Race

“Race questions involve relative speed, lead, and time. They're common in SSC, Railways, Defence, and Banking exams.”

1. Basic Concepts and Formulas

Speed = Distance / Time
If A beats B by x meters, it means A finishes the race x meters ahead of B.
If A beats B by x seconds, then time taken by A = time taken by B – x seconds.
If A gives B a start of x meters in a race of D meters, A runs D meters while B runs (D – x) meters.
When multiple racers are involved, use ratios of speeds to compare performance.

Type 1: One racer beats another by distance
Example: A beats B by 20 m in 100 m race ⇒ A runs 100 m, B runs 80 m ⇒ Speed ratio = 100:80 = 5:4
Type 2: One racer beats another by time
Example: A beats B by 10 seconds, A takes 50 sec ⇒ B takes 60 sec ⇒ Speed ratio = 60:50 = 6:5
Type 3: Start Given by One Racer
Example: A gives B a start of 20 m in 100 m ⇒ A runs 100, B runs 80 ⇒ Speed ratio = 100:80 = 5:4
Type 4: Time-based Lead in a Race
Example: A takes 60 sec, B takes 75 sec ⇒ Lead = 15 sec ⇒ B’s position after 60 sec = (60/75)×100 = 80 m
Type 5: Who wins and by how much?
Example: A and B run 100 m. A = 10 m/s, B = 8 m/s ⇒ Time A = 10 sec, B = 12.5 sec ⇒ A wins by 2.5 sec or 25 m
Type 6: Circular Track Race
Example: A and B start together in opposite directions on a 400 m track. Speeds = 10 & 15 m/s ⇒ They meet every 400 / (10+15) = 16 sec

(SSC CGL 2022): A beats B by 20 m in 100 m race. B beats C by 10 m in 100 m race. By how many meters does A beat C?
Solution: A:B = 100:80, B:C = 100:90 ⇒ A:C = 100:72 ⇒ A beats C by 28 m
(RRB NTPC 2020): A runs 1.5 times faster than B. If B takes 60 sec, find lead of A in 300 m race.
Solution: B speed = 300/60 = 5 m/s ⇒ A speed = 7.5 m/s ⇒ A time = 300/7.5 = 40 sec ⇒ Lead = 20 sec or 100 m
(SSC CHSL 2019): A gives B a start of 40 m in 200 m race. If A wins by 20 m, find ratio of speeds.
Solution: B runs = 200 – 20 = 180 ⇒ Ratio = 200:180 = 10:9
(HSSC 2021): A and B run a race of 100 m. A gives B a 10 m start and still wins by 5 seconds. A’s speed is 5 m/s. Find B’s speed.
Solution: A time = 100/5 = 20 sec ⇒ B time = 25 sec ⇒ B speed = 90/25 = 3.6 m/s