Shares and Dividends Class 10 ICSE — Bansal Chapter 3
Bansal’s ICSE Class 10 Mathematics book, Chapter 3, covers shares and dividends. The chapter defines a share, separates nominal value from market value, and shows how to compute a shareholder’s annual income. Five formulas link money invested, shares bought, dividend rate, and return percent. This page explains shares and dividends class 10 ICSE content section by section, presents each formula in MathJax, and works original examples.
ICSE Class 10 Mathematics Bansal Chapter 3 Shares and Dividend PDF
What is inside Chapter 3
15 pages · 3 sections · 15 worked examples · 35 exercise questions
| Section | Title |
|---|---|
| 3.1 | Introduction |
| 3.2 | Formulae |
| 3.3 | Miscellaneous Problems |
- EXERCISE 3(A): 15 questions
- EXERCISE 3(C): 20 questions
This chapter is part of the ICSE Class 10 Maths chapter list, and its topics follow the CISCE syllabus for Class 10 Mathematics.
3.1 Introduction
Starting a company needs a large sum of money that one person may not be able to invest alone. Interested persons join together and divide the estimated value into small parts, each between ₹ 1 and ₹ 100. Each part is a share. The value fixed on a share is its nominal value (N.V.), and the buyers are called shareholders.
The nominal value is also called the register value, printed value, or face value. It does not change with time. The market value (M.V.) is the price of the share in the market at a particular time. It may rise or fall as the company performs better or worse.
| Situation | Condition |
|---|---|
| At par | \text{M.V.} = \text{N.V.} |
| At a premium (above par) | \text{M.V.} \gt \text{N.V.} |
| At a discount (below par) | \text{M.V.} \lt \text{N.V.} |
A dividend is the profit a shareholder receives out of the company’s profits. Two rules always apply: the dividend is always a percentage of the nominal value, and it never depends on the market value. The company fixes its dividend on the printed value, not on the price you paid. So a ₹ 100 share paying 10% dividend gives ₹ 10 per share whether you bought it at ₹ 90 or at ₹ 130.
3.2 Formulae
This section gives the five formulas used for every share problem in the chapter.
1. The money needed to buy shares:
\text{Sum invested} = \text{No. of shares bought} \times \text{M.V. of 1 share}
If the shares are available at par, the M.V. of each share equals its N.V.
2. The number of shares bought:
\text{No. of shares bought} = \frac{\text{Sum invested}}{\text{M.V. of 1 share}} = \frac{\text{Total dividend}}{\text{Dividend on 1 share}}
3. The total dividend earned:
\text{Total dividend} = \text{No. of shares} \times \text{Rate of dividend} \times \text{N.V. of a share}
4. The return on money invested:
\text{Return } \% = \frac{\text{Income}}{\text{Investment}} \times 100\%
5. For a shareholder, income, return, profit, and dividend paid all mean the same amount.
The worked examples add a cross rule that connects return and dividend: \text{Income } \% \times \text{M.V.} = \text{Dividend } \% \times \text{N.V.}. It holds because both sides express the same income.
Worked example pattern. Suppose you buy 250 shares of ₹ 50 each at a premium of ₹ 8, and the company pays a 10% dividend. The market value of one share is 50 + 8 = \text{₹ }58.
\text{Sum invested} = 250 \times \text{₹ }58 = \text{₹ }14{,}500
\text{Income per share} = 10\% \text{ of } \text{₹ }50 = \text{₹ }5 \quad \Rightarrow \quad \text{Total income} = 250 \times \text{₹ }5 = \text{₹ }1{,}250
\text{Return } \% = \frac{\text{₹ }1{,}250}{\text{₹ }14{,}500} \times 100\% \approx 8.62\%
| Mistake | Correct rule |
|---|---|
| Computing dividend on market value | Always compute dividend on nominal value |
| Expecting per-share income to rise when M.V. rises | Dividend percent is fixed on N.V., so per-share income stays the same |
Half-yearly dividends. A half-yearly rate must be doubled for the year. A 4% half-yearly dividend on ₹ 50 shares means 8% yearly, or 8\% \text{ of } \text{₹ }50 = \text{₹ }4 per share for the year.
3.3 Miscellaneous Problems
Most board problems in this section reduce to a single equating rule:
\text{Rate of dividend} \times \text{N.V.} = \text{Profit (return) } \% \times \text{M.V.}
Why it works: both sides express the same income. The dividend you receive is the dividend percent of the nominal value, and the profit on your money is the return percent of the market value. These two expressions for one income must be equal.
The rule answers three recurring problem types: finding the purchase price for a target return, comparing two investments to pick the better one, and sell-and-reinvest or equal-income problems. The chapter solves them two ways — by direct arithmetic or by letting the unknown be x and forming an equation.
Worked example pattern. A ₹ 60 share pays a 15% dividend. At what price must it be bought so the investor earns a 12% return?
\frac{15}{100} \times 60 = \frac{12}{100} \times \text{M.V.}
\Rightarrow \text{M.V.} = 60 \times \frac{15}{12} = \text{₹ }75
The investor must pay ₹ 75 per share.
Comparing two investments. Return percent decides the better buy, not the dividend percent. Take 9% ₹ 100 shares at ₹ 120 and 5% ₹ 100 shares at ₹ 50. The first gives a return of \frac{9 \times 100}{120} = 7.5\%. The second gives \frac{5 \times 100}{50} = 10\%. The second is better even though its dividend percent is lower. A higher dividend percent never automatically means a better buy — always compare return on market value.
What to practise from this chapter
- EXERCISE 3(A) — 15 questions
- EXERCISE 3(C) — 20 questions
The questions recur as set types: money required to buy shares at a premium or discount, annual income from given shares, rate of dividend, and percentage income or return. Other types include comparing better investments, selling shares and reinvesting the proceeds, and dividing a sum into two parts with equal income. Several questions carry board years from 2000 to 2015, so they double as past-paper practice.
This chapter is one of several in the ICSE Class 10 textbook chapter directory, where the same question types recur across other chapters.
Frequently asked questions
What is the difference between the nominal value and the market value of a share?
The nominal value is the value printed on the share when the company divides its capital; it never changes with time. The market value is the price at which the share trades at a particular time, and it rises or falls with the company’s performance and profits.
Is the dividend calculated on the nominal value or the market value of a share?
Always on the nominal value. The dividend is a percentage of the N.V. and never depends on the M.V., so a fixed dividend percent gives the same income per share no matter what price you paid.
What does it mean when a share is at par, at a premium, or at a discount?
At par means the market value equals the nominal value (\text{M.V.} = \text{N.V.}). At a premium (above par) means \text{M.V.} \gt \text{N.V.}. At a discount (below par) means \text{M.V.} \lt \text{N.V.}.
How do I decide which of two share investments gives a better return?
Compare the return percent on market value using the rule Rate of dividend × N.V. = Return % × M.V. The investment with the higher return percent is better; the dividend percent alone does not decide it.
A company declares a half yearly dividend of 4 percent. How do I find the yearly dividend?
Double the rate. A 4% half-yearly dividend gives 8% yearly, so on a ₹ 50 share the yearly dividend is 8\% \text{ of } \text{₹ }50 = \text{₹ }4.
Reference: ICSE Class 10 Mathematics textbook (Bansal), chapter 3: Shares and Dividend — CISCE-aligned.
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