Rahul Chaudhary

Hello students, I am Rahul Sir from OdTutor, and today we are going to thoroughly understand a chapter that almost every competitive exam aspirant either partially prepares or completely avoids — True Discount. And I completely understand why. When students first encounter this topic, the terminology feels oddly similar to Simple Interest, the formulas look confusingly overlapping, and the questions seem to be asking something that isn’t entirely clear. The result is that most students make a half-hearted attempt at memorizing a formula or two, get confused when the question is even slightly differently worded, and end up skipping these questions entirely in the exam hall. Let me tell you something that I tell every single batch of students I teach at OdTutor: True Discount is not a difficult chapter. It is a misunderstood chapter. And there is a very big difference between those two things. A difficult chapter requires exceptional mathematical ability. A misunderstood chapter simply requires someone to explain it clearly, once, in the right way. Once you genuinely understand what True Discount means — not just the formula, but the actual real-world situation it describes — everything else falls into place almost effortlessly. The relationship between True Discount, Present Worth, and the Amount due is logical and intuitive. The formulas are few, the question types are limited, and the chapter is short enough to master completely within one focused week of preparation. In IBPS PO, IBPS Clerk, SBI PO, SBI Clerk, SSC, and Railway exams, True Discount questions are among the quickest to solve for a prepared student — typically under 45 seconds — which makes this chapter a tremendous scoring opportunity that you absolutely cannot afford to leave on the table. In this article, I am going to teach you True Discount exactly the way I teach it in my live classes at OdTutor — starting from the real-world concept, building up through every formula logically, and walking you through every major question type with fully solved examples. Read carefully, practice every example, and by the end of this article you will approach True Discount questions with complete clarity and genuine confidence. Let’s begin. 1. Understanding True Discount — The Real-World Concept First Before any formula, before any shortcut, I want you to understand the actual situation that True Discount describes. This is the one investment I always insist on in my classes, and it pays back enormously when students sit down to solve questions. Imagine your friend owes you ₹1,100 but this amount is due one year from now — not today. He will pay you ₹1,100 exactly one year later. Now you need money today, so you go to someone and say: “I have a document that says I will receive ₹1,100 one year from now. How much will you give me for it today?” The person calculates that if he gives you some amount today and charges interest at, say, 10% per annum, that amount should grow to ₹1,100 in one year. He works backward from ₹1,100 to find what amount, at 10%, becomes ₹1,100 after one year. That amount is called the Present Worth (PW). In this case: PW × (1 + 10/100) = 1100, so PW = 1100/1.1 = ₹1,000. So you receive ₹1,000 today, and the person waits one year to collect ₹1,100. The difference between what is due in the future (₹1,100) and what is paid today (₹1,000) is called the True Discount (TD). Here, TD = 1100 − 1000 = ₹100. The future amount due — ₹1,100 in this case — is called the Amount (A) or the Bill Value. So the three key quantities are: One line summary I give every student: True Discount is the interest on the Present Worth, not on the Amount. This single distinction — interest on PW, not on A — is what separates True Discount from the concept of Banker’s Discount, which we will revisit later. Internalize this now, and you will never confuse the two again. 2. The Core Formulas of True Discount Now that the concept is crystal clear, let’s derive and list every formula you need. I want you to see where each formula comes from, because that understanding lets you reconstruct any formula you forget rather than panicking during the exam. We know: TD = A − PW … (1) We also know that TD is the Simple Interest on PW for the given time at the given rate. So: TD = (PW × R × T) / 100 … (2) From (1): PW = A − TD Substituting in (2): TD = ((A − TD) × R × T) / 100 Solving for TD: 100 × TD = A × R × T − TD × R × T TD(100 + RT) = A × R × T TD = (A × R × T) / (100 + R × T) … (3) This is the master formula for True Discount. And from this, we can derive Present Worth: Since PW = A − TD: PW = A × 100 / (100 + R × T) … (4) And just as TD is the SI on PW, we have an extremely useful relationship: TD = SI on PW Also: SI on A > TD (always, because SI is calculated on A which is larger than PW) One more important relationship that IBPS exams love to test: TD = (SI × PW) / A Or equivalently: SI − TD = SI × TD / PW And: PW = TD² / (SI − TD) … when SI and TD are given Let me also state the relationship between SI and TD clearly: If SI is the simple interest on Amount A for the same rate and time: TD / SI = PW / A These relationships might look like a lot right now, but each one comes directly from the basic definitions. Once you practice enough questions using the master formula (Formula 3), the others will feel

Hello students, I am Rahul Sir from OdTutor, and today we are going to sit down together and genuinely understand one of the most interesting — and most feared — topics in the quantitative aptitude syllabus: Probability. I use the word “interesting” very deliberately, because unlike most other chapters where you apply a formula and move on, Probability actually makes you think. It connects mathematics to real life in a way that very few other topics do. And yet, it is one of the chapters that students most commonly leave blank in the exam hall, convinced that it is too complex or too unpredictable to master. Let me tell you what I have observed over years of teaching at OdTutor: students don’t struggle with Probability because the mathematics is hard. They struggle because they never developed a clear, structured way of thinking about it. They approach each question as if it’s completely new, rather than recognizing that almost every Probability question in IBPS PO and Clerk exams belongs to one of just five or six repeating patterns. Once you learn to identify those patterns and apply the right formula confidently, Probability transforms from one of your most avoided topics into one of your most reliable scoring areas. The truth is, IBPS examiners love Probability because it can be presented in so many engaging ways — cards, coins, dice, bags of colored balls, committees, and arrangements — but underneath all that variety, the same fundamental logic applies every single time. In this article, I am going to teach you that fundamental logic from the ground up, walk you through every major question type with fully solved examples, and give you the exact practice strategy my OdTutor students use to master this chapter in under two weeks. Read every section carefully, practice every example alongside, and I promise you — by the end of this article, you will look at a Probability question not with dread, but with the quiet confidence of someone who knows exactly what to do. Let’s begin. 1. What Is Probability? The Concept Explained Simply Before any formula touches your notebook, you must understand what probability actually means in plain, human language. I always spend the first part of my Probability class on this, because every formula and every question type makes complete intuitive sense once you understand the concept. Probability is simply a way of measuring how likely something is to happen, expressed as a number between 0 and 1. A probability of 0 means the event is impossible — it will never happen. A probability of 1 means the event is certain — it will always happen. Everything else falls somewhere in between. The closer to 1, the more likely the event. The closer to 0, the less likely. Now here are the three core definitions you must know: Experiment: Any action or process whose outcome cannot be predicted with certainty. For example, tossing a coin is an experiment because you don’t know in advance whether it will land heads or tails. Sample Space (S): The set of all possible outcomes of an experiment. When you toss a coin, the sample space is {Head, Tail} — these are the only two things that can happen. Event (E): Any specific outcome or group of outcomes we are interested in. If we toss a coin and want to know the probability of getting a Head, then “getting a Head” is the event. The Fundamental Formula: P(E) = Number of favorable outcomes / Total number of possible outcomes This single formula is the heartbeat of the entire chapter. Every Probability question you will ever encounter in IBPS exams is ultimately asking you to identify the number of favorable outcomes and divide it by the total number of possible outcomes. The challenge lies in counting these correctly — and that is exactly what the rest of this article will teach you. 2. Essential Probability Rules and Properties Now that the basic definition is clear, let’s build the complete rule set that you need for IBPS exams. I want you to understand each rule logically, not memorize it as an isolated statement. Rule 1 — Basic Range: 0 ≤ P(E) ≤ 1 always. A probability can never be negative and can never exceed 1. Rule 2 — Complementary Events: P(E) + P(E’) = 1, which means P(E’) = 1 − P(E) Here, E’ is the complement of E — meaning “E does not happen.” This rule is enormously useful in exams because it is often far easier to calculate the probability that something does NOT happen and subtract from 1. I will show you this shortcut repeatedly in the solved examples ahead. Rule 3 — Addition Rule (Mutually Exclusive Events): Two events are mutually exclusive if they cannot happen at the same time. For example, when rolling a die, getting a 3 and getting a 5 cannot both happen on the same roll. For mutually exclusive events: P(A or B) = P(A) + P(B) Rule 4 — Addition Rule (Non-Mutually Exclusive Events): When two events can happen simultaneously, we must avoid counting the overlap twice: P(A or B) = P(A) + P(B) − P(A and B) Rule 5 — Multiplication Rule (Independent Events): Two events are independent if the occurrence of one does not affect the other. For example, tossing two separate coins — the result of the first coin has no effect on the second. For independent events: P(A and B) = P(A) × P(B) Rule 6 — Multiplication Rule (Dependent Events): When the second event is affected by the first (such as drawing cards without replacement): P(A and B) = P(A) × P(B | A) where P(B | A) means “the probability of B given that A has already occurred.” These six rules form the complete toolkit for solving 95% of all IBPS Probability questions. Write them on a single card and review them every day until each one comes to mind instantly. 3. Probability With Coins —