On this page
Shares and dividends is a short ICSE chapter with a reliable trap: two different prices for the same share, and questions that switch between them. Once you know which price goes where, every problem follows the same few lines. This post sets out the terms, the two formulas in the syllabus, three worked examples and the slips that cost marks.
What does the ICSE syllabus include?
The ICSE 2027 Mathematics syllabus lists Shares and Dividends under Commercial Mathematics in Class X, with:
terms: face (nominal) value, market value, dividend, rate of dividend, premium;
Income = number of shares × rate of dividend × FV;
Return = (Income / Investment) × 100.
It adds a note that brokerage and fractional shares are not included, so you can ignore broker charges, and the number of shares will always be a whole number.
Which value is which?
Face value (FV): the value printed on the share, such as ₹10 or ₹100. Dividend is calculated on this.
Market value (MV): the price you pay to buy the share today. Investment is calculated on this.
At a premium: MV is above FV. A ₹100 share selling at ₹125 is at a premium of ₹25.
At a discount: MV is below FV.
Rate of dividend: a percent of face value, paid by the company.
The ICSE 2027 specimen paper tests this directly. For 50 shares of ₹100 bought at ₹125 with a 6% dividend, it asks what the dividend is paid on; the marking scheme answer is ₹5,000, the total face value, not the ₹6,250 paid.
Worked example 1: income and return
Arjun buys 200 shares of face value ₹50 at ₹62.50 each. The company pays a 9% dividend.
Investment = 200 × 62.50 = ₹12,500.
Dividend per share = 9% of 50 = ₹4.50, so income = 200 × 4.50 = ₹900.
Return = 900 / 12,500 × 100 = 7.2%.
The return is lower than 9% because he paid a premium.
Worked example 2: which investment is better?
Option A: ₹100 shares at ₹125, paying 10%. Option B: ₹20 shares at ₹24, paying 9%.
A: income per share = ₹10 on ₹125 paid, return = 10 / 125 × 100 = 8%.
B: income per share = 9% of 20 = ₹1.80 on ₹24 paid, return = 1.80 / 24 × 100 = 7.5%.
A gives the better return, even though both are at a premium. Compare returns per rupee invested, not dividend rates.
Worked example 3: shares needed for a target income
How many ₹10 shares paying 12% must Meera buy at ₹16 to earn ₹1,800 a year? What is her investment and return?
Income per share = 12% of 10 = ₹1.20.
Number of shares = 1,800 / 1.20 = 1,500.
Investment = 1,500 × 16 = ₹24,000.
Return = 1,800 / 24,000 × 100 = 7.5%.
A useful shortcut to check step 4: return = rate of dividend × FV / MV = 12 × 10 / 16 = 7.5%.
How do sell-and-reinvest questions work?
Longer questions chain two steps: sell shares at one market price, then use the proceeds, sometimes with the dividend, to buy different shares. The specimen paper has one of these, where an investor sells, adds the first year's dividend, and buys new shares. Treat it as two separate problems: find the cash in hand, then start again with that cash as the new investment. Write the cash amount on its own line so you can carry it forward.
Common mistakes and how to avoid them
Dividend on market value. Always multiply the rate by face value.
Number of shares from face value. Shares bought = investment / market value.
Confusing rate of dividend with return. They are equal only when the share is bought at face value.
Forgetting the dividend when a question says proceeds "including the dividend" are reinvested.
Calling a premium a discount. Premium means paying more than face value.
A practice routine for shares and dividends
Make a two-column card: "uses FV" (dividend, income) and "uses MV" (investment, number of shares bought, sale proceeds). For a week, do three problems a day: one income-and-return, one comparison, one sell-and-reinvest. Then shuffle them with GST and recurring deposit questions; Rohrer and Taylor (2007) found mixed practice beat blocked practice on a test a week later. The syllabus also suggests using a newspaper to study shares and dividends, which is a good way to see real premiums. Our ICSE Class 10 maths paper guide covers the rest of the paper.
When a long question tangles, the Fermi Problem Library has worked problems with a step-by-step solver that explains the reasoning rather than printing an answer.
Next step: redo worked example 2 with option B at ₹18 instead of ₹24, and decide which option wins now.
