Hello students, I am Rahul Sir from OdTutor, and today we are going to tackle one of the most consistently misunderstood topics in the entire quantitative aptitude syllabus — Stocks and Shares. I want to be completely honest with you right at the beginning: this is a chapter where the difficulty is not mathematical at all. The arithmetic involved is actually quite simple — mostly multiplication, division, and percentage calculations. The real challenge is conceptual. Students who have never dealt with the stock market in real life find the terminology confusing, the relationships between terms unclear, and the whole chapter somewhat abstract and disconnected from everyday experience.
Over the years of teaching at OdTutor, I have developed a very specific approach to this chapter. I don’t start with formulas. I start with a story. I help students understand what stocks actually are, why people buy them, what face value and market value mean in real human terms, and how income is generated. Once that real-world picture is clear, every formula becomes an obvious, logical consequence rather than an arbitrary rule to memorize.
In IBPS PO, IBPS Clerk, SBI PO, and SBI Clerk exams, Stocks and Shares questions are not the most frequently tested topic, but when they appear — particularly in IBPS PO Mains — they tend to carry good marks and are attempted by very few students confidently. That gap is your opportunity. A student who has prepared this chapter thoroughly can solve these questions in under a minute while most others skip them entirely, giving you a significant edge in a competitive cutoff environment.
In this article, I am going to walk you through every concept, formula, and question type that matters for competitive exams, with fully solved examples at every step. Read carefully, understand the logic, and practice alongside. By the end, Stocks and Shares will be a topic you actively look forward to seeing in your exam paper.
Let’s begin.
1. Understanding What Stocks and Shares Actually Are
Before any formula, any shortcut, or any question type, you need to understand the real-world concept behind stocks and shares. I always begin here in my live classes, and my students consistently say this 10-minute conceptual explanation alone eliminates 80% of their confusion about the chapter.
Imagine a large company — say, a railway company — wants to build a new rail network. The project costs hundreds of crores of rupees, far more than the company can fund on its own. So the company decides to borrow money from the general public. But instead of taking a bank loan, it divides the total project cost into thousands of small equal units and offers these units to the public for purchase. Each of these small units is called a share or a stock.
When you buy one of these units, you become a part-owner of the company to that extent. In return for your investment, the company promises to pay you a portion of its profits every year. This annual payment is called a dividend.
Now, let’s define the key terms:
Stock or Share: A single unit of ownership in a company, available for public purchase.
Face Value (FV) or Par Value or Nominal Value: The original fixed value printed on the stock certificate when the company first issued it. This is the standard reference value used to calculate dividends. In India, face value is most commonly ₹100 per share in exam problems.
Market Value (MV) or Market Price: The actual price at which the stock is currently being bought and sold in the stock market. This fluctuates daily based on demand and supply. The stock can trade above face value (at a premium), below face value (at a discount), or at exactly face value (at par).
Dividend: The annual income paid to the stockholder, always calculated as a fixed percentage of the face value, not the market value. This is one of the most important distinctions in the entire chapter.
Investment: The actual amount of money you spend to purchase the stock at its current market price.
These five terms are the absolute foundation. Understand them deeply before moving forward.
2. Three Core Concepts: At Par, At Premium, and At Discount
Once you understand face value and market value, the next concept to master is the relationship between them. This relationship determines whether a stock is trading “at par,” “at a premium,” or “at a discount,” and IBPS questions frequently test your ability to identify and work with these three situations.
At Par: When the market value equals the face value exactly. For example, a ₹100 stock trading at ₹100 is “at par.” This is the simplest scenario — you pay exactly what the stock is nominally worth.
At Premium: When the market value is higher than the face value. For example, a ₹100 stock trading at ₹120 is “at a premium of ₹20.” The stock is in demand and the market is willing to pay more than its nominal value. In problems, you will often see this written as “₹100 stock at 120” — meaning the face value is ₹100 but the current market price is ₹120.
At Discount: When the market value is lower than the face value. For example, a ₹100 stock trading at ₹85 is “at a discount of ₹15.” The market values this stock below its nominal worth, perhaps because the company is underperforming.
How to read stock notation in exam problems:
When a problem says “8% stock at 110,” it means:
- Face value = ₹100 (assumed standard)
- Annual dividend rate = 8% (calculated on face value)
- Annual dividend per share = 8% of ₹100 = ₹8
- Market price = ₹110 (what you pay to buy one share)
This notation appears in almost every Stocks and Shares question, and reading it correctly is the gateway to solving the problem accurately. I make my students practice reading this notation until it becomes as natural as reading a price tag.
3. The Key Formulas You Must Know
Now that the concepts are clear, let’s build the formula toolkit. I want you to understand each formula from first principles rather than memorizing it blindly, because that understanding is what lets you adapt when the question is worded unusually.
Formula 1 — Annual Income (Dividend):
Annual Income = (Dividend Rate / 100) × Face Value × Number of Shares
Or simply: Annual Income per share = Dividend% × Face Value / 100
Formula 2 — Investment:
Investment = Market Price × Number of Shares
This is the actual money you spend purchasing shares at the current market price.
Formula 3 — Return on Investment (Income/Investment ratio):
This is the most important formula for exam questions. When you invest in a stock, your return is:
Return% = (Annual Income / Investment) × 100
= (Dividend% × Face Value) / Market Price × 100
Formula 4 — Number of Shares:
Number of Shares = Total Investment / Market Price per Share
= Total Annual Income / Annual Income per Share
Formula 5 — To find what investment gives ₹X annual income:
Investment needed = (Market Price / Annual Income per Share) × X
These five formulas handle the vast majority of IBPS Stocks and Shares questions. Write them all on a single card and review them daily until you can derive any one of them from scratch in under 30 seconds.
4. Solved Examples: Basic Income and Investment Problems
Let’s immediately apply the formulas with exam-style questions. I will walk through every step so you can see exactly how the concept flows into the calculation.
Question 1: Find the annual income from ₹7,200 invested in 8% stock at 90.
Solution:
Face Value = ₹100, Dividend = 8%, Market Price = ₹90
Annual income per share = 8% of ₹100 = ₹8
Number of shares = Total Investment / Market Price = 7200 / 90 = 80 shares
Total annual income = 80 × ₹8 = ₹640
Question 2: How much should one invest in 10% stock at 120 to earn an annual income of ₹500?
Solution:
Face Value = ₹100, Dividend = 10%, Market Price = ₹120
Annual income per share = 10% of ₹100 = ₹10
Number of shares needed = 500 / 10 = 50 shares
Investment required = 50 × ₹120 = ₹6,000
Question 3: Find the annual income from ₹4,500 invested in 6% stock at 75.
Solution:
Annual income per share = 6% of ₹100 = ₹6
Number of shares = 4500 / 75 = 60 shares
Total annual income = 60 × ₹6 = ₹360
In each of these questions, notice the three-step pattern I teach my students: find the annual income per share from the dividend, find the number of shares from the investment, then multiply to get total income. This pattern works every single time for basic income questions, and drilling it until it becomes automatic is the most efficient use of your early practice time.
5. Finding the Rate of Return on Investment
This is the question type that IBPS examiners favor most heavily in Stocks and Shares, because it tests whether students truly understand the difference between the dividend rate (which is on face value) and the actual return on investment (which is on market price). Many students confuse these two and treat them as the same, which leads to consistently wrong answers.
The Core Concept:
The dividend rate is fixed and always applied to the face value. But your actual return depends on how much you actually paid — the market price. If you paid more than face value, your effective return is lower than the dividend rate. If you paid less, your effective return is higher.
Return% = (Annual Income per Share / Market Price per Share) × 100
Question 1: Find the rate of return on investment for 9% stock at 120.
Solution:
Annual income per share = 9% of ₹100 = ₹9
Market price = ₹120
Return% = (9 / 120) × 100 = 7.5%
Notice: the dividend rate is 9% but the actual return is only 7.5% because you paid ₹120 for a ₹100 face value stock.
Question 2: Which is a better investment — 8% stock at 110 or 9% stock at 120?
Solution:
Return on 8% stock at 110 = (8/110) × 100 = 7.27%
Return on 9% stock at 120 = (9/120) × 100 = 7.5%
The 9% stock at 120 gives a better return.
Question 3: Find the market price of a 10% stock if the rate of return on investment is 8%.
Solution:
Let market price = ₹x
Annual income per share = 10% of ₹100 = ₹10
Return% = (10/x) × 100 = 8
10/x = 8/100
x = (10 × 100)/8 = ₹125
This reverse-calculation question type — where return% is given and market price must be found — appears regularly in IBPS PO exams and catches many students off guard. Practice both directions of this formula: calculating return% from market price, and calculating market price from return%.
6. Comparing Two Stocks — A Frequently Tested Pattern
One of the most beloved question formats in IBPS Stocks and Shares is the comparison question, where a person sells one stock and buys another, and you must compare the income before and after, or find the change in annual income. This tests whether students can apply the formulas sequentially across two different stocks without getting confused.
Question 1: A person sells ₹4,500 worth of 8% stock at 90 and reinvests the proceeds in 10% stock at 108. Find the change in annual income.
Solution:
Old Stock (8% at 90):
Number of shares = 4500 / 90 = 50 shares
Annual income = 50 × 8 = ₹400
Proceeds from selling:
Selling price = 4500 (same as investment in this case, since we’re told “₹4,500 worth”)
New Stock (10% at 108):
Number of shares = 4500 / 108 = 41.67 shares
Annual income = 41.67 × 10 = ₹416.67
Wait — let me restructure for clarity the way I do in class:
Annual income per ₹108 invested in new stock = ₹10
Annual income from ₹4500 = (10/108) × 4500 = ₹416.67
Change in income = 416.67 − 400 = ₹16.67 increase
Question 2: By selling 8% stock at 96 and investing proceeds in 10% stock at 120, a person’s annual income increases by ₹250. Find the amount of stock sold.
Solution:
Per ₹96 invested in old stock: Income = 8% of ₹100 = ₹8
Per ₹96 invested in new stock: Income = (10/120) × 96 = ₹8
Hmm — equal income here. Let me restructure this properly.
Old income per share = ₹8 (sold at ₹96 each)
New income per ₹96 spent = (10 × 96)/120 = ₹8 per ₹96 spent
Let the amount realized = ₹x
Old annual income = (8/96) × x = x/12
New annual income = (10/120) × x = x/12
Increase = x/12 − x/12… Both give same return in this case. Let me use a fresh standard question:
Standard Question: A man sells 5% stock at 95 and buys 6% stock at 108. If his annual income increases by ₹120, find the amount of stock sold.
Solution:
Old income per ₹95 spent = ₹5
New income per ₹95 spent = (6/108) × 95 = ₹570/108 = ₹5.278
Increase per ₹95 = 5.278 − 5 = ₹0.278
Total increase = ₹120
Amount of old stock sold = (120 / 0.278) × 95 ≈ ₹40,995
For exam purposes, always set up the income comparison per unit of investment, find the difference, then scale to reach the given total difference. This systematic approach prevents the confusion that arises from jumping between different stock values without a clear structure.
7. Brokerage — The Hidden Cost in Stock Transactions
In many IBPS Stocks and Shares problems, especially in PO exams, the concept of brokerage is introduced. Brokerage is the commission charged by a broker for facilitating a stock transaction. Understanding how brokerage affects the effective buying and selling price is essential for solving these problems correctly.
Key Rules for Brokerage:
When buying a stock, brokerage is added to the market price (you pay more).
Effective Buying Price = Market Price + Brokerage
When selling a stock, brokerage is deducted from the market price (you receive less).
Effective Selling Price = Market Price − Brokerage
Question 1: A man buys 200 shares of a 10% stock at ₹105. If brokerage is 1%, find his total investment.
Solution:
Market price = ₹105
Brokerage = 1% of ₹105 = ₹1.05
Effective buying price = ₹105 + ₹1.05 = ₹106.05
Total investment = 200 × ₹106.05 = ₹21,210
Question 2: A person sells ₹5,000 of 8% stock at 95 with a brokerage of 0.5%. Find the net proceeds.
Solution:
Number of shares = 5000 / 100 = 50 shares (face value basis here)
Effective selling price per share = ₹95 − 0.5% of ₹95 = ₹95 − ₹0.475 = ₹94.525
Net proceeds = 50 × ₹94.525 = ₹4,726.25
I always tell my students: whenever the word “brokerage” appears in a Stocks and Shares question, your very first action should be to calculate the effective price — adjusted buying price if buying, adjusted selling price if selling. Plug this effective price into all subsequent formulas instead of the raw market price. This one habit eliminates brokerage-related errors entirely.
8. Government Bonds and Trust Problems
A specific variant of Stocks and Shares that appears in IBPS PO exams involves government bonds or trust investments, where the question talks about a trustee investing in a specific type of government security. These problems look different on the surface but follow exactly the same formulas. The only reason to discuss them separately is the slightly different language used.
Government bonds are essentially stocks issued by the government rather than private companies. They are considered the safest investment and usually have fixed, predictable returns. In exam problems, they are described identically to regular stocks: “3.5% government stock at 95” means a bond with face value ₹100, dividend of 3.5%, trading at ₹95.
Question: A trustee invests ₹15,000 in 5% government bonds at 75. Find the annual income and the rate of return.
Solution:
Annual income per share = 5% of ₹100 = ₹5
Number of bonds = 15000 / 75 = 200 bonds
Total annual income = 200 × ₹5 = ₹1,000
Rate of return = (5/75) × 100 = 6.67%
Another common variant:
Question: What price should one pay for a 4% bond to earn a return of 5%?
Solution:
Let market price = ₹x
Annual income per bond = 4% of ₹100 = ₹4
Required return = 5%
(4/x) × 100 = 5
x = (4 × 100)/5 = ₹80
So you should pay ₹80 for this bond to achieve a 5% return. Notice the bond is at a discount — you’re paying only ₹80 for a ₹100 face value bond, which is why your return (5%) is higher than the stated dividend rate (4%). This relationship — paying less gives higher return, paying more gives lower return — is a concept I drill into every student because it appears repeatedly in IBPS questions in various forms.
9. Common Mistakes Students Make in Stocks and Shares
Having guided thousands of students through this chapter at OdTutor, I have identified the recurring errors that consistently cost marks. Here are the most important ones, explained in enough detail that you can recognize and avoid them yourself.
Mistake 1 — Calculating dividend on market price instead of face value. This is by far the most common and most costly mistake in this entire chapter. The dividend is ALWAYS calculated on the face value, never on the market price. If you see “8% stock at 120,” the annual income per share is 8% of ₹100 = ₹8, not 8% of ₹120. Write this rule on a sticky note and paste it on your study table.
Mistake 2 — Confusing face value with the number of shares. When a question says “₹5,000 of 8% stock,” students sometimes treat ₹5,000 as the investment at market price, when it actually refers to the total face value, meaning 50 shares of face value ₹100 each. Read carefully whether the amount given is at face value or at market price.
Mistake 3 — Forgetting brokerage adjustment. When brokerage is mentioned, students often apply the formulas using the raw market price, forgetting to adjust for brokerage. Always adjust the effective price first before using any formula.
Mistake 4 — Treating return% and dividend% as the same. These are different when the market price differs from face value. Dividend% applies to face value. Return% applies to market price. Conflating them produces a wrong answer every single time.
Mistake 5 — Not converting “at a premium of X” to actual market price. If a stock is “at a premium of ₹15,” the market price is ₹100 + ₹15 = ₹115. Similarly “at a discount of ₹10” means market price = ₹90. Some students forget to add or subtract and use ₹15 or ₹10 directly as the market price.
Mistake 6 — Mishandling comparison problems by calculating income separately for each stock without a common reference. In comparison questions, always use the same amount of money (the proceeds from selling the first stock) as your reference investment for calculating income from the second stock.
Mistake 7 — Skipping this chapter entirely. The most expensive mistake of all. Stocks and Shares is a short, formula-friendly chapter with limited question variety. Skipping it means guaranteed mark loss on questions that a prepared student solves in 45 seconds.
10. Practice Strategy for Mastering Stocks and Shares Before the Exam
Let me close with the exact preparation plan I give my OdTutor students for this chapter. Follow it consistently and you will be fully prepared within 10 to 12 days.
Days 1–2 — Concept and Terminology: Spend these two days entirely on building real-world understanding of what stocks, dividends, face value, and market value mean. Read section 1 and section 2 of this article multiple times. Close your eyes and explain the concept in your own words as if teaching a friend. If you can do that clearly, your conceptual foundation is solid.
Day 3 — Formula Sheet and Notation Practice: Write all five core formulas from section 3 from memory. Then practice reading stock notation: given “7% stock at 115,” immediately identify face value, dividend rate, annual income per share, and market price. Do this for at least 20 different stock notations until the reading feels completely automatic.
Days 4–5 — Basic Income and Investment Questions: Solve at least 30 direct questions of the types shown in section 4 — finding annual income from a given investment, and finding investment required for a target income. Focus purely on accuracy, not speed. Cross-check every calculation.
Days 6–7 — Return on Investment Problems: Work through all question types from section 5, including the reverse calculation where market price must be found from a given return percentage. This is technically the most demanding formula application in the chapter, so give it extra attention.
Days 8–9 — Comparison and Brokerage Problems: Move to sections 6 and 7. For comparison questions, always draw a two-column structure — Old Stock on the left, New Stock on the right — and fill in face value, dividend, market price, and income per share for each before solving. This visual structure prevents confusion when switching between two different stocks mid-calculation.
Day 10 — Government Bonds and Mixed Questions: Study section 8 and then solve a mixed question set covering all types from the chapter in random order. This simulates exam conditions and forces you to identify the question type quickly rather than relying on section-specific context clues.
Days 11–12 onwards — Timed Practice and Mock Tests: Set a 60-second timer per question and solve timed sets. Include Stocks and Shares in your daily mock test routine so it stays sharp alongside your preparation for other chapters. Review your error log weekly, identifying whether mistakes are conceptual, formulaic, or due to misreading — and target each category specifically.
Stocks and Shares rewards patience in the learning phase and pays back generously in the exam hall. It is a chapter with a relatively small number of question types, a limited set of formulas, and a very high predictability of what will actually be tested. Students who invest 10 focused days in this chapter gain a reliable, fast-scoring advantage that relatively few competitors will have. Be that student.
How Teachers from OdTutor Can Help
At OdTutor, our trainers understand that topics like Stocks and Shares feel abstract to many students simply because of unfamiliar real-world context, and we address that at the very root. Rahul Sir and the OdTutor teaching team build genuine conceptual clarity first through relatable real-world explanations, then layer in formulas, shortcuts, and exam-specific question patterns tailored precisely to IBPS PO and Clerk exam standards. With live doubt-clearing sessions, topic-wise practice sheets, brokerage and comparison problem workshops, and full-length mock tests with detailed performance breakdowns, OdTutor ensures every student moves from confusion to complete confidence in this chapter — turning one of the most commonly skipped topics into a dependable, fast-scoring strength on exam day.