Races and games are part of Section B2 of CUET Maths, the Applied Mathematics section you answer if you choose Applied Mathematics instead of Section B1. Every question compares two players by distance, time or speed, so one habit, reading the margin correctly, settles most of them. Learn each rule here, from beating a rival by a distance or a time to giving a start, dead heats, games of points and runners on a circular track, with worked examples, time-saving shortcuts and the traps CUET sets, then practise on free questions in CUET's own formats, each fully solved.
At a school sports day, Meera wins the 500 m race and Tara is 25 m behind her at the line. That one sentence tells us how their speeds compare, and from it how a longer race, or a race with a head start, would end.
It means that while A runs the whole race of metres, B runs only metres in the same time. Equal times make the speeds proportional to the distances, so A's speed : B's speed .
Example 1 · Meera and Tara
In a 500 m race Meera beats Tara by 25 m. What is the ratio of their speeds?
While Meera runs 500 m, Tara runs m.
Speeds: .
Meera : Tara .
"A beats B by seconds" means B reaches the line seconds after A. When a margin is given both ways, "by 25 m or 5 seconds", the loser covers that distance in that time, which gives the loser's speed at once.
Watch out
Two margins do not simply add. If A beats B by 15 m and B beats C by 20 m in 200 m races, then while A runs 200 m, B runs 185 m and C runs m, so A beats C by 33.5 m, not 35.
A dead heat is a race in which both runners reach the line together. The faster runner A gives the slower runner B a start of exactly the distance B would lose by over the full race: while A runs , B runs , and the rest is the start.
Example 2 · A start for a dead heat
Tara's speed is of Meera's. How much start should Meera give her in a 1,000 m race for a dead heat?
While Meera runs 1,000 m, Tara runs m.
So Tara should start 200 m ahead.
A start of 200 m.
It means that when A scores 50 points, B scores in the same time, so their scoring rates are . Games of points are races in which the distance is counted in points.
With three players, chain the ratios: if A : B and B : C are known, A : C is their product, and the points one can give another follow from it.
Running the same way, they meet each time the faster has gained one full lap, so the time between meetings is lap ÷ (difference of speeds). Running opposite ways, they meet each time they have covered one lap between them: lap ÷ (sum of speeds).
Example 3 · A 300 m track
Two runners start together on a 300 m track at 6 m/s and 4 m/s. When do they first meet, running the same way, and running opposite ways?
Same way: seconds.
Opposite ways: seconds.
150 seconds and 30 seconds.
To find when both are back at the starting point together, take the LCM of their lap times.
Races
Games and tracks
Next in Section B2: comparing quantities with numerical inequalities.
73 questions, grouped by type, easy to hard. Pick an answer and check it. The worked solution opens when you ask for it.
In a 100 m race, A beats B by 20 m. What is the ratio of A's speed to B's?
AnswerB · 5 : 4
While A runs 100 m, B runs m in the same time.
In equal times, speeds are in the ratio of distances: .
Worth noting
4 : 5 is B's speed to A's, the ratio turned round.
A runs 1.5 times as fast as B. By how many metres does A beat B in a 300 m race?
AnswerA · 100 m
While A runs 300 m, B runs m.
A wins by m.
Worth noting
150 m takes half of 300, as if A were twice as fast.
A runs times as fast as B. By how many metres does A beat B in a 600 m race?
AnswerB · 100 m
When A runs 600 m, B runs m.
A wins by m.
Worth noting
120 m takes of the race; the margin is the of A's 600 m that B has not covered.
In a 1,000 m race A beats B by 100 m, and in another 1,000 m race B beats C by 50 m. The runners keep the same speeds in every race.
By how many metres would B beat C in a 400 m race?
AnswerB · 20 m
C runs 950 m for every 1,000 m that B runs, a margin of 5%.
5% of 400 m is 20 m.
Worth noting
50 m keeps the 1,000 m margin; it scales with the length of the race.
In a 200 m race, A finishes in 25 seconds and beats B by 40 m.
What is A's speed in this 200 m race?
AnswerD · 8 m/s
200 m in 25 seconds.
m/s.
Worth noting
6.4 m/s is B's speed.
In a 1,000 m race A beats B by 100 m, and in another 1,000 m race B beats C by 50 m. The runners keep the same speeds in every race.
What is the ratio of A's speed to B's in these races?
AnswerD · 10 : 9
While A runs 1,000 m, B runs 900 m.
.
Worth noting
is B's speed to A's.
In a 400 m race, A beats B by 50 m. What is the ratio of A's speed to B's?
AnswerB · 8 : 7
While A runs 400 m, B runs m.
Speeds are in the ratio of distances in the same time: .
Worth noting
7 : 8 is B's speed to A's.
In a 1,000 m race, A beats B by 100 m. What is the ratio of A's speed to B's?
AnswerD · 10 : 9
While A runs 1,000 m, B runs m.
Speeds are in the ratio of distances in the same time: .
Worth noting
9 : 10 is B's speed to A's.
A runs 1 km in 3 minutes 10 seconds and B runs it in 3 minutes 20 seconds. By how many metres does A beat B?
AnswerC · 50 m
A finishes 10 seconds before B. B's speed is m/s.
In those last 10 seconds B still had m to run.
Worth noting
m uses A's speed for those 10 seconds; it is B who is still running.
In a 200 m race, A beats B by 25 m or by 5 seconds. How long does A take to run the race?
AnswerA · 35 seconds
B covers the 25 m in 5 seconds, so B runs at 5 m/s and takes seconds for the race.
A finishes 5 seconds earlier: 35 seconds.
Worth noting
40 seconds is B's time, not A's.
In a 100 m race, A beats B by 10 m, and in another 100 m race B beats C by 10 m. By how many metres would A beat C in a 100 m race?
AnswerB · 19 m
When A runs 100 m, B runs 90 m. When B runs 90 m, C runs m.
So A beats C by m.
Worth noting
20 m adds the two margins, but B's 10 m lead over C was over a full 100 m, and B only runs 90 m here.
In a 100 m race, A beats B by 10 m, and A runs the race in 9 seconds. By how many seconds does A beat B?
AnswerB · 1 second
In 9 seconds B runs 90 m, so B's speed is 10 m/s and B takes 10 seconds for 100 m.
A beats B by second.
Worth noting
0.9 seconds uses A's speed for B's last 10 m.
In a 300 m race A beats B by 30 m. Running at the same speeds, by how many metres does A beat B in a 1 km race?
AnswerD · 100 m
B runs of A's distance in the same time.
When A runs 1,000 m, B runs 900 m: A wins by 100 m.
Worth noting
30 m keeps the old margin; it grows with the length of the race.
Read the two statements and choose the correct option.
I. If A beats B by m in a m race, A's speed : B's speed .
II. If A beats B by m or by seconds, B's speed is m/s.
AnswerC · Both I and II
I: in the same time A runs and B runs . True.
II: B covers the last m in the seconds after A finishes. True.
A runs times as fast as B. By how many metres does A beat B in a 800 m race?
AnswerA · 160 m
When A runs 800 m, B runs m.
A wins by m.
Worth noting
200 m takes of the race; the margin is the of A's 800 m that B has not covered.
A runs 1 km in 4 minutes and B runs it in 4 minutes 10 seconds. By how many metres does A beat B?
AnswerC · 40 m
A finishes 10 seconds ahead. B's speed is m/s.
In those 10 seconds B still had m to go.
Worth noting
m uses A's speed for the last 10 seconds; it is B who is still running.
In a 400 m race, A beats B by 40 m or by 8 seconds. How long does A take to run the race?
AnswerA · 72 seconds
B runs the last 40 m in 8 seconds, so B's speed is 5 m/s and B takes seconds.
A finishes 8 seconds earlier: 72 seconds.
Worth noting
80 seconds is B's time.
In a 100 m race A beats B by 20 m, and in a 100 m race B beats C by 25 m. By how many metres does A beat C in a 100 m race?
AnswerC · 40 m
When A runs 100 m, B runs m.
C runs of what B runs: m, so A wins by m.
Worth noting
45 m adds the margins, but B's margin over C shrinks because B runs less than the full race.
In a 200 m race A beats B by 20 m, and in a 200 m race B beats C by 20 m. By how many metres does A beat C in a 200 m race?
AnswerB · 38 m
When A runs 200 m, B runs m.
C runs of what B runs: m, so A wins by m.
Worth noting
40 m adds the margins, but B's margin over C shrinks because B runs less than the full race.
In a 200 m race, A finishes in 25 seconds and beats B by 40 m.
What is B's speed in this 200 m race?
AnswerC · 6.4 m/s
When A finishes, B has run m in the same 25 seconds.
m/s.
Worth noting
8 m/s is A's speed.
In a 200 m race, A finishes in 25 seconds and beats B by 40 m.
How long does B take to run the 200 m?
AnswerD · 31.25 seconds
B runs at 6.4 m/s.
seconds.
Worth noting
30 seconds adds 5 seconds for the 40 m at A's speed; B covers it more slowly.
In a 200 m race, A finishes in 25 seconds and beats B by 40 m.
By how many seconds does A beat B?
AnswerB · 6.25 seconds
B takes 31.25 seconds and A 25 seconds.
A wins by 6.25 seconds.
Worth noting
5 seconds is the time A needs for 40 m; B, slower, needs 6.25 seconds for it.
In a 1,000 m race A beats B by 100 m, and in another 1,000 m race B beats C by 50 m. The runners keep the same speeds in every race.
By how many metres does A beat C in a 1,000 m race between them?
AnswerC · 145 m
When A runs 1,000 m, B runs 900 m; C runs of B's distance: m.
A wins by m.
Worth noting
150 m adds the two margins, but B runs only 900 m in A's race, so B's lead over C shrinks to 45 m.
In a 250 m race, A beats B by 10 m. What is the ratio of A's speed to B's?
AnswerA · 25 : 24
While A runs 250 m, B runs m.
Speeds are in the ratio of distances in the same time: .
Worth noting
24 : 25 is B's speed to A's.
In a 1 km race A beats B by 50 m, and in another 1 km race B beats C by 40 m. By how many metres does A beat C in a 1 km race?
AnswerA · 88 m
When A runs 1,000 m, B runs 950 m, and C runs m.
A beats C by m.
Worth noting
90 m adds the two margins.
In a 1,000 m race A beats B by 100 m, and in another 1,000 m race B beats C by 50 m. The runners keep the same speeds in every race.
A gives C a 100 m start in a 1,000 m race. By how many metres does A still win?
AnswerA · 45 m
C has 900 m to run. In the time A runs 1,000 m, C runs 855 m.
C is still m short when A finishes.
Worth noting
50 m takes the start from the added margins, ; the true margin is 145 m.
A runs 100 m in 15 seconds. He gives B a start of 10 seconds, and they finish together. How long does B take to run 100 m?
AnswerD · 25 seconds
B sets off 10 seconds before A and they reach the line together.
So B runs for seconds.
Worth noting
5 seconds subtracts the start; B is the slower runner and takes longer.
A runs at 8 m/s and B at 6 m/s. How many seconds of start should A give B in a 240 m race for a dead heat?
AnswerC · 10 seconds
A takes seconds and B takes seconds.
B must start 10 seconds earlier.
Worth noting
40 seconds is B's whole time, not the difference.
A runs times as fast as B. How much of a start should A give B in a 400 m race so that the race ends in a dead heat?
AnswerC · 100 m
A dead heat means both finish together. While A runs 400 m, B runs m.
So B should start m ahead.
Worth noting
300 m is how far B runs, not the start.
In a 100 m race, A can give B a start of 20 m and C a start of 30 m. How much of a start can B give C in a 100 m race?
AnswerD · 12.5 m
While A runs 100 m, B runs 80 m and C runs 70 m, so B : C = 80 : 70.
While B runs 100 m, C runs m, so B can give C a start of 12.5 m.
Worth noting
10 m subtracts the starts, but they were measured against A's 100 m, not B's.
Read the two statements and choose the correct option.
I. In a dead heat, both runners reach the finishing line at the same moment.
II. If A beats B by m in a m race, then a start of m to B over m gives a dead heat.
AnswerC · Both I and II
I is the meaning of a dead heat.
II: while A runs m, B runs m; with an m start, that is exactly what B needs. True.
A runs 240 m in 30 seconds. He gives B a start of 40 m in a 240 m race, and they finish together. How long does B take to run 240 m?
AnswerD · 36 seconds
B runs 200 m in A's 30 seconds, so B's speed is m/s.
240 m takes B seconds.
Worth noting
30 seconds is the time B took for 200 m, with the start.
A runs 400 m in 80 seconds and B runs it in 100 seconds. How much of a start, in metres, should A give B for a dead heat in a 400 m race?
AnswerD · 80 m
B's speed is m/s. In A's 80 seconds, B runs m.
So B needs a start of m.
Worth noting
20 is the start in seconds, not metres.
In a 100 m race, A can give B a start of 10 m and C a start of 28 m. How much of a start can B give C in a 100 m race?
AnswerD · 20 m
While A runs 100 m, B runs 90 m and C runs 72 m.
So when B runs 100 m, C runs m: B can give C 20 m.
Worth noting
18 m subtracts the starts, , forgetting that B runs only 90 m in A's race.
Assertion (A): If A gives B a start of 30 m in a 300 m race and they dead-heat, then in a 300 m race with no start A beats B by 30 m.
Reason (R): In the time A runs 300 m, B runs 270 m.
AnswerA · Both A and R are true, and R is the correct explanation of A.
R: the dead heat means B covered 270 m while A covered 300 m. True.
So with no start, when A finishes B is 30 m short: A is true, and R is exactly why.
A and B run at speeds in the ratio 3 : 2. How much of a start should A give B in a 600 m race for a dead heat?
AnswerB · 200 m
When A runs 600 m, B runs m.
B must start m ahead.
Worth noting
400 m is how far B runs, not the start.
In a 500 m race, the speeds of A and B are in the ratio 3 : 4. A is given a start of 140 m. Who wins, and by how much?
AnswerD · A, by 20 m
A has m to run. In that time B runs m.
B is still 20 m short when A finishes, so A wins by 20 m.
Worth noting
B is faster, but not by enough to make up 140 m over the distance A still has to run.
In a 1 km race, A beats B by 40 m and C by 64 m. By how many metres does B beat C in a 1 km race?
AnswerB · 25 m
While A runs 1,000 m, B runs 960 m and C runs 936 m.
While B runs 1,000 m, C runs m, so B wins by 25 m.
Worth noting
24 m is , measured over A's kilometre, not B's.
In a 1 km race the speeds of A and B are in the ratio 5 : 4, and A gives B a start of 150 m. By how many metres does A win?
AnswerA · 50 m
When A runs 1,000 m, B runs m.
B had 850 m to run, so A finishes with B still 50 m short.
Worth noting
200 m is A's margin with no start; the 150 m start takes most of it back.
'A can give B 15 points in a game of 60' means that when A scores 60 points, B scores how many?
AnswerC · 45 points
Giving 15 points means B needs only points to keep level.
So when A reaches 60, B has 45.
Worth noting
75 adds the points given instead of taking them away.
In a game of 80, A can give B 16 points. What is the ratio of A's scoring rate to B's?
AnswerB · 5 : 4
When A scores 80, B scores .
.
Worth noting
compares 80 with the 16 points given, not with B's score.
Read the two statements and choose the correct option.
I. 'A can give B 20 points in a game of 100' means A's and B's scoring rates are in the ratio 5 : 4.
II. Then A can give B 20 points in a game of 200 as well.
AnswerA · Only I
I: A scores 100 while B scores 80, and . True.
II: in a game of 200, B scores 160, so A gives 40 points, not 20. False.
In a game of 100 points, A can give B 20 points and C 25 points.
What is the ratio of A's scoring rate to B's in this game?
AnswerD · 5 : 4
When A scores 100, B scores 80.
.
Worth noting
compares 100 with the 20 points given.
In a game of 100 points, A can give B 20 points and C 25 points.
How many points can A give C in a game of 60?
AnswerB · 15 points
C scores of A's points.
When A scores 60, C scores 45: A gives 15 points.
Worth noting
25 points keeps the figure for a game of 100.
In a game of 90, A can give B 15 points. What is the ratio of A's scoring rate to B's?
AnswerA · 6 : 5
When A scores 90, B scores in the same time.
.
Worth noting
5 : 6 is B's rate to A's.
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 100?
AnswerB · 10 points
When A scores 100, B scores 80 and C scores 72.
When B scores 100, C scores , so B can give C 10 points.
Worth noting
8 subtracts the points given, which were measured against A's 100, not B's.
Assertion (A): If A can give B 20 points in a game of 100, then A can give B 10 points in a game of 50.
Reason (R): With fixed scoring rates, the points given are proportional to the length of the game.
AnswerA · Both A and R are true, and R is the correct explanation of A.
A : B = 100 : 80. When A scores 50, B scores 40, so A gives 10 points. A is true.
R is the reason: halving the game halves the points given. Both are true and R explains A.
A scores 3 points for every 2 that B scores. How many points can A give B in a game of 90?
AnswerA · 30 points
When A scores 90, B scores .
So A can give B points.
Worth noting
60 is B's score, not the points given.
In a game of 100, A can give B 10 points and C 19 points. How many points can B give C in a game of 100?
AnswerC · 10 points
When A scores 100, B scores 90 and C scores 81.
When B scores 100, C scores : B gives C 10 points.
Worth noting
9 subtracts the points, , which is B's lead in A's game of 100, not in B's own game of 100.
In a game of 100, A can give B 20 points. How many points can A give B in a game of 150?
AnswerC · 30 points
B scores of A's points.
When A scores 150, B scores 120: A can give 30 points.
Worth noting
20 points keeps the old number; it grows in proportion to the game.
In a game of 100 points, A can give B 20 points and C 25 points.
What is the ratio of B's scoring rate to C's in this game?
AnswerA · 16 : 15
When A scores 100, B scores 80 and C scores 75.
.
Worth noting
treats B as giving C 5 points in a game of 100; it is 5 points in a game of 80.
In a game of 100 points, A can give B 20 points and C 25 points.
How many points can B give C in a game of 80?
AnswerC · 5 points
C scores of B's points.
When B scores 80, C scores 75: B gives 5 points.
Worth noting
4 points scales 5 down to a game of 80, but the 5 points already belong to a game of 80.
In a game of 60, A can give B 10 points, and in a game of 75, B can give C 15 points. How many points can A give C in a game of 90?
AnswerD · 30 points
A : B = 60 : 50 = 6 : 5 and B : C = 75 : 60 = 5 : 4, so A : C = 6 : 4 = 3 : 2.
When A scores 90, C scores : A can give C 30 points.
Worth noting
25 adds the 10 and 15 points given, which belong to games of different lengths.
In a game of 60, A can give B 12 points and C 18 points. How many points can B give C in a game of 80?
AnswerD · 10 points
When A scores 60, B scores 48 and C scores 42, so C scores of B's points.
In a game of 80, C scores : B gives C 10 points.
Worth noting
6 is the gap in A's game of 60; the game here is 80, and B's own pace sets it.
In a game of 50, A can give B 5 points, and in a game of 60, B can give C 12 points. How many points can A give C in a game of 50?
AnswerB · 14 points
When A scores 50, B scores 45. C scores of B's points.
So when A scores 50, C scores : A gives C 14 points.
Worth noting
17 adds the margins, but B's 12-point lead is over a game of 60, and B scores only 45 in A's game.
Two cyclists start together from the same point on a 600 m circular track and ride in opposite directions at 4 m/s and 6 m/s. After how many seconds do they first meet?
AnswerA · 60 seconds
Riding towards each other, they close the gap at m/s.
They meet when together they have covered one lap: seconds.
Worth noting
300 seconds subtracts the speeds, which is for riding the same way.
Assertion (A): Two runners going the same way round a track from the same point first meet when the faster has run exactly one lap more than the slower.
Reason (R): Their relative speed is the difference of their speeds.
AnswerA · Both A and R are true, and R is the correct explanation of A.
R: in the same direction, the gap between them grows at the difference of the speeds. True.
They meet again when that gap reaches one whole lap, so A is true, and R explains how the gap builds up.
Two runners start together from the same point on a 360 m circular track and run in opposite directions at 3 m/s and 5 m/s. After how many seconds do they first meet?
AnswerB · 45 seconds
Running towards each other, they close the gap at m/s.
One lap between them takes seconds.
Worth noting
180 seconds uses the relative speed for the same directions.
A and B run round a 400 m circular track from the same point at the same moment, A at 5 m/s and B at 3 m/s.
If they run in opposite directions round the track, when do they first meet?
AnswerA · 50 seconds
They close the gap at m/s.
seconds.
Worth noting
200 seconds is for running the same way.
A and B start together from the same point on a 400 m circular track and run in the same direction at 5 m/s and 3 m/s. After how many seconds do they first meet again?
AnswerD · 200 seconds
Running the same way, A gains on B at m/s.
They meet when A has gained one full lap: seconds.
Worth noting
50 seconds adds the speeds, which is right only when they run towards each other.
Read the two statements and choose the correct option.
I. Running in opposite directions from the same point, two runners first meet when together they have covered one lap.
II. Running in the same direction from the same point, the faster runner first meets the slower one when he has run one more lap than him.
AnswerC · Both I and II
I: their distances add up to the lap when they meet. True.
II: their distances differ by one lap when the faster catches up. True.
A completes a lap in 40 seconds and B in 56 seconds. They start together from the starting point. After how many seconds are they next at the starting point together?
AnswerC · 280 seconds
Each is at the start after a whole number of its laps: A at multiples of 40, B at multiples of 56.
The first common time is seconds.
Worth noting
2,240 is , a common multiple but not the least.
A completes a lap in 6 minutes and B in 9 minutes, running the same way from the same point. After how many minutes does A first overtake B?
AnswerC · 18 minutes
A gains of a lap a minute.
A full lap's gain takes 18 minutes.
Worth noting
minutes adds the rates, which is for running opposite ways.
Two runners start together from the same point on a 500 m circular track and run in the same direction at 7 m/s and 5 m/s. After how many seconds do they first meet?
AnswerD · 250 seconds
Running the same way, the faster gains at m/s.
One lap between them takes seconds.
Worth noting
seconds uses the relative speed for opposite directions.
Three runners take 30, 40 and 60 seconds to complete a lap. They start together from the starting point. After how many seconds are all three next at the start together?
AnswerB · 120 seconds
They are all at the start at a common multiple of 30, 40 and 60.
seconds.
Worth noting
240 is a common multiple, but 120 comes first.
A completes a lap in 4 minutes and B in 6 minutes. They start together from the same point and run in opposite directions. After how many minutes do they first meet?
AnswerB · 2.4 minutes
Together they cover of a lap a minute.
One lap between them takes minutes.
Worth noting
12 minutes is when both are next at the start, LCM(4, 6), not their first meeting.
Two cyclists ride the same way round a 2 km circular track from the same point, at 18 km/h and 12 km/h. After how many minutes do they first meet?
AnswerD · 20 minutes
The faster gains km/h on the slower.
A lap of 2 km takes hour, that is 20 minutes.
Worth noting
4 minutes adds the speeds, which is for riding towards each other.
A and B run round a 400 m circular track from the same point at the same moment, A at 5 m/s and B at 3 m/s.
If they run the same way round the track, when do they first meet?
AnswerD · 200 seconds
A gains on B at m/s.
A full lap's gain: seconds.
Worth noting
50 seconds adds the speeds, which is for running towards each other.
A completes a lap of a circular track in 60 seconds and B in 84 seconds. They start together from the starting point. After how many seconds are they next at the starting point together?
AnswerC · 420 seconds
A is at the start every 60 seconds and B every 84 seconds, so they are there together at a common multiple.
LCM seconds, which is 7 minutes.
Worth noting
5,040 multiplies 60 by 84; it is a common multiple, but not the least.
On a circular track, A completes a lap in 5 minutes and B in 8 minutes, running the same way from the same point. How many times does A pass B in the first hour?
AnswerB · 4 times
A gains of a lap on B every minute, so a full lap every minutes.
Each full lap gained is one pass. In 60 minutes A gains laps: 4 passes, the fifth coming only after about 66.7 minutes.
Worth noting
5 rounds 4.5 up, but half a lap gained is not a pass.
A and B run the same way round a circular track from the same point, with speeds in the ratio 5 : 3. At how many different points of the track do they meet?
AnswerA ·
With speeds and on a track of length , they meet every , when A has run : 2.5 laps.
So the meetings fall at half a lap and at the start, alternately: 2 points, which is .
Worth noting
8 is , the count for running in opposite directions.
A and B run round a 400 m circular track from the same point at the same moment, A at 5 m/s and B at 3 m/s.
Running the same way, at how many different points of the track do they meet?
AnswerB ·
They meet every 200 s, when A has run 1,000 m, two and a half laps.
So the meetings alternate between the far side and the start: 2 points, which is .
Worth noting
8 is , the count for opposite directions.
A and B run round a 400 m circular track from the same point at the same moment, A at 5 m/s and B at 3 m/s.
After how many seconds are both runners next at the starting point together?
AnswerC · 400 seconds
A laps in s and B in s; both are back at multiples of these.
In thirds of a second: , so 400 seconds (A 5 laps, B 3 laps).
Worth noting
200 seconds is their first meeting anywhere on the track, not at the start.
NTA's Mathematics / Applied Mathematics syllabus has three sections: Section A1, which every candidate answers, then Section B1 (Mathematics) or Section B2 (Applied Mathematics), of which a candidate answers one. Each section lists units and topics but no chapters, so the chapters here are ours. Where both B sections list a topic that Section A also lists, its questions sit once, in Section A.