ICSE Class 10 Maths Chapter 3 Shares and Dividends: answer-first
ICSE Class 10 Maths Chapter 3 Shares and Dividends teaches how to calculate investment in shares, annual dividend income, and percentage return. The key rule is simple: dividend is calculated on face value, while investment is calculated on market value.
This replacement page removes thin summary text and gives formula-based, teacher-style working for the main Selina Concise Mathematics Class 10 Chapter 3 question types. Exercise order can vary slightly by edition, so each solution shows the method clearly.
Formula reference for ICSE Class 10 Maths shares and dividends
| Formula / term | Use |
|---|---|
| \text{F.V.} | Face value or nominal value of one share. Dividend is calculated on this value. |
| \text{M.V.} | Market value of one share. Investment is calculated on this value. |
| \text{M.V.}=\text{F.V.}+\text{premium} | Use when the share is above par. |
| \text{M.V.}=\text{F.V.}-\text{discount} | Use when the share is below par. |
| \text{Investment}=n\times \text{M.V.} | Total money paid for n shares. |
| \text{Dividend}=n\times \dfrac{r}{100}\times \text{F.V.} | Annual income when dividend rate is r\%. |
| \text{Return}\%=\dfrac{\text{annual income}}{\text{investment}}\times 100 | Percentage income on the actual money invested. |
For syllabus verification, students should refer to the official CISCE publications and syllabuses page. For chapter navigation, use the Selina Maths Class 10 solutions directory.
Concept snapshot: face value vs market value
Think of a share as a product with a printed price and a shop price. The printed price is the face value; the company declares dividend on it. The shop price is the market value; the investor actually pays it. Most wrong answers in this chapter come from mixing up these two values.
Exercise 3(A) worked solutions: investment and dividend
Question 1(a): Buy 50, \text{₹}20 shares at 10\% premium
Step 1: Premium on one share is 10\% of \text{₹}20.
\text{Premium}=\frac{10}{100}\times 20=\text{₹}2
Step 2: Market value of one share is:
\text{M.V.}=20+2=\text{₹}22
Step 3: Money required for 50 shares is:
50\times 22=\text{₹}1100
Final answer: \text{₹}1100.
Question 1(b): Buy 50, \text{₹}20 shares at \text{₹}10 discount
Step 1: Market value of one share is:
\text{M.V.}=20-10=\text{₹}10
Step 2: Money required is:
50\times 10=\text{₹}500
Final answer: \text{₹}500.
Question 1(c): Buy 50, \text{₹}20 shares quoted at \text{₹}22
Step 1: Quoted at \text{₹}22 means \text{M.V.}=\text{₹}22.
\text{Investment}=50\times 22=\text{₹}1100
Final answer: \text{₹}1100.
Question 1(d): Market price of 50, \text{₹}200 shares at 20\% discount
Step 1: Discount on one share is:
\frac{20}{100}\times 200=\text{₹}40
Step 2: Market value of one share is:
200-40=\text{₹}160
Step 3: Market price of 50 shares is:
50\times 160=\text{₹}8000
Final answer: \text{₹}8000.
Question 1(e): Rate of dividend when 500, \text{₹}50 shares earn \text{₹}1250
Step 1: Let the dividend rate be x\%.
1250=500\times \frac{x}{100}\times 50
x=\frac{1250\times 100}{500\times 50}=5
Final answer: Dividend rate =5\%.
Question 1(f): Dividend 12\%, return 10\%; decide whether shares are above par
Step 1: Assume face value =\text{₹}100. Dividend on one share is:
\frac{12}{100}\times 100=\text{₹}12
Step 2: Let market value be \text{₹}x.
10=\frac{12}{x}\times 100
x=\frac{12\times 100}{10}=\text{₹}120
Step 3: Since \text{₹}120>\text{₹}100, the shares are above par.
Final answer: Above par.
Question 2: Buy 400, \text{₹}12.50 shares at premium \text{₹}1
Step 1: Market value of one share is:
12.50+1=\text{₹}13.50
Step 2: Money required is:
400\times 13.50=\text{₹}5400
Final answer: \text{₹}5400.
Question 3: Buy 250, \text{₹}15 shares at discount \text{₹}1.50
Step 1: Market value of one share is:
15-1.50=\text{₹}13.50
Step 2: Money required is:
250\times 13.50=\text{₹}3375
Final answer: \text{₹}3375.
Question 4: Annual income from 125, \text{₹}120 shares paying 5\%
Step 1: Use the dividend formula.
\text{Income}=125\times \frac{5}{100}\times 120=\text{₹}750
Final answer: Annual income =\text{₹}750.
Question 5: Investment \text{₹}3072, \text{₹}10 shares bought at \text{₹}16, dividend 5\%
Step 1: Number of shares bought is:
n=\frac{3072}{16}=192
Step 2: Annual income is:
192\times \frac{5}{100}\times 10=\text{₹}96
Step 3: Percentage income is:
\frac{96}{3072}\times 100=3.125\%
Final answer: Annual income =\text{₹}96; percentage income =3.125\%.
Question 6: Investment \text{₹}7770, \text{₹}100 shares at premium \text{₹}5, dividend 5\%
Step 1: Market value of one share is 100+5=\text{₹}105.
n=\frac{7770}{105}=74
Step 2: Annual income is:
74\times \frac{5}{100}\times 100=\text{₹}370
Step 3: Percentage income is:
\frac{370}{7770}\times 100\approx 4.76\%
Final answer: 74 shares; income =\text{₹}370; return \approx 4.76\%.
Question 7: \text{₹}50 shares paying 12\%, bought at \text{₹}10 premium
Step 1: Market value of one share is 50+10=\text{₹}60.
\text{Investment}=320\times 60=\text{₹}19200
Step 2: Annual income is:
320\times \frac{12}{100}\times 50=\text{₹}1920
Step 3: Profit percent is:
\frac{1920}{19200}\times 100=10\%
Final answer: Market value =\text{₹}19200; income =\text{₹}1920; profit percent =10\%.
Question 8: Investment \text{₹}8800, \text{₹}100 shares at 10\% premium, dividend \text{₹}1200
Step 1: Market value is 100+10=\text{₹}110.
n=\frac{8800}{110}=80
Step 2: Let dividend rate be x\%.
1200=80\times \frac{x}{100}\times 100
1200=80x\Rightarrow x=15
Final answer: Number of shares =80; dividend rate =15\%.
Question 9: Investment \text{₹}3360, \text{₹}24 shares at 12\% premium, dividend 15\%
Step 1: Premium on one share is:
\frac{12}{100}\times 24=\text{₹}2.88
Step 2: Market value is 24+2.88=\text{₹}26.88.
n=\frac{3360}{26.88}=125
Step 3: Annual dividend is:
125\times \frac{15}{100}\times 24=\text{₹}450
Final answer: 125 shares; annual dividend =\text{₹}450.
Question 10: Price paid per \text{₹}100 share when \text{₹}7500 gives income \text{₹}500 at 10\%
Step 1: Let price paid per share be \text{₹}x. Number of shares is \dfrac{7500}{x}.
Step 2: Dividend on one share is 10\% of \text{₹}100, which is \text{₹}10.
500=\frac{7500}{x}\times 10
500x=75000\Rightarrow x=150
Final answer: Price paid per share =\text{₹}150.
Exercise 3(B) worked solutions: return and reverse calculation
Question 1(a): Number of \text{₹}25 shares paying 24\%, total dividend \text{₹}1350
Step 1: Let number of shares be n.
1350=n\times \frac{24}{100}\times 25
n=\frac{1350\times 100}{24\times 25}=225
Final answer: 225 shares.
Question 1(b): \text{₹}600 shares at 20\% discount paying 20\% dividend
Step 1: Market value is:
600-\frac{20}{100}\times 600=\text{₹}480
Step 2: Dividend on one share is:
\frac{20}{100}\times 600=\text{₹}120
Step 3: Return is:
\frac{120}{480}\times 100=25\%
Final answer: 25\%.
Question 1(c): 100, \text{₹}120 shares giving 10\% half-yearly dividend
Step 1: Half-yearly 10\% means annual rate =20\%.
100\times \frac{20}{100}\times 120=\text{₹}2400
Final answer: Annual dividend =\text{₹}2400.
Question 1(d): Amit buys 10, \text{₹}100 shares paying 7.5\%; return 10\%
Step 1: Dividend on one share is \text{₹}7.50, so dividend on 10 shares is \text{₹}75.
10=\frac{75}{I}\times 100
I=\frac{75\times 100}{10}=\text{₹}750
Final answer: Investment =\text{₹}750.
Question 1(e): 200, \text{₹}20 shares at 20\% discount giving 10\% dividend
Step 1: Market value of one share is:
20-\frac{20}{100}\times 20=\text{₹}16
Step 2: Dividend on one share is:
\frac{10}{100}\times 20=\text{₹}2
Step 3: Return is:
\frac{2}{16}\times 100=12.5\%
Final answer: 12.5\%.
Additional worked examples for practice
Worked Example 1: Find market value from return rate
Question: A \text{₹}50 share pays 8\% dividend. If return is 10\%, find market value.
Step 1: Dividend on one share is:
\frac{8}{100}\times 50=\text{₹}4
Step 2: Let market value be \text{₹}x.
10=\frac{4}{x}\times 100
x=\text{₹}40
Final answer: Market value =\text{₹}40, so the share is below par.
Worked Example 2: Find investment from income
Question: A person earns \text{₹}900 from \text{₹}100 shares paying 12\%. If each share is bought at \text{₹}150, find investment.
Step 1: Dividend on one share is:
\frac{12}{100}\times 100=\text{₹}12
Step 2: Number of shares is:
\frac{900}{12}=75
Step 3: Investment is:
75\times 150=\text{₹}11250
Final answer: \text{₹}11250.
Worked Example 3: Compare two investments
Question: Compare a \text{₹}100 share bought at \text{₹}125 paying 15\% dividend with a \text{₹}50 share bought at \text{₹}40 paying 8\% dividend.
Step 1: Return on the first share:
\frac{15}{125}\times 100=12\%
Step 2: Return on the second share:
\frac{4}{40}\times 100=10\%
Final answer: The first investment gives the better return because 12\%>10\%.
Examiner’s mindset for this chapter
In shares and dividends, marks are usually earned for the correct method: finding \text{M.V.}, using \text{F.V.} for dividend, and using actual investment for return. Do not write only the option or final number; show the formula and substitution.
A frequent trap is a half-yearly dividend. If the question asks annual dividend and the rate is half-yearly, convert it to annual rate before applying the formula.
Common mistakes students make
- Dividend on market value: Wrong. Dividend is on \text{F.V.}.
- Investment on face value: Wrong when shares are at premium or discount. Investment is on \text{M.V.}.
- Premium percentage error: A 10\% premium on \text{₹}50 is \text{₹}5, not \text{₹}10.
- Ignoring half-yearly: 10\% half-yearly means 20\% annually.
- Early rounding: Keep exact values until the last line, then round if needed.
Quick answer index
| Exercise | Question | Answer |
|---|---|---|
| 3(A) | 1(a) | \text{₹}1100 |
| 3(A) | 1(b) | \text{₹}500 |
| 3(A) | 1(c) | \text{₹}1100 |
| 3(A) | 1(d) | \text{₹}8000 |
| 3(A) | 1(e) | 5\% |
| 3(A) | 1(f) | Above par |
| 3(A) | 2 | \text{₹}5400 |
| 3(A) | 3 | \text{₹}3375 |
| 3(A) | 4 | \text{₹}750 |
| 3(A) | 5 | \text{₹}96, 3.125\% |
| 3(A) | 6 | 74 shares, \text{₹}370, 4.76\% |
| 3(A) | 7 | \text{₹}19200, \text{₹}1920, 10\% |
| 3(A) | 8 | 80 shares, 15\% |
| 3(A) | 9 | 125 shares, \text{₹}450 |
| 3(A) | 10 | \text{₹}150 |
| 3(B) | 1(a) | 225 shares |
| 3(B) | 1(b) | 25\% |
| 3(B) | 1(c) | \text{₹}2400 |
| 3(B) | 1(d) | \text{₹}750 |
| 3(B) | 1(e) | 12.5\% |
Related ICSE Class 10 Maths study links
After this chapter, revise commercial mathematics with the ICSE Class 10 Maths hub, the ICSE Class 10 Maths previous year papers, the Selina chapterwise revision solutions, and the Selina mixed practice solutions.
Frequently Asked Questions
In ICSE Class 10 Maths shares and dividends, is dividend calculated on face value or market value?
Dividend is calculated on the face value or nominal value of the share, not on the market value. Market value is used to calculate investment and return percentage.
How do I find market value when a share is at premium or discount?
At premium, add the premium to the face value. At discount, subtract the discount from the face value. For example, a \text{₹}100 share at 10\% premium has market value \text{₹}110.
What is the formula for return percentage in shares and dividends?
The formula is \text{Return}\%=\dfrac{\text{annual income}}{\text{investment}}\times 100. For one share, use dividend on one share divided by market value of one share.
Why is a share above par when dividend rate is greater than return rate?
If dividend rate is greater than return rate, the investor paid more than the face value. Therefore, the market value is above par.
How should I write Selina shares and dividends solutions in the ICSE exam?
Write the face value, market value, number of shares, annual income and return percentage clearly. Show formula substitution before the final answer.