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## List of Topics Covered in Shares and Dividends

- Share and Value of Shares
- Dividend and Rate of Dividend
- Calculation of Income, Return and Number of Shares
- Problems on Income and Return from Shares
- Problems on Shares and Dividends
- Worksheet on Basic Concept on Shares and Dividends
- Worksheet on Income and Return from Shares
- Worksheet on Share and Dividend

### Share and Value Shares – Definition

The division of money required into some equal parts is called a share. And the person who purchases the shares is known as the shareholder of the company. The original value of a share printed on the certificate of the share is known as the value of the share.

### Dividends – Definition

The sum of money paid for equal parts in any profits is known as the dividends.

### Formula to Calculate Dividends Per Share

D = DPS multiplied by S,

where D = your dividends and

S = the number of shares you own.

### Shares and Dividends Examples

**Example 1.**

Find the dividends received on 80 shares of Rs 30 each if a 7% dividend is declared. Then find the dividend.

**Solution:**

Given that

The value of shares = Rs. 30

The value of 60 shares each = Rs. 30

= 30 × 80 = 2400

The rate of dividend = 8%

The total dividend = Rs. 2400 × 7%

= 2400 × (7/100)

= Rs 168

Therefore the total dividend = 168

**Example 2.**

Virat and Dhoni invest 36000 each in buying shares of two companies. Virat buys 15%. 40 shares at a discount of 20%, while Dhoni buys.75 shares at a premium of 20%. If both receive equal dividends at the end of the year, find the rate percent of the dividend declared by Dhoni’s company.

**Solution:**

In the first case,

we have

Investment made by Virat = ₹ 34000

And market value at a discount of 10% = ₹ 40 x (80/100) = ₹ 32

Thus, total face value = ₹ (36000 x 40)/32 = ₹ 45000

Rate of dividend = 15%

Thus, total dividend = ₹ (45000 x 15)/100 = ₹ 6750

Now, in second case, we have

Investment = ₹ 36000

Dividend of Dhoni = ₹ 6750

Face value of each share = ₹ 75

And market value at premium of 20% = ₹ 75 x (120/100) = ₹ 90

Face value = 36000 x (75/90) = 30000

Thus, rate of dividend = (6750 x 100)/30000 %

= 45/2 % = 22.5%

**Example 3.**

A person invested 20%, 30% and 25% of his savings in buying shares at par values of three different companies A, B and C which declare dividends of 10%, 12% and 15% respectively. If his total income on account of dividends is Rs. 4675, find his savings and the amount which he invested in buying shares of each company.

**Solution:**

Given that,

Investment in 3 companies A, B and C are 20%, 30% and 25%

Let the total investment be Rs. 100

So, the investment in company A = Rs. 20

Rate of dividend = 10%

Thus, dividend = Rs. (20 x 10)/100 = Rs. 2

Investment in company B = Rs. 30

Rate of dividend = 12%

Thus, dividend = Rs. (30 x 12)/100 = Rs. 36/10 = Rs. 3.6

And, investment in company C = Rs. 25

Rate of dividend = 25%

Thus, dividend = Rs. (25 x 15)/100 = Rs. 375/100 = Rs. 3.75

Total dividend = Rs. 2 + Rs. 3.60 + Rs 3.75 = Rs. 9.35

If dividend is Rs 9.35, then total savings = Rs. 100

Then, if dividend is Rs. 4675 the total savings

= (4675 x 100)/9.35

= (4675 x 100 x 100)/935

= Rs. 50000

Hence,

The amount of investment in shares of company A = Rs. 50000 x (20/100) = Rs. 10000

The amount of investment in shares of company B = Rs. 50000 x (30/100) = Rs. 15000

The amount of investment in shares of company A = Rs. 50000 x (25/100) = Rs. 12500

**Example 4.**

Divide Rs. 101410 into two parts such that if one part is invested in 8% Rs. 100 shares at 8% discount and the other in 9% Rs. 50 shares at 8% premium, the annual incomes are equal.

**Solution:**

Given that,

Total investment = Rs. 101410

Let investment in first part be x and in second part will be (101410 – x)

Market value of first kind of shares = Rs. 100 – Rs. 6

= Rs. 92

And rate of dividend = 8%

So, dividend = (x × 8)/92 = Rs. 2x/23

Now, market value of second kind = (101410 – x)

Rate of dividend = 9%

And market value = Rs. (100 + 8)/100 × 50

= Rs. (108/100) × 50

= Rs. 54

So, dividend = Rs. (101410 – x) × 9/(2 × 54)

= Rs. (101410 – x)/12

According to the given in the problem, we have

2x/23 = (101410 – x)/12

24x = 23 (101410 – x)

24x = 101410 × 23 – 23x

47x = 101410 × 23

x = Rs. (101410 × 23)/ 47

= Rs. 49626

Hence, investment of first part = Rs. 49626

And in second part = Rs. (101410 – 49626) = Rs. 51784

**Example 5.**

A man has some shares of Rs. 200 per value paying 7% dividend. He sells half of these at a discount of 11% and invests the proceeds in 8% Rs. 60 shares at a premium of Rs. 20. This transaction decreases his income from dividends by Rs. 130. Calculate:

(i) the number of shares before the transaction.

(ii) the number of shares he sold.

(iii) his initial annual income from shares.

**Solution:**

Let’s consider the no. of shares to be x

Value of x shares = x × 200 = 200x

And dividend = (200x × 7)/100 = Rs. 14x

Dividend on half-shares = Rs. 7x/2 = Rs. 3.5x

Now, the no. shares he sold out = x/2

Amount received at 11% discount = x/2 × 180 = Rs. 90x

In investing Rs. 90x, no. of shares he purchased = 90x/80

Thus, the amount of shares = 90x/80 × 60 = Rs. 67.5x

Income at rate of 4% = 67.5x × 4/100 = 2.7x

Difference in income = 3.5 x – 2.7x = 9.45x

According to the given conditions, we have

9.45x = 130

x = 130/9.45

x = 13.75

Hence,

(i) The number of shares he hold initially = 13.75

(ii) No. of shares he held later = 13.75/2 = 6.87

(iii) Amount of income initially = 13.75 × 7 = Rs. 19.25

### FAQs on Shares and Dividends

**1. What are shares and dividends?**

Shares are units of equity ownership in a corporation. For some companies, shares exist as a financial asset providing for an equal distribution of any residual profits, if any are declared, in the form of dividends. Shareholders of a stock that pays no dividends do not participate in a distribution of profits.

**2. How do you calculate dividends per share?**

Simply use the formula D = DPS multiplied by S, where D = your dividends and S = the number of shares you own.

**3. What are shares in maths?**

The sum of money required is called capital. The required capital is divided into small equal parts, and each part is called a share.