Races and Games Questions for IPMAT 2027: Practice Questions and Expert Tips

Races and Games Questions for IPMAT are an important part of the Quantitative Ability section. These questions are mainly based on speed, distance, time, speed ratios, winning margins, head starts, and games or tournaments. In recent IPMAT papers, this topic has appeared in different forms, with the number of questions varying each year.

In IPMAT Indore, the Quantitative Ability section has 45 questions, including 30 MCQs and 15 Short Answer Questions. While Races and Games does not have a fixed number of questions, understanding its common patterns can help you solve these questions faster and more accurately.

In this guide, you will find important concepts, formulas, solved examples, and practice questions to strengthen your preparation for Races and Games Questions for IPMAT 2027.

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What Are Races and Games in IPMAT Quant?

A race is a contest in which two or more people cover a fixed distance, either on a straight course or a circular track. A game is a contest of points, such as a game of 100 points in billiards. Both are tested as applications of speed ratios.

Races and Games vs Games and Tournaments: Don't Mix Them Up

Students often confuse these two topics because both use the word "games".

Topic	Section	What it tests	Core idea
Races and games (of points)	Quantitative Ability	Speed and scoring ratios	When A scores P, B scores P − x
Games and tournaments	Logical Reasoning / DI-LR	Match structures and outcomes	Knockout with n players needs n − 1 matches; a round robin needs n(n − 1) ÷ 2 matches

This article covers the first. If you are preparing for IPMAT Rohtak's reasoning section or JIPMAT's DILR, also review the IPMAT logical reasoning syllabus.

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Races and Games Questions and Solutions for IPMAT: 7 Solved Patterns

Pattern 1: Distance and Time Margin Together

Question: In a 1 km race, A beats B by 40 m or 8 seconds. How long does A take to finish?

Solution: B covers the last 40 m in 8 seconds, so B's speed = 40 ÷ 8 = 5 m/s. B's time for 1,000 m = 200 seconds. A finishes 8 seconds earlier, so A takes 192 seconds.

Mentor note: The phrase "x m or t seconds" always hands you the loser's speed. Start there.

Pattern 2: Chained Margins

Question: In a 100 m race, A beats B by 10 m and B beats C by 10 m. By how much does A beat C?

Solution: When A runs 100 m, B runs 90 m. When B runs 100 m, C runs 90 m, so when B runs 90 m, C runs 90 × 0.9 = 81 m. A beats C by 100 − 81 = 19 m.

Mentor note: The tempting answer is 20 m, and it often appears among the options.

Pattern 3: Head Start for a Dead Heat (Distance)

Question: A's speed is 5/3 times B's speed. What start should A give B in a 200 m race so that it ends in a dead heat?

Solution: In the time A runs 200 m, B runs 200 × 3/5 = 120 m. B must start 200 − 120 = 80 m ahead.

Pattern 4: Circular Track

Question: A and B start together from the same point on a 600 m circular track at 4 m/s and 6 m/s.

What is asked	Working	What it tests	Answer
First meeting, same direction	600 ÷ (6 − 4)	300 s
First meeting, opposite directions	600 ÷ (6 + 4)	60 s
First meeting at the starting point	LCM of lap times 150 s and 100 s	300 s
Distinct meeting points, same direction	Speed ratio 2 : 3, so 3 − 2	1 point
Distinct meeting points, opposite directions	3 + 2	5 points

Pattern 5: Games of Points

Question: In a game of 100 points, A can give B 20 points and C 28 points. How many points can B give C in a game of 90?

Solution: A : B = 100 : 80 and A : C = 100 : 72, so B : C = 80 : 72 = 10 : 9. When B scores 90, C scores 81. B can give C 9 points.

Mentor note: 28 − 20 = 8 is the trap answer. Points scale like metres, so subtraction does not work.

Pattern 6: Start Given, Still Wins

Question: In a 500 m race, A gives B a start of 50 m and still beats B by 25 m. Find the ratio of their speeds.

Solution: When A runs 500 m, B has run 500 − 50 − 25 = 425 m. A : B = 500 : 425 = 20 : 17.

Mentor note: Subtract both the start and the margin from L to get the loser's distance.

Pattern 7: Head Start in Time

Question: A runs 400 m in 80 seconds and B runs it in 100 seconds. How many seconds' start should A give B for a dead heat? What is that start in metres?

Solution: B needs 20 seconds more than A, so B must start 20 seconds earlier. B's speed is 400 ÷ 100 = 4 m/s, so a 20-second start equals 4 × 20 = 80 m.

Mentor note: A time start and a distance start describe the same advantage. Convert using the slower runner's speed.

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IPMAT Races and Games Practice Questions (10 MCQs with Hints and Answers)

Attempt each Races and Games question for IPMAT on a timer before opening the hint. Aim for about 60 seconds on Q1–Q4, 90 seconds on Q5–Q8 and 2 minutes on Q9–Q10. Questions run from easy to hard.

SA mode for IPMAT Indore aspirants: cover the options and type your answer first. In the SA section, you cannot back-solve from choices, so practise solving without them.

Q1. (Easy) In a 200 m race, A beats B by 25 m. What is the ratio of A's speed to B's speed?

(a) 7 : 8

(b) 9 : 8

(c) 8 : 7

(d) 25 : 8

Hint: When A runs 200 m, how far has B run?
Answer: (c) 8 : 7
Solution: B runs 175 m while A runs 200 m. Ratio = 200: 175 = 8: 7.

Q2. (Easy) In a 500 m race, A beats B by 50 m or 10 seconds. How long does A take to complete the race?

(a) 80 s

(b) 90 s

(c) 95 s

(d) 100 s

Hint: "50 m or 10 seconds" gives you B's speed directly.
Answer: (b) 90 s
Solution: B's speed = 50 ÷ 10 = 5 m/s. B's time = 500 ÷ 5 = 100 s. A's time = 100 − 10 = 90 s.

Q3. (Easy) A runs 1 km in 3 minutes 10 seconds, and B runs it in 3 minutes 20 seconds. By what distance does A beat B?

(a) 40 m

(b) 55 m

(c) 50 m

(d) 60 m

Hint: Find how far B is from the finish line during the 10 seconds by which A is faster.
Answer: (c) 50 m
Solution: B's speed = 1,000 ÷ 200 = 5 m/s. When A finishes, B still needs 10 seconds, which is 5 × 10 = 50 m.

Q4. (Easy) A and B start from the same point on a 400 m circular track and run in opposite directions at 5 m/s and 3 m/s. After how many seconds do they meet for the first time?

(a) 40 s

(b) 80 s

(c) 50 s

(d) 200 s

Hint: Opposite directions, so add the speeds.
Answer: (c) 50 s
Solution: Time = 400 ÷ (5 + 3) = 50 s. Option (d) 200 s is the same-direction answer.

Q5. (Medium) In a 1 km race, A beats B by 100 m and B beats C by 100 m. By how many metres does A beat C?

(a) 200 m

(b) 180 m

(c) 210 m

(d) 190 m

Hint: Do not add the margins. Find how far C has run when B has run 900 m.
Answer: (d) 190 m
Solution: B : C = 1,000: 900. When B runs 900 m, C runs 900 × 0.9 = 810 m. A beats C by 1,000 − 810 = 190 m.

Q6. (Medium) A runs 5/3 times as fast as B. If A gives B a start of 80 m, how long should the race course be so that both reach the finish line together?

(a) 200 m

(b) 160 m

(c) 240 m

(d) 300 m

Hint: Let the course be L. A runs L while B runs L − 80.
Answer: (a) 200 m
Solution: L ÷ (L − 80) = 5/3, so 3L = 5L − 400 and L = 200 m.

Q7. (Medium) In a game of 100 points, A can give B 20 points and C 32 points. How many points can B give C in a game of 100?

(a) 12

(b) 16

(c) 18

(d) 15

Hint: Write A : B and A : C, then combine to get B : C.
Answer: (d) 15
Solution: B : C = 80 : 68 = 20 : 17. When B scores 100, C scores 85. B gives C 15 points. Option (a) 12 is the subtraction trap.

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Q8. (Medium) In a 100 m race, A beats B by 10 m and C by 13 m. In a 180 m race, by how many metres will B beat C?

(a) 6 m

(b) 3 m

(c) 5 m

(d) 7 m

Hint: When A finishes, B and C have run 90 m and 87 m. That is their speed ratio.
Answer: (a) 6 m
Solution: B : C = 90 : 87 = 30 : 29. When B runs 180 m, C runs 174 m. B wins by 6 m.

Q9. (Hard) Two runners start together from the same point on a circular track and run in the same direction with speeds in the ratio 7 : 4. At how many distinct points on the track will they meet?

(a) 11

(b) 3

(c) 4

(d) 7

Hint: Same direction uses the difference of the ratio terms; opposite uses the sum.
Answer: (b) 3
Solution: The ratio 7 : 4 is in lowest terms, so distinct meeting points = 7 − 4 = 3. Option (a) 11 is the opposite-direction answer.

Q10. (Hard) A and B run a 3 km race on a 300 m circular track, starting together and running in the same direction at 7 m/s and 5 m/s. How many times does A overtake B before A finishes the race?

(a) 1

(b) 2

(c) 3

(d) 4

Hint: Each overtake means A has gained one full lap (300 m) on B.
Answer: (b) 2
Solution: A finishes in 3,000 ÷ 7 ≈ 428.6 s. A gains 2 m every second, so an overtake happens every 300 ÷ 2 = 150 s, at 150 s and 300 s. The next would be at 450 s, after A has finished. So A overtakes B twice.

Answer Key

Q	1	2	3	4	5	6	7	8	9	10
Answer	c	b	c	c	d	a	d	a	b	b

How to read your score: 9–10 correct means this topic is a scoring area, so move on to sectional mocks. 6–8 means re-read the terminology table and redo the questions you missed after two days. 5 or fewer means revise Time, Speed and Distance basics first, then return to this set.

Races and Games Questions for IPMAT 2027: Terminology

Here are the common terminologies for the Races and games questions for IPMAT that confuse students during the exam:

Phrase in the question	What it actually means	Relationship you write
A beats B by x m (race of L m)	When A finishes L m, B has run L − x m	A : B = L : (L − x)
A beats B by t seconds	B finishes t seconds after A	B's time − A's time = t
A beats B by x m or t seconds	B covers the last x m in t seconds	B's speed = x ÷ t
A gives B a start of x m	B starts x m ahead, so B runs L − x m	A runs L while B runs L − x
A gives B a start of t seconds	B starts running t seconds before A	B runs for t seconds longer than A. For a dead heat, A's running time = B's running time − t
Dead heat	Both finish together	Finishing moments are equal
A can give B x points in a game of P	When A scores P, B scores P − x	A : B = P : (P − x)

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Formula Sheet: Races and Games Questions for IPMAT 2027

Check out the list of formulas that can be helpful to solve the Races and Games questions for IPMAT 2027 exam:

S.No	Concept	Formula / Rule
1	Core Ratio	If A and B run the same time, distance ratio = speed ratio.Speed of A ÷ Speed of B = L ÷ (L − x)
2	Loser's Speed from Distance-Time Margin	If B loses by a distance x and the time margin is t: Speed of B = x ÷ t
3	Chain Rule	If A beats B by x and B beats C by y in a race of length L: Distance covered by C when A finishes = (L − x)(L − y) ÷ L. A's margin over C = L − [(L − x)(L − y) ÷ L]Note: A's margin over C is always less than x + y.
4	Dead Heat with a Head Start	A is faster and gives B a head start of s metres.For a dead heat:L ÷ (L − s) = Speed of A ÷ Speed of B
5	Circular Track — First Meeting	Track length = C, speeds are a > b, and both start together from the same point.Same direction:Time = C ÷ (a − b)Opposite directions:Time = C ÷ (a + b)
6	First Meeting at Starting Point	Time taken = LCM of individual lap times.Individual lap times:C ÷ a and C ÷ b. For fractions: LCM = LCM of numerators ÷ HCF of denominators
7	Distinct Meeting Points	If runners start together and their speed ratio in lowest terms is p : q:Same direction: p − q distinct meeting points. Opposite directions: p + q distinct meeting points
8	Games of Points	Treat points like metres.If A gives B b points and C c points in a game of P points:B: C = (P − b) : (P − c)

How to Solve Races and Games Questions for IPMAT: A 4-Step Method

1. Translate the phrase into "when the winner has covered L, the loser has covered ___".
2. Write the distance ratio. Same time means distance ratio = speed ratio.
3. Scale the ratio to the new race length or game total the question asks about.
4. Sanity-check the answer. The margin should be smaller than the race length, and chained margins should be less than their sum.

For a broader method of reading Quant questions under exam pressure, see how to approach IIM IPMAT questions.

Common Mistakes Students Make in Races and Games Questions 2027

Here are the common mistakes that must be avoided while solving the IPMAT questions on Races and games topic:

Mistake	Why it happens	Fix
Adding chained margins (10 m + 10 m = 20 m)	Treating margins as fixed distances instead of ratios	Always scale; the second margin applies to a shorter distance
Reading "start of 20 m" as "A runs 20 m more"	Confusing who gets the start	The person receiving the start runs less
Forgetting to subtract both start and margin	Handling only one adjustment	Loser's distance = L − start − margin
Subtracting points in games (32 − 20 = 12)	Games feel like simple scoring	Convert to ratios: (P − b) : (P − c)
Using the winner's speed for "x m or t s"	Not visualising the finish line	The last x m is run by the loser
Not reducing the speed ratio before counting meeting points	Using 6 : 4 instead of 3 : 2	Reduce to lowest terms first
Mixing minutes and seconds	Rushed unit conversion	Convert everything to metres and seconds at the start
Counting the start as a meeting or overtake	Over-counting on circular tracks	The starting moment is not a meeting

Mentor Tips for Races and Games Questions

Think in distances, not speeds. Most race questions never need actual speeds in m/s. A distance ratio is faster and leaves less room for error.

Draw a 5-second line diagram. Mark the start, the finish and where the loser stands. Most misreadings disappear once you can see it.

Learn the trap options. MCQ options often include the "added margins" answer and the "opposite direction" answer. If your answer matches the obvious trap, check once more.

Practise with Time and Work. Both topics rely on rate and ratio logic, so practising them together builds speed. Pair this set with our IPMAT time and work questions.

Strengthen the base. If ratios feel slow, work through how to improve your quantitative aptitude skills for IPMAT before attempting mixed sets.

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A 7-Day Plan to Master Races and Games Questions in IPMAT 2027

Droppers and Class 12 students who already know TSD can compress this into 3 days by combining Days 1–3. To fit this week into your overall schedule, use the IPMAT study plan.

Day	Focus	Target
1	Revise Time, Speed and Distance basics and relative speed	15 basic questions
2	Terminology table and linear races	Patterns 1, 3, 6 and 7; 15 questions
3	Chained races and games of points	Patterns 2 and 5; 15 questions
4	Circular tracks	Pattern 4; 15 questions
5	This article's 10 MCQs under time, then once more in SA mode	Score 8/10 or more
6	Mixed set from IPMAT PYPs	Note every error type
7	Sectional Quant mock	Review the races questions first

Conclusion

Races and games questions for IPMAT reward clear reading more than heavy calculation. Decode the phrase, write the distance ratio, scale it, and check against the common traps. Use relative speed and LCM for circular tracks, convert time starts into distance using the slower runner's speed, and treat points exactly like metres in games.