Practice Questions
Concept Explanation
Race problems compare runners over a fixed distance, often with a head start or a winning margin.
Key Formulas
- Time = Distance / Speed
- Head start: slower runner begins d metres ahead; faster catches when gain equals d
- Winning margin: when winner finishes, find how far behind the loser is
- Same time: distance ratio = speed ratio
Example
A beats B by 20 m in 100 m race. When A finishes 100 m, B has run 80 m, so speed ratio A:B = 5:4.
Common Trap
A head start reduces the distance the faster runner must cover, not the slower runner's total distance.
-
Q1 EasyIn a 100 metre race, runner A completes the distance in 10 seconds while runner B takes 12.5 seconds. What is the ratio of their speeds (A : B)?ExplanationSpeed ratio = inverse of time: 12.5:10 = 5:4.
-
Q2 EasyIn a 100 metre race, A beats B by 10 metres. When A crosses the finish line, how many metres has B covered?ExplanationB is 10 m behind at finish: 100 − 10 = 90 m.
-
Q3 EasyA and B run a 1 km race. A finishes 50 seconds before B. If B takes 250 seconds to complete the race, how long does A take?ExplanationA = 250 − 50 = 200 s.
-
Q4 EasyTwo runners start together from the same point and run at the same constant speed. After 30 seconds, where are they relative to each other?ExplanationEqual speeds ⇒ same distance covered.
-
Q5 EasyTwo runners A and B start together from the same point. A runs at 6 m/s and B runs at 4 m/s. After 20 seconds, by how many metres does A lead B?ExplanationLead = (6 − 4) × 20 = 40 m.
-
Q6 MediumIn a 200 metre race, A beats B by 20 metres. What is the ratio of the speeds of A and B?ExplanationWhen A runs 200 m, B runs 180 m. Ratio = 200:180 = 10:9.
-
Q7 MediumA can beat B by 40 metres in a 500 metre race. If they run a 200 metre race at the same speeds, by how many metres will A beat B?ExplanationMargin ratio = 40/500 = 8/100. In 200 m: 200 × 8/100 = 16 m.
-
Q8 MediumIn a 100 metre race, B is given a head start of 10 metres. A runs at 5 m/s and B runs at 4 m/s. After how many seconds from A's start does A catch up with B?ExplanationRelative gain 1 m/s. Catch after 10 m gain: 10 s. Distance from A start = 50 m.
-
Q9 MediumA runs 100 metres in 12 seconds and B runs 100 metres in 15 seconds. By what percentage is A's speed greater than B's speed?ExplanationA = 25/3 m/s, B = 20/3. Increase = (25−20)/20 × 100 = 25%.
-
Q10 MediumA beats B by 20 metres in a 200 metre race. If they run a 100 metre race at the same speeds, by how many metres will A beat B?ExplanationMargin scales: 20/200 × 100 = 10 m.
-
Q11 HardIn a 100 metre race, A gives B a head start of 15 metres. If A runs at 10 m/s and B runs at 8 m/s, by how many metres does A win the race?ExplanationA finishes in 10 s. B runs 80 + 15 = 95 m. A wins by 5 m.
-
Q12 HardIn a 400 metre race, A beats B by 5 seconds. If A completes the race in 50 seconds, what is B's speed in m/s?ExplanationB time = 55 s. Speed = 400/55 ≈ 7.27 m/s.
-
Q13 HardIn a 150 metre race, A beats B by 15 metres and B beats C by 15 metres. By how many metres will A beat C in the same race?ExplanationA:B = 150:135 = 10:9. B:C = 150:135 = 10:9. A:C = 100:81. A beats C by 150 − 121.5 = 28.5 m.
-
Q14 HardA runs 100 metres in 20 seconds and B runs 100 metres in 25 seconds. In a 200 metre race between A and B, by how many metres will A beat B?ExplanationA finishes 200 m in 40 s. B runs 4 × 40 = 160 m. Margin = 40 m.
-
DS1 Easy
In a 100 metre race between A and B, by how many metres does A beat B?
Statement IIn a 100 metre race, A beats B by 10 metres.
Statement IIWhen A finishes the 100 metre race, B has covered 90 metres.
ExplanationEach gives winning margin = 10 m. -
DS2 Easy
What is the ratio of the speeds of A and B in a 100 metre race?
Statement IA completes 100 metres in 10 seconds.
Statement IIB completes 100 metres in 12.5 seconds.
ExplanationSpeed ratio = 12.5:10 = 5:4.
-
DS3 Easy
What is the time taken by A to complete a 400 metre race?
Statement IIn a 400 metre race, A beats B by 5 seconds.
Statement IIB takes 55 seconds to complete the 400 metre race.
ExplanationA time = 55 − 5 = 50 s. -
DS4 Hard
In a 100 metre race where A gives B a head start, by how many metres does A win?
Statement IA gives B a head start of 15 metres in a 100 metre race.
Statement IIA runs at 10 m/s and B runs at 8 m/s.
ExplanationA finishes in 10 s. B runs 80 + 15 = 95 m. A wins by 5 m.