Races and Games: Concepts, Formulas and Solved Questions for SSC & RRB

Most Races and Games questions reduce to one idea: in the same time, the distances covered by two runners are in the ratio of their speeds. If A beats B by 10 m in a 100 m race, then while A runs 100 m, B runs 90 m — so their speeds are in the ratio 100 : 90. Everything else in this topic is vocabulary and rearrangement.

The terms, in plain language

• A beats B by x metres: when A finishes the race, B is x metres behind the finish line.
• A beats B by t seconds: B needs t more seconds to finish after A crosses the line.
• A gives B a start of x metres: B begins x metres ahead, so in a race of L metres, B only has to run (L − x) metres.
• Dead heat: both finish at exactly the same time.

The core formulas

• In equal time: Speed of A : Speed of B = Distance by A : Distance by B
• If A beats B by x metres in an L-metre race: B's distance when A finishes = L − x
• If A beats B by t seconds: x = (B's speed) × t — the beat distance is what B covers in the beat time.

Solved questions

Q1. In a 100 m race, A beats B by 10 m. A takes 10 seconds. Find B's speed.

When A finishes (10 s), B has run 100 − 10 = 90 m.
B's speed = 90 ÷ 10 = 9 m/s.

Q2. A runs 100 m in 12 s, B in 15 s. By what distance does A beat B?

In A's 12 s, B covers (100/15) × 12 = 80 m.
A beats B by 100 − 80 = 20 m.

Q3. A runs 600 m in 36 s, B in 40 s. By what distance does A beat B?

In 36 s, B covers (600/40) × 36 = 540 m.
A beats B by 600 − 540 = 60 m.

Q4. In a 5 km race, A beats B by 1000 m. A's speed is 15 km/h. Find B's speed.

A's time = 5/15 h = 20 min. In that time B covers 4 km.
B's speed = 4 ÷ (1/3) = 12 km/h.

Q5. A runs 4 laps in the time B runs 3. A takes 24 s per lap. How long does B take per lap?

A runs 4 laps in 96 s; B runs 3 laps in the same 96 s.
B's lap time = 96 ÷ 3 = 32 s.

Q6. A runs 6 laps in the time B runs 5. A takes 15 min per lap. Find B's lap time.

A's 6 laps take 90 min; B does 5 laps in 90 min.
B's lap time = 90 ÷ 5 = 18 min.

Q7. In a 1600 m race, A beats B by 200 seconds. A's speed is 8 m/s. Find B's speed.

A's time = 1600 ÷ 8 = 200 s, so B's time = 200 + 200 = 400 s.
B's speed = 1600 ÷ 400 = 4 m/s.

Q8. In a 400 m race, A (speed 8 m/s) gives B a 40 m start and still beats him by 4 s. Find B's speed.

A runs 400 m in 50 s. B, starting 40 m ahead, must run 360 m and takes 50 + 4 = 54 s.
B's speed = 360 ÷ 54 = 6.67 m/s (20/3 m/s).

Q9. In a 200 m race, A beats B by 20 m. In the same time, by how much would A beat B in a 500 m race (same speeds)?

Speed ratio A : B = 200 : 180 = 10 : 9. When A runs 500 m, B runs 450 m.
A beats B by 50 m.

Q10. A beats B by 100 m in a 1 km race, and B beats C by 100 m in a 1 km race. By how much does A beat C in 1 km?

B/A = 900/1000 = 0.9 and C/B = 0.9, so C/A = 0.81. When A runs 1000 m, C runs 810 m.
A beats C by 190 m.

How this appears in SSC and RRB papers

Expect 0–1 question per paper, usually solvable in under 40 seconds with the ratio idea. The common traps: forgetting that a "start" shortens the slower runner's distance, and mixing up "beats by metres" (distance) with "beats by seconds" (time). Convert everything into "distance covered in the same time" and the ratio does the rest.

Practise this topic with timed quant sectionals and full mocks on Pareeksha.