MathsICSE Class 10 · Shares and Dividends

Investment and Number of Shares: Par, Premium and Discount (ICSE Class 10)

Updated 15 October 2026 · Fact-checked

The money you invest in shares is the number of shares times the market value of one share, so number of shares = investment ÷ market value. A share is at par if its market value equals its face value, at a premium if above it, and at a discount if below. The face value matters only for the dividend.

The dashed face value stays fixed at ₹100 while the market value you pay moves above or below it; divide investment by MV, not FV.

Illustration drawn for QuestionBuddy.

Understand Investment and Number of Shares

When you buy shares you pay the market value (MV), the price at which the share is trading. The face value (FV) printed on it stays fixed. Three words describe how the two compare:

At par: MV = FV (a ₹100 share costs ₹100).
At a premium (above par): MV > FV. 'A ₹100 share at a premium of 25%' costs $100 + 25 = ₹125$ ; 'a ₹100 share at ₹125' means the same thing.
At a discount (below par): MV < FV. 'A ₹50 share at a discount of 10%' costs $50 - 5 = ₹45$ .

The premium or discount percentage is always a percentage of the face value.

The investment equation.

$Investment = number of shares \times MV, number of shares = \frac{Investment}{MV} .$

In 2024 Q1(ix) (15 shares of ₹75 at 20% discount) the answer was $15 \times 60 = ₹900$ ; the examiners reported candidates who stopped at ₹60, the price of one share.

Total face value. The face value of all the shares you hold, $n \times FV$ , is called the nominal value of your holding. It is this amount on which the dividend percentage is applied. If you invest ₹18,000 in ₹100 shares at ₹90, you get 200 shares with a total face value of ₹20,000, which is more than you paid.

Investing for a target income. Work from the income back to the investment:

$target income \to number of shares = \frac{income}{dividend per share} \to investment = n \times MV .$

Selling shares. Sale proceeds = number of shares × selling market price. Gain (or loss) = sale proceeds − original investment, and a percentage gain is taken on the investment. If the proceeds are reinvested, they become the new investment and are divided by the new market value.

Brokerage and fractional shares are outside the CISCE 2027 syllabus, so investments are chosen to give whole numbers of shares.

Investment and Number of Shares: formulas to remember

Investment: $Investment = n \times MV$; $n$ = number of shares.
Number of shares: $n = \frac{Investment}{MV}$; Always divide by the market value.
Market value at a premium of p%: $MV = FV + \frac{p}{100} \times FV$; Premium is a percentage of the face value.
Market value at a discount of d%: $MV = FV - \frac{d}{100} \times FV$; Also called 'below par'.
Total face value (nominal value) of a holding: $n \times FV$; The dividend rate is applied to this.
Gain on selling shares: $Gain = n \times (selling MV - buying MV)$; Gain % = gain ÷ investment × 100.

How to solve Investment and Number of Shares questions

Translate the words into a market value, then use investment = shares × market value.

1Write the face value and convert 'at par', 'at a premium of p%' or 'at a discount of d%' into the market value.
2If the investment is given, divide by the market value to get the number of shares.
3If the number of shares is given, multiply by the market value to get the investment.
4For a target income: dividend per share = FV × rate ÷ 100; shares = income ÷ dividend per share; then investment.
5For selling: proceeds = shares × selling price; compare with the investment for gain or loss.
6For reinvesting, use the proceeds as the new investment and the new company's market value.
7Check that the number of shares is a whole number.

Investment and Number of Shares in real life

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.

How many shares a sum buys

Suppose you have ₹5,000 of birthday money and want to buy shares of face value ₹10 that are quoted at ₹12.50.

How many shares can you buy, and are they at par, at a premium or at a discount?

Try it first, then show the solutionSolution

Number of shares $= \frac{5000}{12.50} = 400$ .
MV ₹12.50 > FV ₹10, so they are at a premium of $\frac{2.50}{10} \times 100 = 25%$ .

Answer: 400 shares, bought at a 25% premium.

Memory hook: Money ÷ Market price = how many shares.

Gain on selling shares

Imagine your uncle bought 150 shares at ₹240 each and later sold them all at ₹276 each.

Find his gain and his gain as a percentage of the investment.

Try it first, then show the solutionSolution

Investment $= 150 \times 240 = 36000$ ; proceeds $= 150 \times 276 = 41400$ .
Gain $= 41400 - 36000 = 5400$ ; gain % $= \frac{5400}{36000} \times 100 = 15%$ .

Answer: Gain ₹5,400, which is 15% of his investment.

Memory hook: Buy at one market price, sell at another; the face value does not enter.

Tricks to remember Investment and Number of Shares

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

PAR, PREMIUM, DISCOUNT on a see-saw
Face value is the pivot: premium lifts the market value above it, discount drops it below, par keeps it level.
Use it when: Turning the words into a market value.
Percent of the Face
A 20% premium is 20% of the face value, not of anything else.
Use it when: ₹75 share at 20% discount → ₹60.
M-n-I triangle
Investment = $n \times$ MV. Cover the one you want: $n = I \div MV$ , MV $= I \div n$ .
Use it when: Any of the three unknowns.

Investment and Number of Shares: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Sum invested at a premium · 1 mark · MCQBoard level

The sum needed to buy 40 shares of face value ₹50 at a premium of 20% is:
(a) ₹2,000
(b) ₹2,400
(c) ₹1,600
(d) ₹60

Try it first, then show the solutionSolution

MV $= 50 + 20%$ of $50 = 60$ .
Sum $= 40 \times 60 = 2400$ .

Answer: (b) ₹2,400

Example 2: Number of shares at a discount · 3 marks · Short answerBoard level

Meera invests ₹18,000 in ₹100 shares available at a discount of 10%. Find (a) the market value of one share, (b) the number of shares, (c) the total face value of her shares.

Try it first, then show the solutionSolution

(a) MV $= 100 - 10 = 90$ .
(b) $n = \frac{18000}{90} = 200$ .
(c) Total face value $= 200 \times 100 = 20000$ .

Answer: (a) ₹90 (b) 200 shares (c) ₹20,000

Example 3: Investment for a target income · 3 marks · Short answerHarder board level

How much must a man invest in ₹10 shares quoted at ₹15, paying a 9% dividend, to obtain an annual income of ₹1,350?

Try it first, then show the solutionSolution

Dividend per share $= 10 \times \frac{9}{100} = 0.90$ .
Shares needed $= \frac{1350}{0.90} = 1500$ .
Investment $= 1500 \times 15 = 22500$ .

Answer: ₹22,500

Example 4: Gain on a sale · 3 marks · Short answerHarder board level

Rohit buys 300 shares of face value ₹20 at ₹25 each and sells them at ₹32 each. Find (a) his investment, (b) his gain, (c) his gain per cent.

Try it first, then show the solutionSolution

(a) $300 \times 25 = 7500$ .
(b) Proceeds $= 300 \times 32 = 9600$ ; gain $= 9600 - 7500 = 2100$ .
(c) $\frac{2100}{7500} \times 100 = 28%$ .

Answer: (a) ₹7,500 (b) ₹2,100 (c) 28%

Example 5: Splitting an investment · 4 marks · Short answerHOTS / competency

A woman invests ₹30,000, half in ₹100 shares at ₹125 paying 10% and half in ₹50 shares at ₹60 paying 12%. Find (a) the number of shares of each kind, (b) her total annual income.

Try it first, then show the solutionSolution

Each half is ₹15,000.
(a) First kind: $\frac{15000}{125} = 120$ shares; second kind: $\frac{15000}{60} = 250$ shares.
Income: $120 \times 100 \times \frac{10}{100} = 1200$ and $250 \times 50 \times \frac{12}{100} = 1500$ .
(b) Total $= 1200 + 1500 = 2700$ .

Answer: (a) 120 and 250 shares (b) ₹2,700

Example 6: Case study: selling part of a holding · 4 marks · Case-basedHOTS / competency

Mr Khan owns 800 shares of face value ₹10. He sells 300 of them at ₹18 each and uses the money to buy ₹100 shares of another company at ₹135 each.
(a) How much does he get from the sale?
(b) How many new shares does he buy?
(c) If the first company pays 15% and the second 10%, find his total annual income now.

Try it first, then show the solutionSolution

(a) $300 \times 18 = 5400$ .
(b) $\frac{5400}{135} = 40$ shares.
(c) He still holds $800 - 300 = 500$ old shares: $500 \times 10 \times \frac{15}{100} = 750$ .
New shares: $40 \times 100 \times \frac{10}{100} = 400$ ; total $= 750 + 400 = 1150$ .

Answer: (a) ₹5,400 (b) 40 shares (c) ₹1,150

Where students lose marks in Investment and Number of Shares

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

Mistake: Stopping at the price of one share
The question asks for the total sum invested.
Wrong working
15 shares of ₹75 at 20% discount: answer ₹60.
Right working
$15 \times 60 = ₹900$ .
Do this: Finish with 'Investment = n × MV'.
Usually costs: The MCQ in 2024 Q1(ix).
Mistake: Taking the premium on the market value
Premium and discount percentages are on the face value.
Wrong working
₹200 share at 25% premium: MV $= 200 \div 0.75 = 266.67$ .
Right working
MV $= 200 + 25%$ of $200 = 250$ .
Do this: Write 'p% of FV' explicitly.
Usually costs: Examiners named this for 2025 Q8(i).
Mistake: Dividing the investment by the face value
You pay the market value for each share.
Wrong working
₹18,000 ÷ ₹100 = 180 shares.
Right working
₹18,000 ÷ ₹90 = 200 shares.
Do this: Underline the market value before dividing.
Usually costs: Every later mark.
Mistake: Forgetting the shares still held
After a partial sale, the remaining shares still pay dividend.
Wrong working
Income only from the 40 new shares: ₹400.
Right working
₹750 from 500 old shares + ₹400 = ₹1,150.
Do this: List every holding after the sale.
Usually costs: The final mark of a case study.

Exam tips

Write 'MV = ₹…' as the first line of every shares answer.
In 2025 Q8(i), the examiners reported candidates who misunderstood 'at 25% premium'; the expected market value of a ₹200 share was ₹250.
In 'how much must be invested' questions, find the number of shares first and then multiply by the market value.
If a number of shares comes out fractional, recheck: brokerage and fractional shares are not in the syllabus.

Practice questions on Investment and Number of Shares

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

Q1 · 1 mark · MCQBoard level
The market value of a ₹100 share at a discount of 15% is:
(a) ₹115
(b) ₹85
(c) ₹15
(d) ₹100
Hint
Discount is subtracted from the face value.
Answer
(b) ₹85
Q2 · 3 marks · Short answerBoard level
Kiran invests ₹27,500 in ₹50 shares quoted at ₹55. Find the number of shares, the total face value, and the percentage premium.
Hint
Premium = ₹5 on a face value of ₹50.
Answer
$\frac{27500}{55} = 500$ shares; total face value ₹25,000; premium $\frac{5}{50} \times 100 = 10%$ .
Q3 · 3 marks · Short answerHarder board level
How much must be invested in ₹100 shares at ₹140 paying a 7% dividend to get an annual income of ₹2,100?
Hint
Dividend per share = ₹7.
Answer
Shares $= \frac{2100}{7} = 300$ ; investment $= 300 \times 140 = ₹42, 000$ .
Q4 · 1 mark · Assertion-reasonHarder board level
Assertion (A): ₹12,000 buys 150 shares of face value ₹100 at a 20% discount.
Reason (R): When a share is at a discount, its market value is less than its face value.
(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
MV = ₹80.
Answer
(c). MV $= 80$ , so $\frac{12000}{80} = 150$ ; the discount lowering the MV below FV is why ₹12,000 buys 150 rather than 120 shares.
Q5 · 3 marks · Short answerHarder board level
A man buys 120 shares at ₹75 each and later sells them at ₹68 each. Find his gain or loss.
Hint
Compare ₹68 with ₹75 per share.
Answer
Loss $= 120 \times (75 - 68) = ₹840$ .
Q6 · 4 marks · Short answerHarder board level
A man's investment in shares is 1.25 times the total face value of the shares he holds. (a) At what premium did he buy them? (b) If the dividend is 10%, what is his return on investment?
Hint
Investment ÷ number of shares = MV.
Answer
(a) MV $= 1.25 \times$ FV, a premium of 25%. (b) Return $= \frac{10}{125} \times 100 = 8%$ .
Q7 · 4 marks · Short answerHOTS / competency
A woman sells 200 shares of face value ₹100 at ₹96 each and invests the proceeds in ₹10 shares at ₹8 each. How many new shares does she get, and how does the total face value of her holding change?
Hint
Proceeds ₹19,200.
Answer
New shares $= \frac{19200}{8} = 2400$ . Total face value changes from $200 \times 100 = ₹20, 000$ to $2400 \times 10 = ₹24, 000$ , a rise of ₹4,000.

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.MV of a ₹20 share at 5% premium?Show answer
₹21.
2.₹4,800 invested in shares at ₹60. Number of shares?Show answer
80.
3.50 shares at ₹110. Investment?Show answer
$50 \times 110 = ₹5, 500$ .
4.What does 'below par' mean?Show answer
The market value is less than the face value (at a discount).
5.Shares bought at ₹45, sold at ₹54. Gain per share and gain per cent?Show answer
₹9 per share; $\frac{9}{45} \times 100 = 20%$ .

Investment and Number of Shares: frequently asked questions

How do I find the number of shares bought?

Divide the money invested by the market value of one share. Do not divide by the face value unless the shares are at par.

What is the difference between at par, at a premium and at a discount?

At par the market value equals the face value; at a premium it is higher; at a discount it is lower. The premium or discount is a percentage of the face value.

Does the face value affect how many shares I can buy?

No. Only the market value does. The face value decides the dividend you receive on each share.