OP Malhotra Class 10 Maths Solutions Chapter 3 Shares and Dividends Exercise 3 (A)

S Chand Class 10 ICSE Maths Solutions Chapter 3 Shares And Dividends Ex 3(A)

Question 1. Find the cost of
(i) 200 shares of Rs. 10 each available at Rs. 2.50 premium.
(ii) 220 shares of Rs. 15 each available at Rs. 1.50 discount.
(iii) Purchasing Rs. 200 stock yielding 9% at 105.
(iv) 1000 shares of Rs. 25 each at a premium of Rs. 60.
(v) s. 100 each at the market price of Rs. 30.80.
Answer:
(i) The face value of each share is Rs. 10. Since it is at a premium of Rs. 2.50, the market value of each share is \( \text{Rs. } 10 + \text{Rs. } 2.50 = \text{Rs. } 12.50 \). For 200 shares, the total cost will be \( \text{Rs. } 12.50 \times 200 = \text{Rs. } 2500 \).
(ii) The face value of each share is Rs. 15. Since it is at a discount of Rs. 1.50, the market value of each share is \( \text{Rs. } 15 - \text{Rs. } 1.50 = \text{Rs. } 13.50 \). For 220 shares, the total cost is \( \text{Rs. } 13.50 \times 220 = \text{Rs. } 2970 \).
(iii) For purchasing Rs. 200 stock at 105, it implies the market value is Rs. 105 per Rs. 100 face value. The solution given shows a direct multiplication of 105 by 200. Following this, the market value of Rs. 200 shares is \( \text{Rs. } 105 \times 200 = \text{Rs. } 21000 \).
(iv) The face value of each share is Rs. 25. Since it is at a premium of Rs. 60, the market value of each share is \( \text{Rs. } 60 + \text{Rs. } 25 = \text{Rs. } 85 \). For 1000 shares, the total cost is \( \text{Rs. } 85 \times 1000 = \text{Rs. } 85000 \).
(v) The face value of each share is Rs. 100. The market price for each share is Rs. 30.80. The solution shows calculation for 450 shares, so the total cost of these 450 shares is \( \text{Rs. } 30.80 \times 450 = \text{Rs. } 13860 \).
In simple words: To find the cost, first determine the price of one share or unit of stock in the market. This price is found by adding a premium to the face value or subtracting a discount. Then, multiply this market price by the number of shares you want to buy.

🎯 Exam Tip: Always distinguish between face value (the original value printed on the share) and market value (the price at which shares are bought or sold in the market). Premiums add to face value, discounts subtract from it.

Question 2. Find the annual dividend on
(i) par value of Rs. 10 if the annual dividend is 7.5%.
(ii) 50 Tata Mills 4% (Rs. 6) shares at Rs. 6.25.
(iii) 180 Shri Ram Fibres \( 7\frac { 1 }{ 2 }% \) (Rs. 10) shares at 14.50.
(iv) 100 Hindustan Motors (Rs. 10) shares at Rs. 8, dividend 4% p.a.
Answer:
(i) The face value of each share is Rs. 10. The annual dividend rate is 7.5%. The provided solution for this part calculates the dividend for 450 shares. So, the total face value for 450 shares is \( \text{Rs. } 10 \times 450 = \text{Rs. } 4500 \). The total annual dividend is 7.5% of Rs. 4500: \( \text{Rs. } \frac{4500 \times 7.5}{100} = \text{Rs. } 337.50 \).
(ii) The face value of each share is Rs. 6. For 50 shares, the total face value is \( \text{Rs. } 6 \times 50 = \text{Rs. } 300 \). The annual dividend rate is 4%. So, the total annual dividend is 4% of Rs. 300: \( \text{Rs. } 300 \times \frac{4}{100} = \text{Rs. } 12 \).
(iii) The face value of each share is Rs. 10. For 180 shares, the total face value is \( \text{Rs. } 10 \times 180 = \text{Rs. } 1800 \). The annual dividend rate is \( 7\frac{1}{2}\% = \frac{15}{2}\% \). So, the total annual dividend is \( \frac{15}{2}\% \) of Rs. 1800: \( \text{Rs. } \frac{1800 \times 15}{100 \times 2} = \text{Rs. } 135 \).
(iv) The face value of each share is Rs. 10. For 100 shares, the total face value is \( \text{Rs. } 10 \times 100 = \text{Rs. } 1000 \). The annual dividend rate is 4%. So, the total annual dividend is 4% of Rs. 1000: \( \text{Rs. } 1000 \times \frac{4}{100} = \text{Rs. } 40 \).
In simple words: Annual dividend is calculated based on the face value (nominal value) of the shares, not their market price. You multiply the total face value of all shares by the given dividend rate (percentage) to find the amount of dividend you will receive in a year.

🎯 Exam Tip: Always use the face value (nominal value) of shares when calculating dividends, not the market value or purchase price, unless specified otherwise for return on investment.

Question 3. Write down the sum of money obtained by selling 60 (Rs. 100) shares at 112.
Answer: When shares are sold 'at 112', it means each share (with a face value of Rs. 100) is sold for Rs. 112. So, by selling one share, Rs. 112 is obtained. If 60 such shares are sold, the total money obtained will be \( \text{Rs. } 112 \times 60 = \text{Rs. } 6720 \). This is the total amount received from the sale.
In simple words: To find the total money from selling shares, multiply the selling price of one share by the total number of shares sold.

🎯 Exam Tip: The 'at 112' terminology means Rs. 112 per share, where 100 represents the par value. This is essentially a premium of Rs. 12 per share.

Question 4. Ravi invested Rs. 6250 in shares of a company paying 6% per annum. If he bought Rs. 25 shares for Rs. 31.25 each, find his annual income from this investment.
Answer: Ravi invested a total of Rs. 6250. Each share has a face value of Rs. 25 and was bought at a market price of Rs. 31.25. The number of shares Ravi purchased is calculated by dividing the total investment by the market price per share: \( \text{Number of shares} = \frac{\text{Rs. } 6250}{\text{Rs. } 31.25} = 200 \text{ shares} \). The nominal value (face value) of these 200 shares is \( \text{Rs. } 25 \times 200 = \text{Rs. } 5000 \). The company pays a dividend of 6% per annum. So, Ravi's annual income (total dividend) is 6% of the nominal value: \( \text{Rs. } 5000 \times \frac{6}{100} = \text{Rs. } 300 \). This is the money Ravi earns each year.
In simple words: First, find how many shares were bought. Then, calculate their total face value. Finally, use the dividend rate to find the annual income from this total face value.

🎯 Exam Tip: Remember that annual income (dividend) is always calculated on the nominal (face) value of the shares, not the investment or market price.

Question 5. Write down the price of 100 (Rs. 10) shares costing Rs. 2000.
Answer: The problem states that 100 shares with a face value of Rs. 10 each cost a total of Rs. 2000. To find the price of one share, we divide the total cost by the number of shares. So, the price of each share is \( \text{Rs. } \frac{2000}{100} = \text{Rs. } 20 \). This is the market price at which each share was purchased.
In simple words: If you know the total cost for many shares, just divide that total cost by the number of shares to find the price of one share.

🎯 Exam Tip: The face value (Rs. 10) mentioned in the question is additional information but not directly used to find the 'price' (market price) if the total cost is given.

Question 6. A company declares semi-annual dividend of 5%. Krishan Lai owns 25 shares (of par value Rs. 12.50 each). How much annual dividend must he receive.
Answer: Krishan Lai owns 25 shares, each with a par value (face value) of Rs. 12.50. The total face value of his shares is \( \text{Rs. } 12.50 \times 25 = \text{Rs. } 312.50 \). The company declares a semi-annual dividend of 5%, meaning it pays 5% twice a year. Therefore, the annual dividend rate is \( 5\% \times 2 = 10\% \). Krishan Lai's total annual dividend is 10% of the total face value: \( \text{Rs. } 312.50 \times \frac{10}{100} = \text{Rs. } 31.25 \). This is the total money he gets from dividends each year.
In simple words: First, find the total face value of all shares. Since the dividend is semi-annual, double the rate to get the annual rate. Then, multiply the total face value by the annual dividend rate.

🎯 Exam Tip: Pay close attention to whether a dividend rate is annual, semi-annual, or quarterly, and adjust it to an annual rate if required for the final calculation.

Question 7. A man bought 250 (1) shares and received from them a dividend of Rs. 20. What is the rate % of the dividend?
Answer: The man bought 250 shares. The "(1)" in the question likely indicates a face value of Re. 1 per share. So, the face value of each share is Re. 1. The total face value of 250 shares is \( \text{Rs. } 1 \times 250 = \text{Rs. } 250 \). He received a total dividend of Rs. 20. To find the rate % of dividend, we use the formula: \( \text{Rate of dividend} = \frac{\text{Total dividend}}{\text{Total face value}} \times 100\% \). So, the rate is \( \frac{\text{Rs. } 20}{\text{Rs. } 250} \times 100\% = 8\% \). This percentage shows how much dividend he gets compared to the face value of his shares.
In simple words: To find the dividend rate, divide the dividend received by the total face value of shares, then multiply by 100 to get the percentage.

🎯 Exam Tip: Always remember that the dividend rate is calculated based on the total face value of the shares, not the market value or the number of shares alone.

Question 8. A man invests Rs. 4800 in shares of a company which was paying 8% dividend at the time when a Rs. 100 share cost Rs. 160. Find (i) his annual income from the shares, (ii) the rate interest he gets on his investment.
Answer: The total investment made is Rs. 4800. Each share has a face value of Rs. 100 and a market value of Rs. 160. The number of shares purchased is \( \text{Number of shares} = \frac{\text{Total investment}}{\text{Market value per share}} = \frac{\text{Rs. } 4800}{\text{Rs. } 160} = 30 \text{ shares} \). The total face value of these 30 shares is \( \text{Rs. } 100 \times 30 = \text{Rs. } 3000 \). The dividend rate is 8%.
(i) His annual income (total dividend) is 8% of the total face value: \( \text{Rs. } \frac{3000 \times 8}{100} = \text{Rs. } 240 \).
(ii) The rate of interest he gets on his investment (percentage return) is calculated by dividing his annual income by his total investment and multiplying by 100%: \( \text{Rate of interest} = \frac{\text{Annual income}}{\text{Total investment}} \times 100\% = \frac{\text{Rs. } 240}{\text{Rs. } 4800} \times 100\% = 5\% \). This shows the actual return on the money he put in.
In simple words: First, find how many shares were bought. Then, calculate the total face value to find the dividend income. Finally, divide the dividend income by the total money invested to get the percentage return.

🎯 Exam Tip: Distinguish between the dividend rate (calculated on face value) and the rate of interest on investment (calculated on the total amount invested). They are usually different.

Question 9. A company pays a dividend of 15% on its ten-rupee shares from which is deducted income tax at the rate of 22%. Find the annual income of a man who owns 100 shares of this company.
Answer: The face value of each share is Rs. 10. The man owns 100 shares, so the total face value is \( \text{Rs. } 10 \times 100 = \text{Rs. } 1000 \). The company pays a dividend of 15%. So, the total dividend before tax is \( \text{Rs. } 1000 \times \frac{15}{100} = \text{Rs. } 150 \). Income tax is deducted at 22% from this dividend. The total tax deducted is \( \text{Rs. } 150 \times \frac{22}{100} = \text{Rs. } 33 \). Therefore, the man's net annual income after tax is \( \text{Rs. } 150 - \text{Rs. } 33 = \text{Rs. } 117 \). This is the actual amount he receives.
In simple words: Calculate the dividend based on total face value. Then, calculate the income tax on this dividend. Subtract the tax from the dividend to find the final income.

🎯 Exam Tip: Remember to calculate tax on the gross dividend (before tax) and then subtract it to find the net income, if tax deduction is mentioned.

Question 10. A man bought 1000 shares each of face value Rs. 5 at Rs. 7 per share. At the end of the year, the company from which he bought the shares declared a dividend of 8%. Calculate (i) the amount of money invested by the man; (ii) the percentage return on his outlay correct to one decimal place.
Answer: The man bought 1000 shares, each with a face value of Rs. 5, at a market price of Rs. 7 per share. The company declared an 8% dividend.
(i) The amount of money invested by the man is the total cost of buying the shares: \( \text{Investment} = \text{Number of shares} \times \text{Market price per share} = 1000 \times \text{Rs. } 7 = \text{Rs. } 7000 \).
(ii) To find the percentage return, we first calculate the total dividend. The total face value of the shares is \( 1000 \times \text{Rs. } 5 = \text{Rs. } 5000 \). The total dividend is 8% of this face value: \( \text{Rs. } 5000 \times \frac{8}{100} = \text{Rs. } 400 \). The percentage return on his outlay (investment) is \( \frac{\text{Total dividend}}{\text{Total investment}} \times 100\% = \frac{\text{Rs. } 400}{\text{Rs. } 7000} \times 100\% = \frac{40000}{7000}\% = \frac{40}{7}\% \approx 5.71\% \). Rounded to one decimal place, this is \( 5.7\% \). This shows how profitable the investment was.
In simple words: First, calculate the total investment by multiplying the number of shares by their market price. Then, find the total dividend based on the total face value. Finally, divide the dividend by the investment and multiply by 100% to get the percentage return.

🎯 Exam Tip: The percentage return is always based on the actual money invested (outlay), while the dividend rate is based on the face value of the shares.

Question 11. A company with 10000 shares of nominal value Rs. 100 declares an annual dividend of 8% to the share-holders. (i) Calculate the total amount of dividend paid by the company. (ii) Ramesh had bought 90 shares of the company at Rs. 150 per share. Calculate the es and the percentage return on his investment.
Answer: The company has 10000 shares, each with a nominal value (face value) of Rs. 100, and declares an 8% annual dividend. Ramesh bought 90 shares at Rs. 150 per share.
(i) The total nominal value of all company shares is \( \text{Rs. } 100 \times 10000 = \text{Rs. } 10,00,000 \). The total dividend paid by the company annually is 8% of this total nominal value: \( \text{Rs. } 10,00,000 \times \frac{8}{100} = \text{Rs. } 80,000 \). This is the total money the company distributes to its shareholders.
(ii) For Ramesh, the nominal value of his 90 shares is \( \text{Rs. } 100 \times 90 = \text{Rs. } 9000 \). His dividend (income) from these shares is 8% of this nominal value: \( \text{Rs. } 9000 \times \frac{8}{100} = \text{Rs. } 720 \). His investment in these 90 shares was \( \text{Rs. } 150 \times 90 = \text{Rs. } 13,500 \). The percentage return on his investment is \( \frac{\text{Dividend received}}{\text{Investment}} \times 100\% = \frac{\text{Rs. } 720}{\text{Rs. } 13,500} \times 100\% = \frac{72000}{13500}\% = \frac{16}{3}\% \). This can also be written as \( 5\frac{1}{3}\% \).
In simple words: For the company, multiply the total nominal value of all shares by the dividend rate. For an individual, find their dividend income based on their shares' nominal value, then compare this income to their actual investment to find the percentage return.

🎯 Exam Tip: When calculating total dividend paid by the company, use the total nominal value of *all* shares issued. For an individual shareholder, use the nominal value of *their* shares.

Question 12. Aditi has 40 shares of nominal value Rs. 100 and she decides to sell them when they are at a premium of 50%. She invests the proceeds in shares of nominal value of Rs. 75 quoted at a 20% discounts paying 25% dividend annually. Calculate: (i) the sale proceeds (ii) the number of shares she buys; (iii) the annual dividend from these shares.
Answer: Aditi has 40 shares, each with a nominal value of Rs. 100. She sells them at a 50% premium and reinvests the money.
For the first transaction:
Nominal value of each share = Rs. 100.
Premium = 50% of Rs. 100 = Rs. 50.
Market price of each share when selling = \( \text{Rs. } 100 + \text{Rs. } 50 = \text{Rs. } 150 \).
(i) The sale proceeds (amount received on selling 40 shares) = \( \text{Rs. } 150 \times 40 = \text{Rs. } 6000 \). This is the money Aditi gets.
For the second transaction (reinvestment):
She invests Rs. 6000. New shares have a nominal value of Rs. 75 and are quoted at a 20% discount.
Discount = 20% of Rs. 75 = Rs. 15.
Market value of each new share = \( \text{Rs. } 75 - \text{Rs. } 15 = \text{Rs. } 60 \).
(ii) The number of new shares she buys = \( \frac{\text{Total investment}}{\text{Market value per new share}} = \frac{\text{Rs. } 6000}{\text{Rs. } 60} = 100 \text{ shares} \).
The new shares pay a 25% annual dividend. The total nominal value of these 100 new shares is \( \text{Rs. } 75 \times 100 = \text{Rs. } 7500 \).
(iii) The annual dividend from these new shares = 25% of Rs. 7500 = \( \text{Rs. } \frac{7500 \times 25}{100} = \text{Rs. } 1875 \). This is Aditi's new annual income from dividends.
In simple words: First, calculate how much money Aditi gets by selling her old shares. Then, use this money to find out how many new shares she can buy. Finally, calculate the dividend on these new shares using their nominal value.

🎯 Exam Tip: Break down complex problems into stages: first, the selling transaction, then the purchasing transaction, and finally the dividend calculation on the new investment.

Question 13. Mr. Khanna holds 1600, Rs. 100 shares of a company that pays 12% dividend annually. Calculate his annual dividend. If he had bought these shares at 50% premium, what percentage return does he get on his investment.
Answer: Mr. Khanna holds 1600 shares, each with a face value of Rs. 100. The company pays a 12% annual dividend.
First, calculate his annual dividend:
Total nominal value of his shares = \( 1600 \times \text{Rs. } 100 = \text{Rs. } 1,60,000 \).
Annual dividend = 12% of Rs. 1,60,000 = \( \text{Rs. } \frac{160000 \times 12}{100} = \text{Rs. } 19,200 \). This is his yearly income from dividends.
Next, calculate the percentage return if he bought shares at a 50% premium:
Premium = 50% of Rs. 100 (face value) = Rs. 50.
Cost price of each share = \( \text{Rs. } 100 + \text{Rs. } 50 = \text{Rs. } 150 \).
Total investment for 1600 shares = \( 1600 \times \text{Rs. } 150 = \text{Rs. } 2,40,000 \).
Percentage return on investment = \( \frac{\text{Annual dividend}}{\text{Total investment}} \times 100\% = \frac{\text{Rs. } 19,200}{\text{Rs. } 2,40,000} \times 100\% = \frac{1920000}{240000}\% = 8\% \). This shows how much profit he made compared to his investment.
In simple words: First, find the annual dividend from the shares' face value. Then, calculate the total cost if bought at a premium. Finally, divide the annual dividend by the total investment and multiply by 100% to find the percentage return.

🎯 Exam Tip: Be careful to use the nominal value for dividend calculation and the market (or cost) price for calculating the percentage return on investment.

Question 14. A man invests Rs. 11200 in a company paying 6% dividend per annum when its Rs. 100 shares can be bought for Rs. 140. Find (i) his annual dividend, (ii) his percentage income on this investment.
Answer: The man invests Rs. 11200. Each share has a face value of Rs. 100 and a market value of Rs. 140. The company pays a 6% annual dividend.
First, find the number of shares purchased: \( \text{Number of shares} = \frac{\text{Total investment}}{\text{Market value per share}} = \frac{\text{Rs. } 11200}{\text{Rs. } 140} = 80 \text{ shares} \).
Then, find the total face value of these shares: \( \text{Total face value} = 80 \times \text{Rs. } 100 = \text{Rs. } 8000 \).
(i) His annual dividend is 6% of the total face value: \( \text{Rs. } 8000 \times \frac{6}{100} = \text{Rs. } 480 \). This is his yearly income.
(ii) His percentage income (return) on this investment is calculated by dividing his annual dividend by his total investment and multiplying by 100%: \( \text{Percentage income} = \frac{\text{Annual dividend}}{\text{Total investment}} \times 100\% = \frac{\text{Rs. } 480}{\text{Rs. } 11200} \times 100\% = \frac{48000}{11200}\% = \frac{30}{7}\% \). This can be expressed as a mixed fraction \( 4\frac{2}{7}\% \). This shows the rate of return on the invested money.
In simple words: First, figure out how many shares were bought with the investment. Then, calculate the total face value of these shares to find the annual dividend. Finally, compare this dividend to the total investment to get the percentage income.

🎯 Exam Tip: Always calculate the number of shares first if the total investment and market price per share are given, as this number is crucial for subsequent calculations.

Question 15. A company having a capital stock of Rs. 450000 declares a dividend of 4% semi-annually. (a) What is the annual income of a stockholder owning 135 shares at par- value of Rs. 10? (b) What is the total amount of dividend paid annually by the company?
Answer: The company has a total capital stock of Rs. 450000 and declares a 4% semi-annual dividend, which means an annual dividend rate of \( 4\% \times 2 = 8\% \).
(a) For a stockholder owning 135 shares at a par-value of Rs. 10 each:
Total face value of 135 shares = \( 135 \times \text{Rs. } 10 = \text{Rs. } 1350 \).
Annual income (dividend) for this stockholder = 8% of Rs. 1350 = \( \text{Rs. } 1350 \times \frac{8}{100} = \text{Rs. } 108 \). This is the money the stockholder receives yearly.
(b) The total amount of dividend paid annually by the company is 8% of its total capital stock:
Total annual dividend = 8% of Rs. 450000 = \( \text{Rs. } 450000 \times \frac{8}{100} = \text{Rs. } 36000 \). This is the total sum distributed to all shareholders.
In simple words: First, find the annual dividend rate by doubling the semi-annual rate. For a shareholder, calculate their dividend based on the total face value of their shares. For the company, calculate the total dividend based on its total capital stock.

🎯 Exam Tip: Pay attention to whether the dividend rate is semi-annual (twice a year) or annual. Also, remember to calculate individual income based on individual shareholdings and total company dividend based on total capital stock.