Practice Quantitative Aptitude questions on Races and Games, covering race distances, speed comparisons, head starts, winning margins, relative speeds, and problems involving points, matches, and game outcomes. Takes about 20–25 minutes and is useful for placement tests, TCS NQT, SSC, banking and MBA entrance exams.
Question 1
If in a race of 80m, A covers the distance in 20 seconds and B in 25 seconds, then A beats B by:
Explanation
B's speed = 8025 m/s. In the 20 seconds A takes to finish, B covers 8025 × 20 = 64 m. A beats B by 80 – 64 = 16 m.
Question 2
If X can run 48m and Y 42m, then in a race of 1km, X beats Y by:
Explanation
When X covers 1000 m, Y covers 1000 × 4248 = 875 m. X beats Y by 1000 – 875 = 125 m.
Question 3
In a race of 800m, if the ratio of the speeds of two participants P and R is 3:4, and P has a start of 120m, then R beats P by:
Explanation
Since P has a 120m start, P only needs to cover 800 – 120 = 680 m. When R covers 800 m, P (at 34 R's speed) covers 800 × 34 = 600 m, which is 680 – 600 = 80 m short of finishing. R beats P by 80 m.
Question 4
If in a race of 120m X can beat Y by 20m and Z by 35m, then Y can beat Z by:
Explanation
When X runs 120 m, Y runs 100 m and Z runs 85 m (at the same instant). Scaling Y up to 120 m: Z = 120 × 85100 = 102 m. Y beats Z by 120 – 102 = 18 m.
Question 5
If in a game of 80, P can give 16 points to Q and R can give 20 points to P, then in a game of 150, how many points can R give to Q?
Explanation
Speed ratios: P:Q = 80:64 = 5:4, and R:P = 80:60 = 4:3. Combining, R:P:Q = 20:15:12, so R:Q = 5:3. When R = 150, Q = 150 × 35 = 90. Points given by R to Q = 150 – 90 = 60.
Question 6
A 100 m race is organised. X covers the distance in 36 seconds while Y covers it in 45 seconds. By how many metres does X beat Y?
Explanation
When X finishes (at 36 sec), Y has covered (10045)x36 = 80 m. X beats Y by 100-80=20 m.
Question 7
A can run 22.5 m while B runs 25 m. In a race of 1 km, by how many meters can B beat A?
Explanation
Speed ratio A:B = 22.5:25 = 9:10. When B covers 1000m, A covers (910)x1000=900m. B beats A by 100m.
Question 8
A and B run a 1560 m race ending in a dead heat. At first, the speeds of A and B are in the ratio of 7:5. B then quickens his pace and for the remainder of the race runs 40 percent faster than A. How many metres did A run before B quickened his pace?
Explanation
Let A run d metres before B speeds up. Up to then the speeds are 7 : 5, so B has run 5d7 m.
After that B runs 40% faster than A: 1.4 × 7 = 9.8 against A's 7.
Both finish together: d7 + 1560 − 5d/79.8 = 15607, so 9.8d + 10920 − 5d = 15288, 4.8d = 4368 and d = 910 m.
After that B runs 40% faster than A: 1.4 × 7 = 9.8 against A's 7.
Both finish together: d7 + 1560 − 5d/79.8 = 15607, so 9.8d + 10920 − 5d = 15288, 4.8d = 4368 and d = 910 m.
Question 9
A and B started running simultaneously from a point P in opposite directions along a circular track of radius 7 m. After every meeting, they exchange their speeds as well as directions. B started running with a speed thrice that of A. They meet at point Q for the first time, at point R for the second time, at point S for the third time, and so on. At how many different points on the track do they meet?
Explanation
Swapping both speed and direction at each meeting is equivalent (from an outside observer's view) to the two runners simply passing through each other unchanged. With speed ratio 1:3, the two velocity profiles going around the circle coincide at exactly 4 distinct points before repeating.
Question 10
In a race, A beats B by 15 metres and C by 29 metres. If B and C run over the course together, B wins by 15 metres. What is the length of the course?
Explanation
Let the length of the course be L metres. When A finishes, B has run L - 15 and C has run L - 29, so the speeds of B and C are in the ratio (L - 15) : (L - 29).
When B and C run the course together, B wins by 15 m, so when B runs L, C runs L - 15: L - 15L = L - 29L - 15.
(L - 15)² = L(L - 29), so L² - 30L + 225 = L² - 29L and L = 225 m.
When B and C run the course together, B wins by 15 m, so when B runs L, C runs L - 15: L - 15L = L - 29L - 15.
(L - 15)² = L(L - 29), so L² - 30L + 225 = L² - 29L and L = 225 m.
Question 11
Sam, Suresh and Sanket run a race of 1400 meters. Sam runs twice as fast as Suresh while Suresh runs thrice as fast as Sanket. If Sanket finishes the race by clocking 15 minutes, how far was Suresh from the finish line when Sam must have finished the race?
Explanation
Let Sanket's speed be v. Suresh runs at 3v and Sam at 6v. Sanket takes 15 minutes, so v = 140015 m per minute.
Sam takes 156 = 2.5 minutes. In that time Suresh covers 3 × 140015 × 2.5 = 700 m.
Suresh is 1400 - 700 = 700 m from the finish line.
Sam takes 156 = 2.5 minutes. In that time Suresh covers 3 × 140015 × 2.5 = 700 m.
Suresh is 1400 - 700 = 700 m from the finish line.
Question 12
In a 200 m race, A takes 40 seconds and B takes 50 seconds. By how many metres does A beat B?
Explanation
B's speed = 200 ÷ 50 = 4 m/s.
In the 40 seconds A takes, B covers 4 × 40 = 160 m.
A beats B by 200 − 160 = 40 m.
In the 40 seconds A takes, B covers 4 × 40 = 160 m.
A beats B by 200 − 160 = 40 m.
Shortcut Method
B: 200 m in 50 s → 4 m/s
in 40 s B covers 4 × 40 = 160 m
∴ A wins by 200 − 160 = 40 m ✓
in 40 s B covers 4 × 40 = 160 m
∴ A wins by 200 − 160 = 40 m ✓
Question 13
A and B run a 120 m race. A finishes in 30 s while B needs 36 s. A wins by:
Explanation
B's speed = 12036 = 103 m/s.
In the 30 seconds A takes, B covers 103 × 30 = 100 m.
A wins by 120 − 100 = 20 m.
In the 30 seconds A takes, B covers 103 × 30 = 100 m.
A wins by 120 − 100 = 20 m.
Shortcut Method
B covers 120 m in 36 s → in 30 s: 120 × 3036 = 100 m
∴ A wins by 120 − 100 = 20 m ✓
∴ A wins by 120 − 100 = 20 m ✓
Question 14
Two athletes run a 400 m race. P finishes in 40 seconds and Q in 50 seconds. What is the ratio of the speeds of P and Q?
Explanation
For the same distance, speed is inversely proportional to time.
Ratio of times P : Q = 40 : 50 = 4 : 5.
So the ratio of speeds P : Q = 5 : 4.
Ratio of times P : Q = 40 : 50 = 4 : 5.
So the ratio of speeds P : Q = 5 : 4.
Shortcut Method
same distance → speed ratio = inverse of time ratio
times 40 : 50 = 4 : 5
∴ speeds = 5 : 4 ✓
times 40 : 50 = 4 : 5
∴ speeds = 5 : 4 ✓
Question 15
In a 200 m race, A takes 14 seconds and B takes 16 seconds. Find the ratio of the speeds of A and B.
Explanation
For the same distance, speed is inversely proportional to time.
Ratio of times A : B = 14 : 16 = 7 : 8.
So the ratio of speeds A : B = 8 : 7.
Ratio of times A : B = 14 : 16 = 7 : 8.
So the ratio of speeds A : B = 8 : 7.
Shortcut Method
times 14 : 16 = 7 : 8
speeds = inverse
∴ 8 : 7 ✓
speeds = inverse
∴ 8 : 7 ✓
Question 16
Runner A runs at 8 m/s and runner B at 10 m/s over the same course. If A completes the course in 25 minutes, how long does B take?
Explanation
The distance is the same, so speed × time is the same for both.
8 × 25 = 10 × t
t = 200 ÷ 10 = 20 minutes.
8 × 25 = 10 × t
t = 200 ÷ 10 = 20 minutes.
Shortcut Method
same distance → speed × time constant
8 × 25 = 10 × t → t = 200 ÷ 10
∴ B takes 20 min ✓
8 × 25 = 10 × t → t = 200 ÷ 10
∴ B takes 20 min ✓
Question 17
In a long-distance event, A runs at 6 m/s while B runs at 4 m/s. If A completes the event in 30 minutes, B will take:
Explanation
The distance is the same, so speed × time is the same for both.
6 × 30 = 4 × t
t = 180 ÷ 4 = 45 minutes.
6 × 30 = 4 × t
t = 180 ÷ 4 = 45 minutes.
Shortcut Method
same distance → speed × time constant
6 × 30 = 4 × t → t = 180 ÷ 4
∴ B takes 45 min ✓
6 × 30 = 4 × t → t = 180 ÷ 4
∴ B takes 45 min ✓
Question 18
In a 400 m race A beats B by 40 m or by 5 seconds. A's time over the course is:
Explanation
B covers the last 40 m in 5 seconds, so B's speed = 40 ÷ 5 = 8 m/s.
B's time over 400 m = 400 ÷ 8 = 50 seconds.
A finishes 5 seconds before B, so A's time = 50 − 5 = 45 seconds.
B's time over 400 m = 400 ÷ 8 = 50 seconds.
A finishes 5 seconds before B, so A's time = 50 − 5 = 45 seconds.
Shortcut Method
B: 40 m in 5 s → 8 m/s
B's time = 400 ÷ 8 = 50 s
∴ A's time = 50 − 5 = 45 s ✓
B's time = 400 ÷ 8 = 50 s
∴ A's time = 50 − 5 = 45 s ✓
Question 19
In a 300 m race, A beats B by 36 m or 6 seconds. How long does A take to complete the race?
Explanation
B covers the last 36 m in 6 seconds, so B's speed = 36 ÷ 6 = 6 m/s.
B's time over 300 m = 300 ÷ 6 = 50 seconds.
A finishes 6 seconds before B, so A's time = 50 − 6 = 44 seconds.
B's time over 300 m = 300 ÷ 6 = 50 seconds.
A finishes 6 seconds before B, so A's time = 50 − 6 = 44 seconds.
Shortcut Method
B: 36 m in 6 s → 6 m/s
B's time = 300 ÷ 6 = 50 s
∴ A's time = 50 − 6 = 44 s ✓
B's time = 300 ÷ 6 = 50 s
∴ A's time = 50 − 6 = 44 s ✓
Question 20
In a 500 m race A beats B by 50 m or 10 seconds. B's time over the course is:
Explanation
B covers 50 m in 10 seconds, so B's speed = 50 ÷ 10 = 5 m/s.
B's time over 500 m = 500 ÷ 5 = 100 seconds.
B's time over 500 m = 500 ÷ 5 = 100 seconds.
Shortcut Method
B: 50 m in 10 s → 5 m/s
500 ÷ 5
∴ B's time = 100 s ✓
500 ÷ 5
∴ B's time = 100 s ✓
Question 21
In a 240 m race, A beats B by 32 m or by 8 seconds. How much time does B take to finish the race?
Explanation
B covers 32 m in 8 seconds, so B's speed = 32 ÷ 8 = 4 m/s.
B's time over 240 m = 240 ÷ 4 = 60 seconds.
B's time over 240 m = 240 ÷ 4 = 60 seconds.
Shortcut Method
B: 32 m in 8 s → 4 m/s
240 ÷ 4
∴ B's time = 60 s ✓
240 ÷ 4
∴ B's time = 60 s ✓
Question 22
In a 200 m race A beats B by 40 m. Also, at the finish line, A is 8 seconds ahead of B. Find the time A takes to complete the race.
Explanation
B covers the last 40 m in 8 seconds, so B's speed = 40 ÷ 8 = 5 m/s.
B's time over 200 m = 200 ÷ 5 = 40 seconds.
A is 8 seconds ahead, so A's time = 40 − 8 = 32 seconds.
B's time over 200 m = 200 ÷ 5 = 40 seconds.
A is 8 seconds ahead, so A's time = 40 − 8 = 32 seconds.
Shortcut Method
B: 40 m in 8 s → 5 m/s
B's time = 200 ÷ 5 = 40 s
∴ A's time = 40 − 8 = 32 s ✓
B's time = 200 ÷ 5 = 40 s
∴ A's time = 40 − 8 = 32 s ✓
Question 23
A 180 m race ends with A 36 m ahead of B and 9 seconds ahead of B. How long did A take to finish?
Explanation
B covers 36 m in 9 seconds, so B's speed = 36 ÷ 9 = 4 m/s.
B's time over 180 m = 180 ÷ 4 = 45 seconds.
A is 9 seconds ahead, so A's time = 45 − 9 = 36 seconds.
B's time over 180 m = 180 ÷ 4 = 45 seconds.
A is 9 seconds ahead, so A's time = 45 − 9 = 36 seconds.
Shortcut Method
B: 36 m in 9 s → 4 m/s
B's time = 180 ÷ 4 = 45 s
∴ A's time = 45 − 9 = 36 s ✓
B's time = 180 ÷ 4 = 45 s
∴ A's time = 45 − 9 = 36 s ✓
Question 24
In a 240 m race A beats B by 48 m, and A reaches the winning post 12 seconds before B. How many seconds does A take for the race?
Explanation
B covers 48 m in 12 seconds, so B's speed = 48 ÷ 12 = 4 m/s.
B's time over 240 m = 240 ÷ 4 = 60 seconds.
A's time = 60 − 12 = 48 seconds.
B's time over 240 m = 240 ÷ 4 = 60 seconds.
A's time = 60 − 12 = 48 seconds.
Shortcut Method
B: 48 m in 12 s → 4 m/s
B's time = 240 ÷ 4 = 60 s
∴ A's time = 60 − 12 = 48 s ✓
B's time = 240 ÷ 4 = 60 s
∴ A's time = 60 − 12 = 48 s ✓
Question 25
In a 210 m race, A finishes 35 m ahead of B and 7 seconds earlier. What is A's time for the race?
Explanation
B covers 35 m in 7 seconds, so B's speed = 35 ÷ 7 = 5 m/s.
B's time over 210 m = 210 ÷ 5 = 42 seconds.
A's time = 42 − 7 = 35 seconds.
B's time over 210 m = 210 ÷ 5 = 42 seconds.
A's time = 42 − 7 = 35 seconds.
Shortcut Method
B: 35 m in 7 s → 5 m/s
B's time = 210 ÷ 5 = 42 s
∴ A's time = 42 − 7 = 35 s ✓
B's time = 210 ÷ 5 = 42 s
∴ A's time = 42 − 7 = 35 s ✓
Question 26
In a 600 m race the speeds of P and Q are in the ratio 5 : 6. If P is given a start of 150 m, who wins and by what distance?
Explanation
P has a start of 150 m, so P runs 600 − 150 = 450 m while Q runs 600 m.
Speeds are in the ratio 5 : 6, so when P runs 450 m, Q runs 450 × 65 = 540 m.
Q has covered only 540 m of 600 m, so Q is 60 m short and P wins by 60 m.
Speeds are in the ratio 5 : 6, so when P runs 450 m, Q runs 450 × 65 = 540 m.
Q has covered only 540 m of 600 m, so Q is 60 m short and P wins by 60 m.
Shortcut Method
P runs 450 m, Q runs 450 × 65 = 540 m
Q still needs 600 − 540 = 60 m
∴ P wins by 60 m ✓
Q still needs 600 − 540 = 60 m
∴ P wins by 60 m ✓
Question 27
In a 400 m race the speeds of X and Y are in the ratio 7 : 8. X is given a start of 40 m. Who wins the race and by how many metres?
Explanation
X has a start of 40 m, so X runs 400 − 40 = 360 m while Y runs 400 m.
Speeds are in the ratio 7 : 8. When Y finishes 400 m, X has run 400 × 78 = 350 m.
X has covered 350 m of his 360 m, so X is 10 m short and Y wins by 10 m.
Speeds are in the ratio 7 : 8. When Y finishes 400 m, X has run 400 × 78 = 350 m.
X has covered 350 m of his 360 m, so X is 10 m short and Y wins by 10 m.
Shortcut Method
Y runs 400 m, X runs 400 × 78 = 350 m
X needs 360 m → short by 10 m
∴ Y wins by 10 m ✓
X needs 360 m → short by 10 m
∴ Y wins by 10 m ✓
Question 28
A runs 112 times as fast as B. A gives B a start of 60 m. How far from the starting point must the winning post be so that both reach it at the same time?
Explanation
A's speed : B's speed = 112 : 1 = 3 : 2.
In the same time, when A runs 3 m, B runs 2 m, so A gains 1 m on B for every 3 m A runs.
A must gain the 60 m start, so A runs 60 × 3 = 180 m.
The winning post is 180 m from A's starting point.
In the same time, when A runs 3 m, B runs 2 m, so A gains 1 m on B for every 3 m A runs.
A must gain the 60 m start, so A runs 60 × 3 = 180 m.
The winning post is 180 m from A's starting point.
Shortcut Method
speeds 3 : 2 → A gains 1 m per 3 m run
gain needed = 60 m
∴ Post = 60 × 3 = 180 m ✓
gain needed = 60 m
∴ Post = 60 × 3 = 180 m ✓
Question 29
A runs 212 times as fast as B and gives B a start of 90 m. For both to reach the winning post together, the post must be at what distance from A's starting point?
Explanation
A's speed : B's speed = 212 : 1 = 5 : 2.
When A runs 5 m, B runs 2 m, so A gains 3 m on B for every 5 m A runs.
A must gain the 90 m start, so A runs 90 ÷ 3 × 5 = 30 × 5 = 150 m.
When A runs 5 m, B runs 2 m, so A gains 3 m on B for every 5 m A runs.
A must gain the 90 m start, so A runs 90 ÷ 3 × 5 = 30 × 5 = 150 m.
Shortcut Method
speeds 5 : 2 → A gains 3 m per 5 m run
90 ÷ 3 = 30 units, 30 × 5
∴ Post = 150 m ✓
90 ÷ 3 = 30 units, 30 × 5
∴ Post = 150 m ✓
Question 30
In a 200 m race A beats B by 20 m and C by 38 m. In a race of 270 m, B beats C by:
Explanation
When A runs 200 m, B runs 180 m and C runs 162 m.
So B : C = 180 : 162 = 10 : 9.
In a 270 m race, when B runs 270 m, C runs 270 × 910 = 243 m.
B beats C by 270 − 243 = 27 m.
So B : C = 180 : 162 = 10 : 9.
In a 270 m race, when B runs 270 m, C runs 270 × 910 = 243 m.
B beats C by 270 − 243 = 27 m.
Shortcut Method
A runs 200: B 180, C 162 → B : C = 10 : 9
B runs 270 → C runs 270 × 910 = 243
∴ B wins by 27 m ✓
B runs 270 → C runs 270 × 910 = 243
∴ B wins by 27 m ✓
Question 31
In a 100 m race A beats B by 4 m and C by 9 m. In a race of 192 m, by how much does B beat C?
Explanation
When A runs 100 m, B runs 96 m and C runs 91 m.
So B : C = 96 : 91.
In a 192 m race, when B runs 192 m, C runs 192 × 9196 = 182 m.
B beats C by 192 − 182 = 10 m.
So B : C = 96 : 91.
In a 192 m race, when B runs 192 m, C runs 192 × 9196 = 182 m.
B beats C by 192 − 182 = 10 m.
Shortcut Method
A runs 100: B 96, C 91 → B : C = 96 : 91
B runs 192 → C runs 192 × 9196 = 182
∴ B wins by 10 m ✓
B runs 192 → C runs 192 × 9196 = 182
∴ B wins by 10 m ✓
Question 32
In a 200 m race, A can beat B by 40 m and B can beat C by 10 m. In the same race, A can beat C by:
Explanation
When A runs 200 m, B runs 160 m.
When B runs 200 m, C runs 190 m, so when B runs 160 m, C runs 160 × 190200 = 152 m.
So when A runs 200 m, C runs 152 m, and A beats C by 200 − 152 = 48 m.
When B runs 200 m, C runs 190 m, so when B runs 160 m, C runs 160 × 190200 = 152 m.
So when A runs 200 m, C runs 152 m, and A beats C by 200 − 152 = 48 m.
Shortcut Method
A 200 → B 160
B 160 → C 160 × 190200 = 152
∴ A beats C by 200 − 152 = 48 m ✓
B 160 → C 160 × 190200 = 152
∴ A beats C by 200 − 152 = 48 m ✓
Question 33
In a 100 m race A beats B by 25 m and B beats C by 20 m. By how much does A beat C in the same race?
Explanation
When A runs 100 m, B runs 75 m.
When B runs 100 m, C runs 80 m, so when B runs 75 m, C runs 75 × 80100 = 60 m.
So when A runs 100 m, C runs 60 m, and A beats C by 100 − 60 = 40 m.
When B runs 100 m, C runs 80 m, so when B runs 75 m, C runs 75 × 80100 = 60 m.
So when A runs 100 m, C runs 60 m, and A beats C by 100 − 60 = 40 m.
Shortcut Method
A 100 → B 75
B 75 → C 75 × 80100 = 60
∴ A beats C by 100 − 60 = 40 m ✓
B 75 → C 75 × 80100 = 60
∴ A beats C by 100 − 60 = 40 m ✓
Question 34
In a game of 100 points, A can give B 25 points and C 40 points. In a game of 100 points, how many points can B give C?
Explanation
When A scores 100, B scores 75 and C scores 60.
So B : C = 75 : 60 = 5 : 4.
When B scores 100, C scores 100 × 45 = 80.
B can give C 100 − 80 = 20 points.
So B : C = 75 : 60 = 5 : 4.
When B scores 100, C scores 100 × 45 = 80.
B can give C 100 − 80 = 20 points.
Shortcut Method
A 100: B 75, C 60 → B : C = 5 : 4
B 100 → C 80
∴ B gives C 20 points ✓
B 100 → C 80
∴ B gives C 20 points ✓
Question 35
In a game of 100 points, A can give B 40 points and C 55 points. How many points can B give C in a game of 100?
Explanation
When A scores 100, B scores 60 and C scores 45.
So B : C = 60 : 45 = 4 : 3.
When B scores 100, C scores 100 × 34 = 75.
B can give C 100 − 75 = 25 points.
So B : C = 60 : 45 = 4 : 3.
When B scores 100, C scores 100 × 34 = 75.
B can give C 100 − 75 = 25 points.
Shortcut Method
A 100: B 60, C 45 → B : C = 4 : 3
B 100 → C 75
∴ B gives C 25 points ✓
B 100 → C 75
∴ B gives C 25 points ✓
Question 36
In a game of 50 points, A can give B 10 points and C 15 points. In a game of 120 points, how many points can B give C?
Explanation
When A scores 50, B scores 40 and C scores 35.
So B : C = 40 : 35 = 8 : 7.
When B scores 120, C scores 120 × 78 = 105.
B can give C 120 − 105 = 15 points.
So B : C = 40 : 35 = 8 : 7.
When B scores 120, C scores 120 × 78 = 105.
B can give C 120 − 105 = 15 points.
Shortcut Method
A 50: B 40, C 35 → B : C = 8 : 7
B 120 → C 105
∴ B gives C 15 points ✓
B 120 → C 105
∴ B gives C 15 points ✓
Question 37
In a game of 45 points, A can give B 9 points and C 18 points. In a game of 36 points, how many points can B give C?
Explanation
When A scores 45, B scores 36 and C scores 27.
So B : C = 36 : 27 = 4 : 3.
When B scores 36, C scores 36 × 34 = 27.
B can give C 36 − 27 = 9 points.
So B : C = 36 : 27 = 4 : 3.
When B scores 36, C scores 36 × 34 = 27.
B can give C 36 − 27 = 9 points.
Shortcut Method
A 45: B 36, C 27 → B : C = 4 : 3
B 36 → C 27
∴ B gives C 9 points ✓
B 36 → C 27
∴ B gives C 9 points ✓
Question 38
In a 100 m race, A can give B a start of 10 m and C a start of 19 m. How much start can B give C in a 100 m race?
Explanation
When A runs 100 m, B runs 90 m and C runs 81 m.
So B : C = 90 : 81 = 10 : 9.
When B runs 100 m, C runs 100 × 910 = 90 m.
B can give C a start of 100 − 90 = 10 m.
So B : C = 90 : 81 = 10 : 9.
When B runs 100 m, C runs 100 × 910 = 90 m.
B can give C a start of 100 − 90 = 10 m.
Shortcut Method
A 100: B 90, C 81 → B : C = 10 : 9
B 100 → C 90
∴ Start = 10 m ✓
B 100 → C 90
∴ Start = 10 m ✓
Question 39
In a 100 m race A can give B a start of 25 m and C a start of 28 m. What start can B give C in a race of 100 m?
Explanation
When A runs 100 m, B runs 75 m and C runs 72 m.
So B : C = 75 : 72 = 25 : 24.
When B runs 100 m, C runs 100 × 2425 = 96 m.
B can give C a start of 100 − 96 = 4 m.
So B : C = 75 : 72 = 25 : 24.
When B runs 100 m, C runs 100 × 2425 = 96 m.
B can give C a start of 100 − 96 = 4 m.
Shortcut Method
A 100: B 75, C 72 → B : C = 25 : 24
B 100 → C 96
∴ Start = 4 m ✓
B 100 → C 96
∴ Start = 4 m ✓
