Frank Solutions for Class 10 Maths Chapter 4 Shares and Dividends are available in PDF here. These Solutions will help students to clear their doubts quickly and also assist in learning the topic effectively. Students can refer to these solutions whenever they face difficulty while answering the textbook questions. Students of Class 10 are suggested to practise Frank Solutions for Class 10 Maths to strengthen their fundamentals and be able to solve questions that are usually asked in the board examination.
In Chapter 4, Shares and Dividends, the dividend is defined as a payment made by a corporation to its shareholders. Usually, these payments are made in cash, but sometimes companies will also distribute stock dividends, whereby additional stock shares are distributed to shareholders. This chapter contains topics related to dividends, shares and investments, etc.
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1. Calculate the investment required to buy:
(a) 500 shares of Rs 75 each at a premium of Rs 17.
Solution:-
From the question, it is given that,
The number of shares 500
Then, shares of ₹ 75 each at a premium of ₹ 17 = 75 + 17 = ₹ 92
So, the investment required to buy 500 shares = 92 × 500
= ₹ 46,000
(b) 315 shares of Rs 60 each at a premium of Rs 12.
Solution:-
From the question, it is given that,
The number of shares 315
Then, shares of ₹ 60 each at a premium of ₹ 12 = 60 + 12 = ₹ 72
So, the investment required to buy 315 shares = 72 × 315
= ₹ 22,680
(c) 600 shares of Rs 25 each at a discount of Rs 3.
Solution:-
From the question, it is given that,
The number of shares 600
Then, shares of ₹ 25 each at a discount of ₹ 3 = 25 – 3 = ₹ 22
So, the investment required to buy 600 shares = 22 × 600
= ₹ 13,200
(d) 425 shares of Rs 10 each at a discount of Rs 1.50.
Solution:-
From the question, it is given that,
The number of shares 425
Then, shares of ₹ 10 each at a discount of ₹ 1.50 = 10 – 1.50 = ₹ 8.50
So, the investment required to buy 600 shares = 8.50 × 425
= ₹ 3,612.50
(e) 250 shares of Rs 20 each at par.
Solution:-
From the question, it is given that,
The number of shares 250
Then, shares of ₹ 20 each at par
So, the investment required to buy 250 shares = 20 × 250
= ₹ 5,000
(f) 150 shares of Rs 100 each at a premium of 12%.
Solution:-
From the question, it is given that,
The number of shares 150
Then, shares of ₹ 100 each at a premium of 12% = (100 + 12% of ₹ 100)
= 100 + ((12/100) × 100)
= 100 + 12
= ₹ 112
So, the investment required to buy 150 shares = 112 × 150
= ₹ 16,800
(g) 220 shares of Rs 75 each at a premium of 15%.
Solution:-
From the question, it is given that,
The number of shares 220
Then, shares of ₹ 75 each at a premium of 15% = (75 + 15% of ₹ 75)
= 75 + ((15/100) × 75)
= 75 + 11.25
= ₹ 86.25
So, the investment required to buy 220 shares = 86.25 × 220
= ₹ 18,975
(h) 340 shares of Rs 125 each at a discount of 20%.
Solution:-
From the question, it is given that,
The number of shares 340
Then, shares of ₹ 125 each at a discount of 20% = (125 – 20% of ₹ 125)
= 125 – ((20/100) × 125)
= 125 – 25
= ₹ 100
So, the investment required to buy 220 shares = 340 × 100
= ₹ 34,000
(i) 750 shares of Rs 100 each at a discount of 24%.
Solution:-
From the question, it is given that,
The number of shares 750
Then, shares of ₹ 100 each at a discount of 24% = (100 – 24% of ₹ 100)
= 100 – ((24/100) × 100)
= 100 – 24
= ₹ 76
So, the investment required to buy 750 shares = 750 × 76
= ₹ 57,000
(j) 116 shares of Rs 125 each at par.
Solution:-
From the question, it is given that,
The number of shares 116
Then, shares of ₹ 125 each at par
So, the investment required to buy 116 shares = 125 × 116
= ₹ 14,500
2. Calculate the annual income of the following:
(a) 180 shares of Rs 50 each paying a 12% dividend.
Solution:-
From the question, it is given that,
The number of shares 180
Then, shares of ₹ 50,
Therefore, total investment = ₹ (50 × 180) = ₹ 9,000
Dividend = 12%
So, the annual Income = (12 × 9,000)/100
= ₹ 1,080
(b) 424 shares of Rs 125 each paying 8% dividend.
Solution:-
From the question, it is given that,
The number of shares 424
Then, shares of ₹ 125,
Therefore, total investment = ₹ (125 × 424) = ₹ 53,000
Dividend = 8%
So, the annual Income = (8 × 53,000)/100
= ₹ 4,240
(c) 60 shares of Rs 100 each available at Rs 75 and paying 5% dividend.
Solution:-
From the question, it is given that,
The number of shares 60
Then, shares of ₹ 100,
Therefore, total investment = ₹ (100 × 60) = ₹ 6,000
Dividend = 5%
So, the annual Income = (5 × 6,000)/100
= ₹ 300
(d) 120 shares of Rs 50 each available at Rs 62 and paying 13% dividend.
Solution:-
From the question, it is given that,
The number of shares 120
Then, shares of ₹ 50,
Therefore, total investment = ₹ (50 × 120) = ₹ 6,000
Dividend = 13%
So, the annual Income = (13 × 6,000)/100
= ₹ 780
3. Calculate the percentage income in the following investments:
(a) Rs 7,225 paying 12% when a Rs 100 share is available at 15% discount.
Solution:-
From the question, it is given that,
The nominal value of each share = ₹ 100 is available at 15% discount
Therefore, Market value = ₹ (100 – 15 % of ₹ 100)
= ₹ 100 – ₹ 15
= ₹ 85
Then, the number of shares purchased = 7,225/85
= ₹ 85
So, the face value of 85 shares = ₹ 100 × 85
= ₹ 8,500
Given, dividend = 12%
Annual income = (12 × 8,500)/100
= ₹ 1,020
Therefore, percentage income = (1,020 × 100)/7,225
= 14.12%
(b) Rs 7,168 paying 15% when Rs 80 share is available at 40% premium.
Solution:-
From the question, it is given that,
The nominal value of each share = ₹ 80 is available at 40% premium
Therefore, Market value = ₹ (80 + 40 % of ₹ 80)
= ₹ 80 + ₹ 32
= ₹ 112
Then, the number of shares purchased = 7,168/112
= ₹ 64
So, the face value of 64 shares = ₹ 80 × 64
= ₹ 5,120
Given, dividend = 15%
Annual income = (15 × 5,120)/100
= ₹ 768
Therefore, percentage income = (768 × 100)/7,168
= 10.71%
(c) Rs 36,250 in a Rs 125 share, paying 8% and available at a premium of Rs 20.
Solution:-
From the question, it is given that,
The nominal value of each share = ₹ 125 is available at 8% premium
Therefore, Market value = ₹ (125 + ₹ 20)
= ₹ 145
Then, the number of shares purchased = 36,250/145
= ₹ 250
So, the face value of 250 shares = ₹ 125 × 250
= ₹ 31,250
Given, dividend = 8%
Annual income = (8 × 31,250)/100
= ₹ 2,500
Therefore, percentage income = (2,500 × 100)/36,250
= 6.9%
(d) Rs 12,375 in a Rs 75 share paying 4% and available at a discount of Rs 20.
Solution:-
From the question, it is given that,
The nominal value of each share = ₹ 75 is available at discount
Therefore, Market value = (₹ 75 – ₹ 20)
= ₹ 55
Then, the number of shares purchased = 12,375/55
= ₹ 255
So, face value of 225 shares = ₹ 75 × ₹ 225
= ₹ 16,875
Given, dividend = 4%
Annual income = (4 × 16,875)/100
= ₹ 675
Therefore, percentage income = (675 × 100)/12,375
= 5.45%
4. Rani has 500 shares of Rs 125 each of a company paying 12% dividend. Find her net income after paying 5% income tax.
Solution:-
From the question, it is given that,
Number of shares = 500
Then, the nominal value of each share = ₹ 125
So, face value of 500 shares = ₹ 125 × ₹ 500
= ₹ 62,500
Rate of dividend = 12%
Therefore, total dividend = (62,500 × 12)/100
= ₹ 7,500
So, the rate of income tax = 5%
Total tax = (5 × 7500)/100
= ₹ 375
Hence, net income = ₹(7,500 – 375)
= ₹ 7,125
5. Yash has 1200 shares of Rs 150 each of ‘Honeywell Corporation’ paying 18% dividend. Find his net income after paying.
Solution:-
From the question, it is given that,
Number of shares = 1200
Then, the nominal value of each share = ₹ 150
So, face value of 1200 shares = ₹ 150 × ₹ 1200
= ₹ 1,80,000
Rate of dividend = 18%
Therefore, total dividend = (1,80,000 × 18)/100
= ₹ 32,400
So, the rate of income tax = 8%
Total tax = (8 × 32,400)/100
= ₹ 2,592
Hence, net income = ₹(32,400 – 2,592)
= ₹ 29,808
6. Anu has 750 shares of Rs 60 each of ‘Tata Infotech’ paying 15% dividend. Find her net income after paying 6% income tax.
Solution:-
From the question, it is given that,
Number of shares = 750
Then, the nominal value of each share = ₹ 60
So, face value of 750 shares = ₹ 60 × ₹ 750
= ₹ 45,000
Rate of dividend = 15%
Therefore, total dividend = (45,000 × 15)/100
= ₹ 6,750
So, rate of income tax = 6%
Total tax = (6 ×6,750)/100
= ₹ 405
Hence, net income = ₹(6,750 – 405)
= ₹ 6,345
7. 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.
Solution:-
From the question, it is given that,
Number of shares = 600
Then, the nominal value of each share = ₹ 50
So, investment by Mahesh = ₹ (50 × 600)
= ₹ 30,000
Mahesh sold shares at premium = (1/3) × 600
= 200
Market value of a share with premium = ₹ (50 + 20) = ₹ 70
Then, value of 200 shares = ₹ (70 × 200)
= ₹ 14,000
Shares sold at discount = 600 – 200 = ₹ 400
Then, market value of a share with discount = ₹ 50 – ₹ 5 = ₹ 45
Value of 400 shares = ₹ (45 × 400)
= ₹ 18,000
By adding the value of 200 shares and the value of 400 shares, we get the total money received by selling his shares,
= 14,000 + 18,000
= ₹ 32,000
Difference in selling price and cost price = ₹ (32,000 – 30,000)
= ₹ 2,000
Therefore, Mahesh gained ₹ 2,000.
8. 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.
Solution:-
From the question, it is given that,
Divya invested ₹ 50,000
Then, the nominal value of each share = ₹ 125
Number of shares purchased by Divya = 50,000/125
= 400
Divya sold shares at premium = ₹ 200
Market value of a share with premium = ₹ (125 + 24% of ₹ 125)
= 125 + 30
= ₹ 155
Then, value of 200 shares = ₹ (155× 200)
= ₹ 31,000 … [i]
Shares sold at discount = ₹ 200
Then, market value of a share with discount = ₹ (125 – 20% of ₹ 125)
= ₹ 125 – ₹ 25
= ₹ 100
Value of 200 shares = ₹ (100 × 200)
= ₹ 20,000 … [ii]
By adding i and ii we get the total money received by selling her shares,
= 31,000 + 20,000
= ₹ 51,000
Therefore, Divya gained ₹ 1,000.
9. 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.
Solution:-
From the question, it is given that,
Ashutosh invested ₹ 58,500
Then, price at which Ashutosh purchased one share = ₹ (150 + 30% of ₹150)
= ₹ (150 + 45)
= ₹ 195
So, the number of shares purchased by Ashutosh = 58,500/195
= 300
Shares sold at ₹ 215 = 1/3 × 300
= 100
Then, the selling price of 100 shares at ₹ 215
= ₹ 100 × ₹ 215
= ₹ 21,500 … [1]
Now, shares sold at ₹ 195 = 195 × 100
= ₹ 19,500 … [2]
Selling price of 100 shares at ₹ 175 = 100 × 175
= ₹ 17,500 … [3]
By adding 1, 2 and 3 we get the total money received by selling his shares,
= 21,500 + 19,500 + 17,500
= ₹ 58,500
So, the difference in selling price and cost price = ₹ (58,500 – 58,500)
= ₹ 0
Therefore, Ashutosh sold his shares at no loss or gain.
10. 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.
Solution:-
Let us assume the total savings be y.
From the question, it is given that,
Saurav invested 10%, 30% and 40% of his savings in buying shares of 3 different companies A, B and C.
Companies A, B and C declared dividends of 12%, 15% and 16%, respectively.
Then,
Investment in company A = 10 % of y = (10/100) × y
= y/10
Investment in company B = 30 % of y = (30/100) × y
= (3/10) × y
= 3y/10
Investment in company C = 40 % of y = (40/100) × y
= 4/10 × y
= 2y/5
Now,
Dividend given by company A = 12% of y/10
= (12 × y)/(100 × 10)
= 0.012y … [1]
Dividend given by company B = 15% of 3y/10
= (15 × 3y)/(100 × 10)
= 0.045y … [2]
Dividend given by company C = 16% of 2y/5
= (16 × 2y)/(100 × 5)
= 0.064y … [3]
Given, the sum of 1, 2 and 3 is equal to ₹ 3,025
So, 1 + 2 + 3 = ₹ 3,025
0.012y + 0.045y + 0.064y = ₹ 3,025
y (0.012 + 0.045 + 0.064) = ₹ 3,025
0.121y = ₹ 3,025
y = ₹ 3,025/0.121
y = ₹ 25,000
Therefore, Saurav’s savings = ₹ 25,000
Investment in company A = (y/10) = 25,000/10
= ₹ 2,500
Investment in company B = (3y/10) = 75,000/10
= ₹ 7,500
Investment in company C = (2y/10) = 50,000/5
= ₹ 10,000
11. 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.
Solution:-
Let us assume the total savings be y.
From the question, it is given that,
Akanksha invested 15%, 25% and 35% of her savings in buying shares of ‘Infosys’, ‘Wipro’ and ‘Reliance’.
Companies ‘Infosys’, ‘Wipro’ and ‘Reliance’ declared dividends of 16%, 18% and 20%, respectively.
Then,
Investment in ‘Infosys’ company = 15 % of y = (15/100) × y
= (3/20) × y
= 3y/20
Investment in ‘Wipro’ company = 25 % of y = (25/100) × y
= y/4
Investment in ‘Reliance’ company = 35 % of y = (35/100) × y
= 7/20 × y
= 7y/20
Now,
Dividend given by ‘Infosys’ company = 16% of 3y/20
= (16 × 3y)/(100 × 20)
= 0.024y … [1]
Dividend given by ‘Wipro’ company = 18% of y/4
= (18 × y)/(100 × 4)
= 0.045y … [2]
Dividend given by ‘Reliance’ company = 20% of 7y/20
= (20 × 7y)/(100 × 20)
= 0.07y … [3]
Given, the sum of 1, 2 and 3 is equal to ₹ 52,125
So, 1 + 2 + 3 = ₹ 52,125
0.024y + 0.045y + 0.07y = ₹ 52,125
y (0.024 + 0.045 + 0.07) = ₹ 52,125
0.139y = ₹ 52,125
y = ₹ 52,125/0.139
y = ₹ 3,75,000
Therefore, Akanksha’s savings = ₹ 3,75,000
Investment in ‘Infosys’ company = (3y/20) = (3 × 3,75,000)/10
= ₹ 56,250
Investment in ‘Wipro’ company = (y/4) = (3,75,000)/4
= ₹ 93,750
Investment in ‘Reliance’ company = (7y/20) = (7 × 3,75,000)/20
= ₹ 1,31,250
12. 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 dividends 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.
Solution:-
From the question, it is given that,
Tarun invested ₹ 24,000 and ₹ 30,000 in buying ₹ 100 at par shares of ‘Vam Organics’ and ‘Hero Honda’.
Then, total investment = ₹ 24,000 + ₹ 30,000 = ₹ 54,000
So, the number of shares of ‘Vam Organics’ = money invested/cost of one share
= 24,000/100
= 240
Number of shares of ‘Hero Honda’ = money invested/cost of one share
= 30,000/100
= 300
Now, dividend given by ‘Vam Organics’ = 12% = (12 × 24,000)/100 = ₹ 2,880
Dividend given by ‘Hero Honda’ = 15% = (15 × 30,000)/100 = ₹ 4,500
Then, total dividend earned = ₹ 2,880 + ₹ 4,500
= ₹ 7,380
So, money earned by selling shares of ‘Vam Organics’ = ₹ 95 × ₹ 240
= ₹ 22,800
Money earned by selling shares of ‘Hero Honda’ = ₹ 90 × ₹ 300
= ₹ 27,000
Therefore, total money earned by selling shares = ₹ 22,800 + ₹ 27,000
= ₹ 49,800
Hence, total earnings = money earned by selling shares + dividends earned
= ₹ 49,800 + ₹ 7,380
= ₹ 57,180
Tarun’s earnings from the transactions = ₹ 57,180 – ₹ 54,000
= ₹ 3,180
13. Bhavana invested Rs 20,000 and Rs 25,000 in buying shares of ‘Bharati Telecom’ and ‘Satyam Infoways’ which later declared dividends 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.
Solution:-
From the question, it is given that,
Bhavana invested ₹ 20,000 and ₹ 25,000 in buying ‘Bharati Telecom’ and ‘Satyam Infoways’.
Then, ‘Bharati Telecom’ which declared a dividend of 10% = (10 × 20,000)/100 = ₹ 2,000
‘Satyam Infoways ‘ which declared dividend of 12.5% = (12.5 × 25,000)/(10 × 100) = ₹3,125
So, money earned by selling shares of ‘Bharati Telecom’ = (20,000 – 4% of ₹ 20,000)
= ₹ 20,000 – 800
= ₹ 19,200
Money earned by selling shares of ‘Satyam Infoways’ = (25,000 – 5% of ₹ 25,000)
= ₹ 25,000 – 1250
= ₹ 23,750
Therefore, total money earned by selling shares = ₹ 19,200 + ₹ 23,750
= ₹ 42,950
Then, total earning = money earned by selling shares + dividends earned
= ₹ (42,950 + 5,125)
= ₹ 48,075
Hence, Bhavana’s earnings from the transaction = ₹ (48,075 – 45,000)
= ₹ 3,075
14. 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?
Solution:-
Let us assume that, Karan’s investment is y.
Then, face value of 125 shares = ₹ (100 × 125)
= ₹ 12,500
So, dividend for 125 shares = 6% of 12,500 = (6 × 12,500)/100 = ₹ 750
Karan gets ₹ 750 as dividend, which is equal to 4% of the money invested = 4y/100 = ₹ 750
4y = ₹ 75,000
y = 75,000/4
y = ₹ 18,750
Then, Karan invested ₹ 18,750
Number of shares bought by Karan = 125
Value of a share = ₹ 18,750/125
= ₹ 150
Therefore, Karan bought a share for ₹ 150.
15. Vikram bought 200 shares of Rs 25 each of ‘Calcutta Jute Co.’, paying 8% of the dividend. Vikram bought them at such a price that he gets 10% of his money. At what price did he buy the share?
Solution:-
Let us assume that, Vikram’s investment is y.
Then, face value of 200 shares = ₹ (25 × 200)
= ₹ 5,000
So, dividend for 200 shares = 8% of ₹ 5,000 = (8 × 5000)/100 = ₹ 400
Vikram gets ₹ 400 as dividend, which is equal to 10% of the money invested,
10y/100 = ₹ 400
10y = ₹ 40,000
y = 40,000/10
y = ₹ 4,000
Then, Vikram invested ₹ 4,000
Number of shares bought by Vikram = 200
Value of a share = ₹ 4,000/200
= ₹ 20
Therefore, Vikram bought a share for ₹ 20.
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