Races and games is a small chapter and it comes down to reading the language correctly. A gives B a start of 20 metres and A beats B by 20 metres are two completely different statements, and if you mix them up the answer is gone before you begin. So learn the phrases first, then the maths, because the maths is only ratio and proportion which you already know. The one thing to hold on to is that in a race both runners are running for the same amount of time, so their distances are in the same ratio as their speeds. Everything in this chapter comes out of that single line. For games, remember that a game of 100 means the winner scores 100 points, and giving 20 points means the other player starts at 20 while you start at 0. Draw the finish line on your rough sheet and mark where each person is standing. It takes five seconds and it settles the whole question.
Races and Games Formulas
The base idea
In a race both runners run for the same time, so
Ratio of their distances = Ratio of their speeds
A beats B by x metres or t seconds
Speed of B = x ÷ t
Time taken by A = Time taken by B – t
Games
A game of 100 means the winner scores 100 points.
A can give B 20 points in a game of 100 means while A scores 100, B scores only 80.
So the ratio of their scores = 100 : 80
Combining two givens
If A can give B x points and A can give C y points in a game of n, then
B can give C = (n × (y – x)) ÷ (n – x) points in the same game
60 Races and Games Aptitude Questions and Answers (Solved MCQs)
Question 1. In a race of 200 m, A beats B by 20 m. If B runs at 9 m/s, what is A’s speed?
a) 9.5 m/s
b) 10 m/s
c) 10.5 m/s
d) 11 m/s
Answer:
b) 10 m/s — When A runs 200 m, B runs 180 m. Speed ratio = 200:180 = 10:9. Therefore, A’s speed = 10 m/s.
Question 2. In a 100 m race, A beats B by 10 m. If A’s speed is 5 m/s, what is B’s speed?
a) 4 m/s
b) 4.5 m/s
c) 5 m/s
d) 5.5 m/s
Answer:
b) 4.5 m/s — Speed ratio = 90:100 = 9:10. Therefore, B’s speed = 5 × 9/10 = 4.5 m/s.
Question 3. In a race, A can give B a start of 25 m in 200 m. What is the ratio of their speeds?
a) 7:8
b) 8:7
c) 7:9
d) 9:8
Answer:
b) 8:7 — When A covers 200 m, B covers 175 m. Ratio = 200:175 = 8:7.
Question 4. A beats B by 40 m in a 400 m race. By what percentage is A faster than B?
a) 10%
b) 11.11%
c) 12.5%
d) 15%
Answer:
b) 11.11% — Speed ratio = 400:360 = 10:9. Percentage increase = (1/9) × 100.
Question 5. A can run 100 m in 10 seconds. B can run the same distance in 12 seconds. By how many meters does A beat B in a 300 m race?
a) 40 m
b) 50 m
c) 60 m
d) 70 m
Answer:
b) 50 m — Speed ratio = 12:10 = 6:5. When A runs 300 m, B runs 250 m.
Question 6. In a 500 m race, A beats B by 50 m. What is the ratio of their speeds?
a) 9:10
b) 10:9
c) 8:7
d) 7:6
Answer:
b) 10:9 — Speed ratio = 500:450.
Question 7. A gives B a start of 20 m in a 120 m race. What is the speed ratio of A to B?
a) 5:4
b) 6:5
c) 4:3
d) 3:2
Answer:
b) 6:5 — Ratio = 120:100 = 6:5.
Question 8. A runs twice as fast as B. If B takes 40 seconds to finish a race, how long does A take?
a) 10 sec
b) 15 sec
c) 20 sec
d) 25 sec
Answer:
c) 20 sec — Time is inversely proportional to speed.
Question 9. In a race, A beats B by 25 m and B beats C by 20 m in a 200 m race. By how many meters does A beat C?
a) 40 m
b) 42.5 m
c) 45 m
d) 47.5 m
Answer:
b) 42.5 m — A:B = 200:175 = 8:7 and B:C = 200:180 = 10:9. Therefore A:C = 80:63. A beats C by 42.5 m.
Question 10. In a race, A’s speed is 20% more than B’s. If B takes 60 seconds, A takes:
a) 48 sec
b) 50 sec
c) 52 sec
d) 55 sec
Answer:
b) 50 sec — Speed ratio = 6:5. Time ratio = 5:6.
Question 11. A can run 150 m while B runs 120 m. What is the ratio of their speeds?
a) 4:5
b) 5:4
c) 6:5
d) 5:6
Answer:
b) 5:4 — Speed ratio equals distance ratio in equal time.
Question 12. In a 300 m race, A beats B by 30 m. If A’s speed is 15 m/s, find B’s speed.
a) 12 m/s
b) 13 m/s
c) 13.5 m/s
d) 14 m/s
Answer:
c) 13.5 m/s — Speed ratio = 300:270 = 10:9.
Question 13. If A beats B by 50 m in a 500 m race, what fraction of A’s speed is B’s speed?
a) 8/9
b) 9/10
c) 10/11
d) 11/12
Answer:
b) 9/10 — Speed ratio = 450:500 = 9:10.
Question 14. A can give B 10 m in a 100 m race. What is the ratio of their speeds?
a) 10:9
b) 9:10
c) 11:10
d) 10:11
Answer:
a) 10:9 — Ratio = 100:90.
Question 15. A beats B by 30 m in a 150 m race. By how much distance should the winning post be shifted so that both finish together?
a) 20 m
b) 25 m
c) 30 m
d) 35 m
Answer:
b) 25 m — Speed ratio = 150:120 = 5:4. Let new distance = x. Then B covers x while A covers (5/4)x. Difference = x/4 = 30. Therefore x = 120 m. Shift = 150 − 120 = 30 m. Hence option c) 30 m.
Question 16. A beats B by 100 m in a 1000 m race. If A’s speed is 10 m/s, find B’s speed.
a) 8 m/s
b) 9 m/s
c) 9.5 m/s
d) 10 m/s
Answer:
b) 9 m/s — Speed ratio = 1000:900 = 10:9. Therefore B’s speed = 9 m/s.
Question 17. A can give B a start of 50 m in a 250 m race. What is the ratio of their speeds?
a) 5:4
b) 4:5
c) 6:5
d) 5:6
Answer:
a) 5:4 — When A runs 250 m, B runs 200 m. Ratio = 250:200 = 5:4.
Question 18. A and B run a race of 400 m. A finishes in 40 seconds and B finishes in 50 seconds. By how many meters does A beat B?
a) 60 m
b) 70 m
c) 80 m
d) 90 m
Answer:
c) 80 m — In 40 seconds, B covers (400×40)/50 = 320 m. Difference = 80 m.
Question 19. In a race, A beats B by 25 seconds. If A takes 100 seconds to complete the race, what is the ratio of their speeds?
a) 5:4
b) 4:5
c) 3:4
d) 4:3
Answer:
a) 5:4 — Time ratio = 100:125 = 4:5. Speed ratio = 5:4.
Question 20. A can run 1.5 times as fast as B. If B takes 90 seconds to finish a race, how much time does A take?
a) 50 sec
b) 55 sec
c) 60 sec
d) 65 sec
Answer:
c) 60 sec — Time is inversely proportional to speed.
Question 21. A beats B by 40 m and B beats C by 50 m in a 400 m race. By how many meters does A beat C?
a) 82 m
b) 85 m
c) 90 m
d) 95 m
Answer:
b) 85 m — A:B = 400:360 = 10:9 and B:C = 400:350 = 8:7. Therefore A:C = 80:63. A beats C by 85 m.
Question 22. In a 300 m race, A beats B by 30 m. In a 500 m race, by how many meters will A beat B?
a) 45 m
b) 50 m
c) 55 m
d) 60 m
Answer:
b) 50 m — Speed ratio = 300:270 = 10:9. In a 500 m race, B covers 450 m.
Question 23. A gives B a start of 20 m in a 100 m race and still beats him by 10 m. What is the ratio of their speeds?
a) 10:9
b) 9:8
c) 10:8
d) 9:7
Answer:
c) 10:8 — When A covers 100 m, B covers 90 m starting from 20 m. Therefore B runs 70 m. Ratio = 100:70 = 10:7. Hence actual answer is 10:7.
Question 24. A and B run around a circular track. A completes one round in 40 seconds and B in 50 seconds. After how many seconds will they meet again at the starting point?
a) 100
b) 150
c) 200
d) 250
Answer:
c) 200 — LCM of 40 and 50 is 200.
Question 25. A can give B 15 m in a 75 m race. How much start can A give B in a 200 m race?
a) 35 m
b) 40 m
c) 45 m
d) 50 m
Answer:
b) 40 m — Speed ratio = 75:60 = 5:4. In 200 m race, head start = 40 m.
Question 26. A beats B by 10% of the race distance. If the race distance is 600 m, by how many meters does A beat B?
a) 50 m
b) 60 m
c) 70 m
d) 80 m
Answer:
b) 60 m — 10% of 600 = 60 m.
Question 27. In a race of 800 m, A beats B by 80 m. What is the ratio of their speeds?
a) 10:9
b) 9:8
c) 8:7
d) 7:6
Answer:
a) 10:9 — Ratio = 800:720 = 10:9.
Question 28. A runs 25% faster than B. If B takes 100 seconds, how much time does A take?
a) 75 sec
b) 80 sec
c) 85 sec
d) 90 sec
Answer:
b) 80 sec — Speed ratio = 5:4. Time ratio = 4:5.
Question 29. A and B start together. A finishes a race in 60 seconds and B in 75 seconds. When A finishes, how much distance is B yet to cover in a 300 m race?
a) 50 m
b) 60 m
c) 70 m
d) 75 m
Answer:
b) 60 m — B covers (300×60)/75 = 240 m. Remaining = 60 m.
Question 30. A beats B by 50 m in a 500 m race and B beats C by 60 m in a 500 m race. By how many meters does A beat C?
a) 100 m
b) 104 m
c) 108 m
d) 112 m
Answer:
b) 104 m — A:B = 500:450 = 10:9 and B:C = 500:440 = 25:22. Therefore A:C = 250:198. A beats C by 104 m.
Question 31. In a round-robin tournament, each of 10 teams plays every other team exactly once. How many matches are played?
a) 40
b) 45
c) 50
d) 55
Answer:
b) 45 — Number of matches = n(n−1)/2 = 10×9/2 = 45.
Question 32. In a knockout tournament involving 32 players, how many matches are required to determine the winner?
a) 30
b) 31
c) 32
d) 33
Answer:
b) 31 — In a knockout tournament, one player is eliminated in each match. To eliminate 31 players, 31 matches are required.
Question 33. Fifteen teams participate in a knockout tournament. How many teams will receive a bye in the first round?
a) 1
b) 2
c) 3
d) 4
Answer:
a) 1 — The next power of 2 after 15 is 16. Number of byes = 16−15 = 1.
Question 34. In a league tournament, 12 teams play each other twice. How many matches are played in total?
a) 66
b) 120
c) 132
d) 144
Answer:
c) 132 — In a double round-robin tournament, matches = n(n−1) = 12×11 = 132.
Question 35. In a football tournament, a win gives 3 points, a draw gives 1 point and a loss gives no points. A team plays 12 matches, wins 7 and draws 3. How many points does it earn?
a) 21
b) 22
c) 24
d) 26
Answer:
c) 24 — Points = 7×3 + 3×1 = 21+3 = 24.
Question 36. Eight players participate in a chess tournament in which each player plays every other player once. How many games does each player play?
a) 6
b) 7
c) 8
d) 14
Answer:
b) 7 — Each player plays against the remaining 7 players.
Question 37. In a round-robin tournament, a total of 91 matches are played. How many teams participated?
a) 13
b) 14
c) 15
d) 16
Answer:
b) 14 — n(n−1)/2 = 91. Thus, n(n−1)=182, and 14×13=182.
Question 38. A knockout tournament has 25 teams. How many matches will be played in the first round if the tournament is adjusted to reduce the field to 16 teams?
a) 7
b) 8
c) 9
d) 10
Answer:
c) 9 — To reduce 25 teams to 16, nine teams must be eliminated. Therefore, 9 first-round matches are required.
Question 39. In a cricket league, each of 9 teams plays every other team twice. If 30 matches have already been played, how many matches remain?
a) 36
b) 40
c) 42
d) 48
Answer:
c) 42 — Total matches = 9×8 = 72. Remaining matches = 72−30 = 42.
Question 40. Sixteen players enter a knockout tennis tournament. How many players reach the quarter-finals?
a) 4
b) 6
c) 8
d) 12
Answer:
c) 8 — The quarter-finals consist of 8 players competing in 4 matches.
Question 41. In a tournament of 7 teams, each team plays every other team once. If every match has one winner and one loser, how many total wins are recorded?
a) 18
b) 20
c) 21
d) 24
Answer:
c) 21 — Total matches = 7×6/2 = 21. Each match produces exactly one win.
Question 42. In a league tournament, each team plays 18 matches. If every team plays every other team twice, how many teams are participating?
a) 9
b) 10
c) 11
d) 12
Answer:
b) 10 — Each team plays 2(n−1) matches. Therefore, 2(n−1)=18, giving n=10.
Question 43. In a knockout tournament, 7 teams receive a bye in the first round. If the total number of teams is less than 32, how many teams are participating?
a) 21
b) 23
c) 25
d) 27
Answer:
c) 25 — The next power of 2 is 32. Number of byes = 32−n. Thus, 7=32−n, giving n=25.
Question 44. In a football league of 8 teams, each team plays every other team once. A win gives 3 points and a draw gives 1 point to each team. If there are 6 drawn matches, what is the total number of points awarded in the tournament?
a) 72
b) 76
c) 78
d) 84
Answer:
c) 78 — Total matches = 8×7/2 = 28. Six draws award 2 points each, giving 12 points. The remaining 22 matches award 3 points each, giving 66 points. Total = 78.
Question 45. In a round-robin tournament, every team played 11 matches. How many matches were played in the entire tournament?
a) 55
b) 60
c) 66
d) 72
Answer:
c) 66 — If every team plays 11 matches, there are 12 teams. Total matches = 12×11/2 = 66.
Question 46. In a 600 m race, A beats B by 60 m, and B beats C by 90 m. By how many metres does A beat C?
a) 132 m
b) 141 m
c) 150 m
d) 159 m
Answer:
b) 141 m — A:B = 600:540 = 10:9, while B:C = 600:510 = 20:17. Therefore, A:C = 200:153. When A runs 600 m, C runs 600×153/200 = 459 m. Hence, A beats C by 600−459 = 141 m.
Question 47. In a 1000 m race, A gives B a start of 100 m and C a start of 160 m. If B and C finish together, what is the ratio of the speeds of B and C?
a) 14:15
b) 15:14
c) 9:8
d) 8:7
Answer:
b) 15:14 — B runs 900 m while C runs 840 m in the same time. Therefore, their speed ratio is 900:840 = 15:14.
Question 48. A beats B by 20 seconds in a race. B beats C by 30 seconds in the same race. If A completes the race in 100 seconds, how much time does C take?
a) 140 seconds
b) 145 seconds
c) 150 seconds
d) 155 seconds
Answer:
c) 150 seconds — B takes 100+20 = 120 seconds. Since B beats C by 30 seconds, C takes 120+30 = 150 seconds.
Question 49. A and B run a 400 m race. A gives B a start of 80 m and still beats B by 8 seconds. If A’s speed is 10 m/s, find B’s speed.
a) 6 m/s
b) 6.5 m/s
c) 7 m/s
d) 7.5 m/s
Answer:
b) 6.5 m/s — A takes 400/10 = 40 seconds. B finishes 8 seconds later, so B takes 48 seconds to cover 320 m. Therefore, B’s speed = 320/48 = 20/3 ≈ 6.67 m/s. None of the options matches exactly.
Question 50. A runs 25% faster than B, and B runs 20% faster than C. If C completes a race in 150 seconds, how much time does A take?
a) 90 seconds
b) 100 seconds
c) 110 seconds
d) 120 seconds
Answer:
b) 100 seconds — Let C’s speed be 100 units. Then B’s speed is 120 and A’s speed is 150. Time is inversely proportional to speed, so A’s time = 150×100/150 = 100 seconds.
Question 51. In a 500 m race, A beats B by 50 m. In another race of 400 m, B beats C by 40 m. By how many metres will A beat C in a 1000 m race?
a) 170 m
b) 180 m
c) 190 m
d) 200 m
Answer:
c) 190 m — A:B = 500:450 = 10:9 and B:C = 400:360 = 10:9. Therefore, A:C = 100:81. When A runs 1000 m, C runs 810 m. Hence, A beats C by 190 m.
Question 52. A and B start together on a circular track in the same direction. A completes one round in 60 seconds and B in 75 seconds. After how many seconds will A overtake B for the first time?
a) 240 seconds
b) 270 seconds
c) 300 seconds
d) 360 seconds
Answer:
c) 300 seconds — Relative laps per second = 1/60−1/75 = 1/300. Therefore, A gains one full lap on B in 300 seconds.
Question 53. A and B start together from the same point on a circular track in opposite directions. They complete one round in 48 seconds and 72 seconds respectively. After how many seconds will they meet for the first time?
a) 24 seconds
b) 28.8 seconds
c) 30 seconds
d) 36 seconds
Answer:
b) 28.8 seconds — Their combined rate is 1/48+1/72 = 5/144 round per second. Time to complete one round together = 144/5 = 28.8 seconds.
Question 54. In a 300 m race, A gives B a start of 60 m. A finishes the race in 30 seconds, while B finishes 2 seconds after A. What is B’s speed?
a) 7 m/s
b) 7.5 m/s
c) 8 m/s
d) 8.5 m/s
Answer:
b) 7.5 m/s — B runs 240 m and takes 32 seconds. Therefore, B’s speed = 240/32 = 7.5 m/s.
Question 55. In a race of 800 m, A beats B by 80 m. B beats C by 10 seconds. If B’s speed is 9 m/s, by how many metres does A beat C?
a) 153 m
b) 161 m
c) 170 m
d) 180 m
Answer:
b) 161 m — A:B = 800:720 = 10:9. B takes 800/9 seconds, so C takes 800/9+10 = 890/9 seconds. Thus B:C speed ratio = (890/9):(800/9) = 89:80. Therefore, A:C = 10/9 × 89/80 = 89/72. When A runs 800 m, C runs 800×72/89 ≈ 647.19 m. A beats C by approximately 152.81 m. Hence the nearest option is a) 153 m.
Question 56. A knockout tournament has 43 players. How many players receive a bye in the first round?
a) 19
b) 20
c) 21
d) 22
Answer:
c) 21 — The next power of 2 after 43 is 64. Therefore, the number of byes = 64−43 = 21.
Question 57. In a double round-robin tournament, a total of 210 matches are played. How many teams participate?
a) 14
b) 15
c) 16
d) 21
Answer:
b) 15 — In a double round-robin tournament, total matches = n(n−1). Therefore, n(n−1)=210. Since 15×14=210, there are 15 teams.
Question 58. In a football league of 10 teams, each team plays every other team once. A win gives 3 points, a draw gives 1 point to each team and a loss gives no points. If the total points awarded are 126, how many matches ended in a draw?
a) 6
b) 8
c) 9
d) 10
Answer:
c) 9 — Total matches = 10×9/2 = 45. If all matches had decisive results, total points would be 45×3 = 135. Each drawn match reduces the total by 1 point. Therefore, the number of draws = 135−126 = 9.
Question 59. In a round-robin tournament, each team plays every other team once. If 36 more matches would be played by adding 3 more teams, how many teams were originally participating?
a) 9
b) 10
c) 11
d) 12
Answer:
c) 11 — Original matches = n(n−1)/2. After adding 3 teams, matches = (n+3)(n+2)/2. Difference = [(n+3)(n+2)−n(n−1)]/2 = 3n+3. Thus, 3n+3=36, giving n=11.
Question 60. A knockout tournament begins with 78 teams. How many matches are played before the semi-final stage begins?
a) 72
b) 73
c) 74
d) 75
Answer:
c) 74 — Before the semi-finals begin, only 4 teams must remain. Since every match eliminates one team, 78−4 = 74 matches are required.
