Shares and Dividends ICSE Class 10: Concepts, Formulas and Solved Questions

What Shares and Dividends is about

Weightage: CISCE publishes no chapter or unit weightage for ICSE Mathematics. Shares and Dividends is in the 1. Commercial Mathematics (iii) Shares and Dividends part of the 2027 syllabus and can be asked in both Section A and Section B of the 80-mark paper.Source: CISCE ICSE Mathematics syllabus, examination year 2027

Key concepts

Face value, market value, premium and discount

• Face value (FV): the value printed on the share certificate, e.g. a ₹100 share.
• Market value (MV): the price of one share in the market today.
• At par: MV = FV.
• At a premium (above par): MV > FV. 'A ₹100 share at 20% premium' means MV $=100+20\%$ of $100=₹120$.
• At a discount (below par): MV < FV. 'A ₹100 share at 15% discount' means MV $=₹85$.

The premium or discount percent is always worked on the face value. Saying 'a ₹100 share at ₹120' and 'a ₹100 share at 20% premium' mean the same thing.

Worked example

Find the market value of a ₹50 share (a) at 20% premium, (b) at 10% discount.

Try it first, then show the solutionSolution

1. (a) Premium $=20\%$ of $50=₹10$, so MV $=50+10=₹60$.
2. (b) Discount $=10\%$ of $50=₹5$, so MV $=50-5=₹45$.

Answer: (a) ₹60 (b) ₹45

Investment and the number of shares

Shares are bought at the market value, so
$\text{Investment}=\text{number of shares}\times \text{MV},\text{number of shares}=\frac{\text{Investment}}{\text{MV}}.$
Since fractional shares are not in the syllabus, the number of shares in a board question always comes out a whole number. If yours does not, check that you divided by the market value and not by the face value.

Worked example

Asif invests ₹18,000 in ₹100 shares available at ₹120. How many shares does he buy?

Try it first, then show the solutionSolution

1. Each share costs its market value, ₹120.
2. Number of shares $=\frac{18000}{120}=150$.

Answer: 150 shares

Dividend and annual income

The rate of dividend is declared as a percentage of the face value, whatever the market value is. So
$\text{Dividend on one share}=\frac{r}{100}\times \text{FV},$
$\text{Income}=\text{number of shares}\times \frac{r}{100}\times \text{FV}.$
This is the syllabus formula. Do not use the market value here: two people holding the same share get the same dividend per share, even if one bought it at ₹80 and the other at ₹150.

Worked example

Asif holds 150 shares of face value ₹100. The company declares a dividend of 9%. Find his annual income.

Try it first, then show the solutionSolution

1. Dividend on one share $=9\%$ of $₹100=₹9$.
2. Income $=150\times 9=₹1,350$.

Answer: ₹1,350

Return (yield) on an investment

The return tells you how good the investment is, as a percentage of the money actually spent:
$\text{Return \%}=\frac{\text{Income}}{\text{Investment}}\times 100.$
For one share this is $\frac{\text{dividend on one share}}{\text{MV}}\times 100=\frac{r\times \text{FV}}{\text{MV}}$.

So:

• at par, return = rate of dividend;
• at a premium (MV > FV), return < rate of dividend;
• at a discount (MV < FV), return > rate of dividend.

The 2025 board paper tested exactly this: a 12% dividend giving a 10% return means the shares were bought above par.

Worked example

For Asif's investment (₹18,000, income ₹1,350), find the return percent. Check it using one share.

Try it first, then show the solutionSolution

1. Return $=\frac{1350}{18000}\times 100=7.5\%$.
2. One share: dividend ₹9 on a cost of ₹120, so return $=\frac{9}{120}\times 100=7.5\%$. Same.

Answer: 7.5%

Comparing two investments

To decide which of two shares is the better investment, compare their returns, not their dividend rates. A high dividend rate on a share bought at a big premium can give a low return.

For each share, return $=\frac{\text{dividend on one share}}{\text{MV}}\times 100$. The one with the higher return gives more income for the same amount invested.

Worked example

Which is the better investment: 8% ₹100 shares at ₹120, or 10% ₹50 shares at ₹70?

Try it first, then show the solutionSolution

1. First: dividend per share $=₹8$; return $=\frac{8}{120}\times 100=6\frac{2}{3}\%\approx 6.67\%$.
2. Second: dividend per share $=10\%$ of $50=₹5$; return $=\frac{5}{70}\times 100\approx 7.14\%$.
3. The second gives a higher return.

Answer: The 10% ₹50 shares at ₹70 are better.

Selling shares and reinvesting

When shares are sold, the seller receives the current market value for each share:
$\text{Sale proceeds}=\text{number of shares}\times \text{selling price}.$
Gain (or loss) on the sale = proceeds − original investment.

If the proceeds are reinvested in other shares, work the new investment from scratch: new number of shares = proceeds ÷ new MV, then new income from the new FV and dividend rate. Finally compare old and new incomes if asked.

Worked example

Mala bought 200 shares of face value ₹10 at ₹16 each. She sells them at ₹19 each and invests the proceeds in ₹20 shares at ₹25. Find her gain on the sale and the number of new shares.

Try it first, then show the solutionSolution

1. Gain $=200\times (19-16)=₹600$.
2. Proceeds $=200\times 19=₹3,800$.
3. New shares $=\frac{3800}{25}=152$.

Answer: Gain ₹600; 152 new shares

Maths in real life: Shares and Dividends

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

Topics in this chapter

• Dividend and Annual Income from Shares
• Investment and Number of Shares
• Return on Investment in Shares

Shares and Dividends formula sheet

Market value at a premium or discount

$\text{MV}=\text{FV}\left(1\pm \frac{p}{100}\right)$

+ for premium, − for discount; p% is on the face value.

Number of shares

$n=\frac{\text{Investment}}{\text{MV}}$

Always a whole number (no fractional shares).

Investment

$\text{Investment}=n\times \text{MV}$

Shares are bought at the market value.

Annual income (dividend)

$\text{Income}=n\times \frac{r}{100}\times \text{FV}$

Dividend is always on the face value.

Return percent

$\text{Return}=\frac{\text{Income}}{\text{Investment}}\times 100$

Also equals (r × FV) ÷ MV for one share.

Return from one share

$\text{Return}=\frac{r\times \text{FV}}{\text{MV}}\%$

Return < r above par, = r at par, > r below par.

Sale proceeds

$n\times \text{selling price}$

Gain = proceeds − investment.

How the board asks Shares and Dividends

The question patterns to expect, and the method that works for each.

Tricks to remember Shares and Dividends

Short memory aids. Say each one aloud once, then use it on a question the same day.

• Pay on Market, Paid on Face

  You PAY the Market value; you are PAID dividend on the Face value.

  Use it when: Every income and investment calculation.

• Above par, return falls

  Pay more than face value (premium) and your return drops below the dividend rate; pay less (discount) and it rises above.

  Use it when: Par/premium/discount MCQs.

• Premium is a percent of the face

  '₹100 share at 25% premium' → 100 + 25 = ₹125. Never 25% of something else.

  Use it when: Turning premium or discount into MV.

• Return compares, rate declares

  The company declares the rate of dividend; you compare investments by return.

  Use it when: Which is the better investment?

Shares and Dividends: board-level solved questions

Ordered from board level to HOTS. Cover the solution, write your own, then compare step by step.

Case-study practice (Section B style)

Read the situation, then answer every part. In the board paper this is a 10-mark question split into 3 + 3 + 4 marks.

Where the marks are

How a typical answer is split into step marks. Show every step: a right final answer alone rarely earns full marks.

Where students lose marks in Shares and Dividends

The slips examiners see most often, and what to write instead.

• ✗Mistake: Misreading 'at a premium' and getting the market value wrong

  CISCE examiners' comments, 2024 and 2025: candidates did not add the premium to the face value, so they divided the investment by ₹100 instead of ₹110 and got the wrong number of shares; others were not familiar with the term 'premium' at all.

  Wrong working

  ₹33,000 in ₹100 shares at 10% premium: $\frac{33000}{100}=330$ shares.

  Right working

  MV $=₹110$; $\frac{33000}{110}=300$ shares.

  ✓Do this: Write 'MV = …' as your first line whenever a premium or discount is mentioned.

  Usually costs: The number of shares and every answer that depends on it.

• ✗Mistake: Working the dividend on the market value

  CISCE examiners' comments, 2025: candidates used the market value instead of the face value to find the dividend rate, mixing up 'dividend' and 'return'.

  Wrong working

  Dividend on one ₹200 share bought at ₹250 at 4%: $4\%$ of $250=₹10$.

  Right working

  Dividend $=4\%$ of $200=₹8$.

  ✓Do this: Dividend → face value. Return → investment (market value).

  Usually costs: 1 to 2 marks.

• ✗Mistake: Giving the cost of one share when all the shares were asked for

  CISCE examiners' comments, 2024: in an MCQ on the sum invested in 15 shares, many chose the price of one share.

  ✓Do this: Underline the number of shares in the question; the last step multiplies by it.

  Usually costs: 1 mark.

• ✗Mistake: Comparing the dividend rate with the return the wrong way round

  CISCE examiners' comments, 2025: told that a 12% dividend gave a 10% return, candidates treated 10% as the market value and chose 'below par', or chose 'cannot be determined'.

  ✓Do this: Use return = r × FV ÷ MV. A lower return than the dividend rate means MV > FV, i.e. above par.

  Usually costs: 1 mark.

• ✗Mistake: Comparing investments by dividend rate instead of return

  A higher declared rate looks better, but the share may cost much more.

  ✓Do this: Always compute the return of each option before deciding.

  Usually costs: The reasoning mark in a comparison question.

Practice questions on Shares and Dividends

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

1. Q1 · 1 mark · MCQBoard level

   A ₹100 share is quoted at ₹115. The share is at:
   (a) par
   (b) 15% discount
   (c) 15% premium
   (d) 115% premium

   Hint

   Compare MV with FV.

   Answer

   (c) 15% premium

2. Q2 · 1 mark · MCQBoard level

   The annual dividend on 200 shares of face value ₹10 at a dividend rate of 15% is:
   (a) ₹30
   (b) ₹150
   (c) ₹300
   (d) ₹3,000

   Hint

   Dividend on one share is 15% of ₹10.

   Answer

   (c) ₹300

3. Q3 · 1 mark · MCQHarder board level

   A man invests in a company paying an 8% dividend and gets a 10% return on his investment. The shares were bought:
   (a) at par
   (b) above par
   (c) below par
   (d) cannot be determined

   Hint

   Return = r × FV ÷ MV.

   Answer

   (c) below par, since $10=\frac{8\times \text{FV}}{\text{MV}}$ gives MV $=0.8$FV.

4. Q4 · 1 mark · Assertion-reasonBoard level

   Assertion (A): A ₹50 share bought at ₹40 is bought at a discount of 20%.
   Reason (R): Discount percent = (FV − MV) ÷ FV × 100.
   (a) (A) is true and (R) is false.
   (b) (A) is false and (R) is true.
   (c) Both (A) and (R) are true, and (R) is the correct explanation for (A).
   (d) Both (A) and (R) are true, but (R) is not the correct explanation for (A).

   Hint

   Find (50 − 40) ÷ 50.

   Answer

   (c). $\frac{10}{50}\times 100=20\%$, using (R).

5. Q5 · 4 marks · Short answerHarder board level

   Sunita invests ₹14,400 in ₹100 shares at ₹90. The company pays a 7.5% dividend. Find (a) the number of shares, (b) her annual income, (c) her return percent.

   Hint

   Divide by ₹90.

   Answer

   (a) $\frac{14400}{90}=160$ (b) $160\times 7.50=₹1,200$ (c) $\frac{1200}{14400}\times 100=8\frac{1}{3}\%$

6. Q6 · 4 marks · Short answerHarder board level

   How many ₹20 shares available at a 20% discount must be bought to get an annual income of ₹1,800, if the dividend is 12.5%? Find the investment.

   Hint

   Dividend per share = 12.5% of ₹20; MV = ₹16.

   Answer

   Dividend per share $=₹2.50$; shares $=\frac{1800}{2.50}=720$; MV $=₹16$; investment $=720\times 16=₹11,520$.

7. Q7 · 3 marks · Long answerBoard level

   Rohit buys 250 shares of face value ₹50 at ₹65 each. The company declares a 10% dividend. Find his investment, his annual dividend and his return correct to two decimal places.

   Hint

   Investment at MV, dividend on FV.

   Answer

   Investment $=250\times 65=₹16,250$; dividend $=250\times 5=₹1,250$; return $=\frac{1250}{16250}\times 100=7.69\%$.

8. Q8 · 4 marks · Long answerHarder board level

   A woman invests ₹25,000 in ₹100 shares at ₹125 and receives an annual income of ₹1,800. Find the rate of dividend and her return.

   Hint

   Number of shares first.

   Answer

   Shares $=\frac{25000}{125}=200$; dividend per share $=\frac{1800}{200}=₹9$, so the rate is 9%. Return $=\frac{1800}{25000}\times 100=7.2\%$.

9. Q9 · 4 marks · Long answerHOTS / competency

   Kabir holds 500 shares of face value ₹10, bought at ₹14, paying a 10% dividend. He sells them at ₹16 and buys ₹100 shares at ₹160 paying an 18% dividend. Find (a) his gain on the sale, (b) the change in annual income, (c) the return on the new shares. Comment on whether his income per rupee invested improved.

   Hint

   Proceeds = 500 × 16.

   Answer

   (a) $500\times 2=₹1,000$ (b) Old income $=500\times 1=₹500$; proceeds ₹8,000 buy $\frac{8000}{160}=50$ shares; new income $=50\times 18=₹900$; increase ₹400. (c) $\frac{18}{160}\times 100=11.25\%$. The old shares at today's price ₹16 return only $\frac{1}{16}=6.25\%$, so income per rupee has improved.

10. Q10 · 4 marks · Long answerHarder board level

    A man invests ₹29,000 partly in 8% ₹100 shares at ₹120 and partly in 10% ₹100 shares at ₹140. His incomes from the two are equal. Find the amount invested in each and his total income.

    Hint

    Income from ₹x in the first is $\frac{8x}{120}$.

    Answer

    Let ₹$x$ go into the first. $\frac{8x}{120}=\frac{10(29000-x)}{140}$ gives $\frac{x}{15}=\frac{29000-x}{14}$, so $14x=435000-15x$, $x=15000$. First ₹15,000 (125 shares, income ₹1,000); second ₹14,000 (100 shares, income ₹1,000). Total ₹2,000.

11. Q11 · 1 mark · MCQHOTS / competency

    Which gives the highest return?
    (a) 10% ₹100 shares at ₹125
    (b) 12% ₹50 shares at ₹80
    (c) 9% ₹10 shares at ₹10
    (d) 15% ₹20 shares at ₹40

    Hint

    Return = dividend per share ÷ MV.

    Answer

    (c): returns are 8%, 7.5%, 9% and 7.5%.

12. Q12 · 3 marks · Short answerHOTS / competency

    Show that the return percent on any share is $\frac{r\times \text{FV}}{\text{MV}}$, where r% is the dividend rate. Hence explain why a share bought at a premium always returns less than its dividend rate.

    Hint

    Work with one share.

    Answer

    For one share, income $=\frac{r}{100}\times \text{FV}$ and investment $=\text{MV}$, so return $=\frac{r\times \text{FV}/100}{\text{MV}}\times 100=\frac{r\times \text{FV}}{\text{MV}}$. At a premium MV > FV, so $\frac{\text{FV}}{\text{MV}}<1$ and the return is less than r.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1. 1.On which value is the dividend calculated?Show answer

   The face (nominal) value.

2. 2.What does 'at par' mean?Show answer

   Market value equals face value.

3. 3.MV of a ₹100 share at 15% premium?Show answer

   ₹115

4. 4.Write the syllabus formula for income.Show answer

   Income = number of shares × rate of dividend × FV.

5. 5.Write the formula for return.Show answer

   Return = (Income ÷ Investment) × 100.

6. 6.If the return is greater than the dividend rate, how were the shares bought?Show answer

   Below par (at a discount).

7. 7.Are brokerage and fractional shares in the ICSE syllabus?Show answer

   No.

8. 8.How do you find the number of shares bought?Show answer

   Investment ÷ market value.

Quick revision checklist

The night before the exam: can you do each of these without looking?

• ☐Can you turn '₹50 share at 20% premium' or '₹100 share at 15% discount' into a market value?
• ☐Do you always divide the investment by the market value to get the number of shares?
• ☐Do you always work the dividend on the face value?
• ☐Can you find the return and say whether shares were bought at par, above or below par?
• ☐Can you find the investment needed for a given annual income?
• ☐Can you compare two investments by their returns?
• ☐Can you handle selling shares and reinvesting the proceeds?

Shares and Dividends: frequently asked questions