 1200 shares $=\operatorname{Rs}(150 \times 1200)=\operatorname{Rs} 1,80,000$
Rate of dividend $=18 \%$
Total dividend $=\frac{180000 \times 18}{100}=$ Rs 32400
Rate of income tax $=8 \%$
Total tax $=\frac{8 \times 32400}{100}=$ Rs 2592
Net income $=$ Rs $(32,400-2,592)=$ Rs 29,808

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Question 63 Marks

Rani has 500 shares of Rs 125 each of a company paying 12% dividend. Find her net income after paying 5% income tax.

Answer

No. of shares $=500$
Nominal value of each share $=$ Rs 125
Face value of 500 shares $=\operatorname{Rs}(125 \times 500)=$ Rs 62,500
Rate of dividend $=12^{\circ} 10$
Total dividend $=\frac{62500 \times 12}{100}=$ Rs 7500
Rate of income tax $=5 \%$
Total tax $=\frac{5 \times 7500}{100}=$ Rs 375
Net income $=\operatorname{Rs}(7,500-375)=$ Rs 7, 125

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Question 73 Marks

Calculate the percentage income in the following investment:
Rs 12,375 in a Rs 75 share paying 4% and available at a discount of Rs 20.

Answer

Investment $=$ Rs 12,375
Nominal value of each share $=$ Rs 75
Market value $=$ Rs (7 5 - Rs 20) $=$ Rs 55
No. of shares purchased $=\frac{12375}{55}=225$
Face value of 225 shares $=$ Rs $75 \times 225=$ Rs 16,875
Dividend $=4 \%$
Therefore, , Annual Income $=\frac{4 \times 16875}{100}=$ Rs 675
Hence, percentage income $=\frac{675 \times 100}{12375}=5.45 \%$

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Question 83 Marks

Calculate the percentage income in the following investments:
Rs 36,250 in a Rs 125 share paying 8% and available at a premium of Rs 20.

Answer

Investment= Rs 36,250
Nominal value of each share =Rs 125
Market value =Rs ( $125+$ Rs 20) $=$ Rs 145
No. of shares purchased $=\frac{36250}{145}=250$
Face value of 250 shares $=$ Rs $125 \times 250=$ Rs 31,250
Dividend $=8 \%$
Therefore, Annual Income $=\frac{8 \times 31250}{100}=$ Rs 2500
Hence, percentage income $=\frac{2500 \times 100}{36250}=6.9 \%$

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Question 93 Marks

Calculate the percentage income in the following investment:
Rs 7,168 paying 15% when a Rs 80 share is available at 40% premium.

Answer

Investment $=$ Rs 7, 168
Nominal value of each share $=$ Rs 80
Market value $=\operatorname{Rs}(80+40 \%$ of Rs 80$)=\operatorname{Rs}(80+32)=\operatorname{Rs} 112$
No. of shares purchased $=\frac{7168}{112}=64$
Face value of 64 shares $=$ Rs $80 \times 64=$ Rs 5, 120
Dividend $=15 \%$
Therefore, Annual Income $=\frac{15 \times 5120}{100}=$ Rs 768
Hence, percentage income $=\frac{768 \times 100}{7168}=10.71 \%$

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Question 103 Marks

Calculate the percentage income in the following investment:
Rs 7,225 paying 12% when a Rs 100 share is available at 15% discount.

Answer

Investment $=$ Rs 7,225
Nominal value of each share $=$ Rs 100
Market value $=\operatorname{Rs}(100-15 \%$ of Rs 100) $=\operatorname{Rs}(100-15)=\operatorname{Rs} 85$
No. of shares purchased $=\frac{7225}{85}=85$
Face value of 85 shares $=$ Rs $100 \times 85=$ Rs 8,500
Dividend $=12 \%$
Therefore, Annual Income $=\frac{12 \times 8500}{100}=$ Rs 1020
Hence, percentage income
$
=\frac{1020 \times 100}{7225}=140117 \%=14.12 \%
$

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Mathematics [3 marks sum]

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