Hello students, I am Rahul Sir from OdTutor, and today I want to talk about a topic that most students either completely ignore during preparation or treat as a low-priority chapter — Races and Games. Let me tell you something important right at the beginning: this is a mistake that costs serious marks.
In IBPS PO, IBPS Clerk, SBI PO, and SBI Clerk exams, Races and Games questions appear regularly in both prelims and mains, and they are among the quickest questions to solve in the entire quantitative aptitude section once you understand the underlying logic. Unlike complex calculation-heavy chapters such as Time and Work or Probability, Races and Games problems are almost entirely based on clean, straightforward reasoning about relative speeds and headstarts. A student who has prepared this chapter well can solve most Races and Games questions in under 40 seconds, which is an enormous advantage in a time-pressured competitive exam.
The reason students struggle with this topic is almost never mathematical — it is almost always a language problem. The terminology used in Races and Games questions is specific and slightly unusual, and students who haven’t studied these terms carefully misread the question entirely, setting up the wrong equation and arriving at the wrong answer even though their calculation skill is perfectly fine.
At OdTutor, I solve this problem by spending dedicated time on vocabulary and concept-building before touching a single formula. In this article, I will take you through the complete chapter exactly as I teach it in my live batches — clear definitions, solid concepts, proven shortcuts, and fully solved exam-style examples at every step. Read carefully, practice alongside, and I am confident you will walk into your next exam ready to attempt every Races and Games question with complete confidence.
Let’s begin.
1. Understanding the Basic Terminology of Races
Before any formula or shortcut, you must be completely comfortable with the specific language used in Races and Games problems. I cannot stress this enough — every year, students who know the formulas still get these questions wrong because they misinterpret what “beats by 10 metres” or “gives a start of 20 seconds” actually means in mathematical terms.
Let me define every key term clearly.
Race: A contest of speed between two or more competitors over a fixed distance, called the length of the race or the course.
Start (or Head Start): When a stronger competitor gives the weaker competitor an advantage at the beginning of the race. This advantage can be of two types — distance start or time start.
Distance Start: “A gives B a start of 20 metres” means A starts the race from the starting line while B starts 20 metres ahead of A. So if the total race is 100 metres, A runs the full 100 metres while B runs only 80 metres.
Time Start: “A gives B a start of 10 seconds” means A starts 10 seconds after B has already begun running. So B gets a 10-second head start in terms of time.
Dead Heat: When two or more competitors finish the race at exactly the same time, it is called a dead heat.
A beats B by X metres: This means when A finishes the race (reaches the finish line), B is still X metres behind the finish line.
A beats B by T seconds: This means A finishes the race T seconds before B finishes.
A can give B X metres in a Y-metre race: Same as A beats B by X metres in a Y-metre race.
I always tell my students: read the terminology definitions five times, then close this article and write them from memory. Only then proceed to the formulas. Clarity in language is 60% of success in Races and Games.
2. The Core Concept: Speed Ratio and Distance Relationship
Every Races and Games problem, no matter how it is worded, ultimately comes down to one fundamental concept: the ratio of speeds of the two competitors. Once you find the speed ratio, everything else follows automatically.
Here is the foundational principle:
In the same time, two competitors cover distances proportional to their speeds.
So if A’s speed is twice that of B, then in the time A runs 100 metres, B runs only 50 metres.
More generally: Speed of A / Speed of B = Distance covered by A / Distance covered by B (in the same time)
Now let’s connect this to the race language:
If A beats B by X metres in a race of Y metres:
This means when A completes Y metres, B has completed only (Y − X) metres.
Therefore: Speed of A / Speed of B = Y / (Y − X)
This is the single most important formula in the entire Races and Games chapter.
Example: In a 100-metre race, A beats B by 20 metres. Find the ratio of their speeds.
Solution:
Speed of A / Speed of B = 100 / (100 − 20) = 100 / 80 = 5 : 4
That’s it. This ratio is the key to unlocking every subsequent question involving these two competitors. Once you know the speed ratio is 5:4, you can find how much A would beat B in any other race distance, or determine what head start B needs to make a dead heat — all from this single ratio.
I always tell my students: finding the speed ratio is Step 1 in every race problem. Train yourself to extract this ratio as your very first action upon reading any Races and Games question.
3. Solved Examples: Basic Race Problems
Let’s now apply the core concept with some typical exam-style questions.
Question 1: In a 500-metre race, A beats B by 50 metres. By how many metres would A beat B in a 1000-metre race?
Solution:
Speed ratio of A : B = 500 : (500 − 50) = 500 : 450 = 10 : 9
In a 1000-metre race, when A finishes 1000 metres, B covers:
Distance by B = (9/10) × 1000 = 900 metres
So A beats B by 1000 − 900 = 100 metres
Notice how the answer neatly doubles when the race distance doubles — this makes intuitive sense because the speed ratio remains the same.
Question 2: In a 200-metre race, A beats B by 20 metres and B beats C by 10 metres. By how many metres does A beat C in a 200-metre race?
Solution:
Speed ratio A : B = 200 : 180 = 10 : 9
Speed ratio B : C = 200 : 190 = 20 : 19
Now we need Speed ratio A : C.
A : C = (A/B) × (B/C) = (10/9) × (20/19) = 200 / 171
When A finishes 200 metres, C covers: (171/200) × 200 = 171 metres
A beats C by 200 − 171 = 29 metres
This “chain ratio” question type — where A beats B and B beats C, and you need A vs C — is extremely popular in IBPS exams. The trick is to find A:B and B:C separately, then multiply the fractions to get A:C directly.
4. Head Start Problems — Distance and Time Starts
Head start problems are where most students make errors due to misreading the language, which is exactly why I spent so much time on terminology in section 1. Let’s now convert that language knowledge into solved problems.
Question 1: In a 100-metre race, A runs at a speed of 10 m/s and B runs at 8 m/s. How many metres of head start should A give B so that the race ends in a dead heat?
Solution:
Time taken by A to finish 100 metres = 100/10 = 10 seconds
In 10 seconds, B covers = 8 × 10 = 80 metres
So when A finishes, B is at 80 metres — 20 metres short.
For a dead heat, B must start 20 metres ahead.
A should give B a head start of 20 metres.
Question 2: In a kilometre race, A beats B by 100 metres. A gives B a head start of 50 metres in the next race. Who wins and by how much?
Solution:
Speed ratio A : B = 1000 : 900 = 10 : 9
In the new race, A runs 1000 metres and B starts 50 metres ahead, so B runs only 950 metres.
When A finishes 1000 metres, B covers: (9/10) × 1000 = 900 metres
But B started 50 metres ahead, so B’s effective position = 900 + 50 = 950 metres.
B needs 1000 metres total to finish, but has covered only 950 metres.
So A still wins, beating B by 1000 − 950 = 50 metres.
This is a beautifully structured question that IBPS loves to ask. The key error students make is forgetting to add the head start to B’s covered distance at the end. Always track B’s position from the starting line of the course, not from B’s starting position.
5. Time-Based Race Problems
Some race problems don’t give distances at all — instead, they work entirely with time. These can feel confusing at first but are actually very straightforward once you apply the speed-time relationship correctly.
Question 1: A beats B by 10 seconds in a race. A completes the race in 40 seconds. Find the ratio of their speeds.
Solution:
A finishes in 40 seconds. B finishes in 40 + 10 = 50 seconds.
Since both run the same distance: Speed of A / Speed of B = Time of B / Time of A = 50 / 40 = 5 : 4
This is the critical insight I drill into my students: when distance is the same, speed is inversely proportional to time. Faster competitors take less time, so if B takes more time, B is slower, and the speed ratio is flipped relative to the time ratio.
Question 2: In a 200-metre race, A takes 25 seconds and B takes 30 seconds. By how many metres does A beat B?
Solution:
Speed of A = 200/25 = 8 m/s
Speed of B = 200/30 = 20/3 m/s
When A finishes in 25 seconds, B has run: (20/3) × 25 = 500/3 ≈ 166.67 metres
A beats B by 200 − 500/3 = 600/3 − 500/3 = 100/3 metres ≈ 33.33 metres
A quick mental check: The ratio A:B = 8 : 20/3 = 24 : 20 = 6:5. When A finishes 200 metres, B finishes 200 × 5/6 = 166.67 metres. This confirms our answer. I always encourage this double-check using the ratio method, as it’s faster and catches calculation errors before you commit to an answer.
6. Understanding Games — The Concept of Points
Up until now, we’ve been discussing Races, which are purely about distance and speed. Now let’s shift to Games, which is the second half of this chapter and involves a scoring-based competition rather than a distance-based one.
The most commonly tested game in IBPS exams is a game of billiards or points, typically structured as follows:
“A game of N points” means the first player to reach N points wins the game.
The key terminology in Games:
“A can give B X points in a game of N”: This means that in a game where A scores N points, B scores only (N − X) points. A is the stronger player, and despite giving B a head start of X points, A wins or the situation is as described.
“A can give B X points and C Y points in a game of N”: This sets up a scenario involving three players with two separate relationships.
The speed-ratio concept applies directly to Games:
Scoring rate of A / Scoring rate of B = N / (N − X)
This is the exact same formula as for races, just replacing “metres covered” with “points scored.” Once students realize this, their fear of Games questions completely disappears.
Example: In a game of 100 points, A can give B 20 points. Find the ratio of their scoring rates.
Solution:
Scoring rate A : B = 100 : (100 − 20) = 100 : 80 = 5 : 4
The interpretation: when A scores 100 points, B scores only 80 points. If you start B at 20 points, both will reach 100 at the same time.
7. Solved Examples: Three-Player Problems in Games and Races
Three-player problems are where IBPS really tests whether students have understood the chain-ratio concept deeply. These questions look intimidating but follow a beautifully simple pattern once you recognize it.
Question: A can give B 20 points and C 32 points in a game of 100. How many points can B give C in a game of 100?
Solution:
Scoring ratio A : B = 100 : 80 = 5 : 4
Scoring ratio A : C = 100 : 68 = 25 : 17
Now, B : C = (B/A) × (A/C) = (4/5) × (25/17) = 100/85 = 20 : 17
In a game of 100, when B scores 100 points:
C scores = (17/20) × 100 = 85 points
So B can give C = 100 − 85 = 15 points
Another three-player race question:
Question: In a 500-metre race, A beats B by 50 metres. In a 200-metre race, B beats C by 20 metres. By how many metres does A beat C in a 500-metre race?
Solution:
A : B = 500 : 450 = 10 : 9
B : C = 200 : 180 = 10 : 9
A : C = (10/9) × (10/9) = 100 : 81
When A finishes 500 metres, C covers (81/100) × 500 = 405 metres.
A beats C by 500 − 405 = 95 metres.
The pattern is identical whether the question uses race language or game language. Chain-multiply the individual ratios to get the overall ratio, then find the winning margin. Practice this pattern until it feels as natural as breathing.
8. Circular Races and Meeting Points
IBPS PO exams occasionally include a slightly advanced variant of race problems involving circular tracks, where two or more runners race around a loop rather than a straight line. Let me cover the essential concepts here.
Key Concept: When two runners run in the same direction on a circular track of length L, they meet at the starting point after a time based on their relative speed. When they run in opposite directions, they meet much more frequently.
Formula — Time to first meeting:
Same direction: Time = L / (Speed of A − Speed of B)
Opposite direction: Time = L / (Speed of A + Speed of B)
Question: Two runners A and B run around a circular track of 400 metres. A runs at 8 m/s and B runs at 6 m/s in the same direction. After how much time do they first meet?
Solution:
Relative speed (same direction) = 8 − 6 = 2 m/s
Time to meet = 400 / 2 = 200 seconds
Question: If A and B run in opposite directions on the same 400-metre track at 8 m/s and 6 m/s respectively, how often do they meet?
Solution:
Relative speed (opposite direction) = 8 + 6 = 14 m/s
Time between meetings = 400/14 = 200/7 ≈ 28.57 seconds
The intuitive explanation I give students: going in the same direction, A has to “lap” B — gain an entire 400-metre lead — before they meet again, which takes much longer. Going in opposite directions, they’re rushing toward each other, so they meet far more frequently. This mental picture prevents students from applying the wrong formula under exam pressure.
9. Common Mistakes Students Make in Races and Games
After teaching thousands of students at OdTutor, I have identified the mistakes that repeatedly drain marks in this chapter. Here they are, along with how to avoid each one.
Mistake 1 — Misreading the head start direction. Students often add the head start to A’s distance instead of subtracting it from B’s required running distance. Remember: if B gets a 20-metre head start in a 100-metre race, B runs 80 metres, not 120 metres.
Mistake 2 — Inverting the speed-time ratio. When time is given instead of distance, remember speed is inversely proportional to time. If A takes 40 seconds and B takes 50 seconds, the speed ratio is 50:40, not 40:50. I’ve seen even strong students get this backwards under exam pressure.
Mistake 3 — Forgetting to add the head start to B’s position in the final step. In head start race problems, after calculating how far B runs from their starting position, students often forget to add the initial head start to find B’s actual position on the course.
Mistake 4 — Treating Games differently from Races. Many students treat Games as a completely different topic and study it separately, missing the fact that the same speed-ratio formula applies directly. Recognizing this connection cuts preparation time in half.
Mistake 5 — Not converting to the same base in chain-ratio problems. When finding A:C through A:B and B:C, students sometimes forget to make the B values equal before combining. Always ensure the common player’s value matches across both ratios before multiplying.
Mistake 6 — Using wrong relative speeds in circular races. Always check whether the runners go in the same or opposite direction before choosing addition or subtraction for relative speed. This is a quick check that takes two seconds but prevents a guaranteed wrong answer.
Mistake 7 — Rushing through the question without noting what is asked. Races questions sometimes ask for the winning margin in metres, sometimes in seconds, and sometimes as a ratio. Students who solve correctly but answer the wrong thing lose full marks. Always underline what is being asked before calculating.
10. Practice Strategy for Mastering Races and Games Before the Exam
Let me close this article with the exact preparation roadmap I give my OdTutor students for mastering this chapter efficiently.
Days 1–2 — Terminology Mastery: Do not open any formula sheet or question set. Instead, spend these two days reading and rewriting all the terminology from section 1. Cover every term, write examples for each in your own words, and quiz yourself. Ask a friend or family member to read you a definition and see if you can give the correct mathematical interpretation without hesitation. This seems slow, but it is the single most impactful investment you can make for this chapter.
Days 3–4 — Core Formula and Basic Questions: Learn the speed-ratio formula from section 2 and solve at least 25 direct questions of the type “A beats B by X metres in a Y-metre race, find the speed ratio.” Focus entirely on accuracy at this stage. Do not time yourself yet.
Days 5–7 — Head Start and Time-Based Problems: Move to sections 4 and 5. These question types require a slightly more careful reading of the problem, so slow down and draw a simple diagram for each question if needed — mark the starting point, finish line, and each competitor’s starting position. Visual mapping eliminates misreading errors almost entirely.
Days 8–9 — Three-Player Chain Ratio Problems: Practice chain-ratio questions from section 7 until the pattern of “find A:B, find B:C, multiply to get A:C” becomes completely automatic. Aim to do these questions in under 60 seconds each.
Days 10–11 — Games and Circular Race Problems: Study sections 6 and 8. Since Games follow identical logic to Races, most students find this section quick to master after solid Race preparation. Circular races need a bit more attention, particularly on same vs. opposite direction distinction.
Day 12 onwards — Timed Mixed Practice: Set a strict 45-second timer per question and solve mixed sets that include all question types from this chapter. Log every wrong answer, identify the specific mistake type, and revisit the relevant section of this article.
Ongoing — Error Log and Mock Tests: Include at least 2–3 Races and Games questions in your daily mock test practice. Because this is a relatively short chapter, it’s easy to forget under the pressure of preparing larger chapters. Keeping it active in your daily practice ensures you don’t lose the fluency you’ve built.
Races and Games is one of those chapters where disciplined, structured preparation over 10–12 days can make you genuinely unbeatable on exam day. The concept ceiling is low, the formula count is small, and the question variety is limited — meaning there are no surprises if you’ve prepared every type. That kind of predictability is rare in competitive exam preparation, and you should take full advantage of it.
How Teachers from OdTutor Can Help
At OdTutor, our trainers go beyond textbook formulas to build real exam-day sharpness in every student. For topics like Races and Games, Rahul Sir and the OdTutor team provide structured live sessions that break down every question type with clear visual explanations, language-focused concept-building, and shortcut-driven problem-solving techniques tailored to IBPS PO and Clerk exam patterns. Through personalized doubt-clearing sessions, curated practice sheets, and full-length mock tests with detailed performance analysis, OdTutor ensures that students don’t just understand every concept once but can apply it reliably under timed exam pressure — turning this often-neglected chapter into a consistent and confident source of easy marks.