Races & Games
Races & Games of Skill
Races & Games tests proportional reasoning about speed, distance, and head starts. SSC CGL Tier 1 carries a guaranteed 1-mark question; RRB NTPC also tests this topic regularly. Every race problem reduces to a single speed ratio: when A finishes L metres, B has covered L\u2212x metres. Games of skill (billiards) follow the same ratio logic \u2014 treat points scored as distance covered.
Key Idea
Speed ratio = Distance ratio (for equal time). If A beats B by x metres in a race of L metres, then when A finishes (L metres), B has run only L−x metres. So Speed_A / Speed_B = L / (L−x). All race and game problems reduce to this one ratio.
Core Formulas
Speed Ratio from Race Distance
S_A / S_B = L / (L − x) where L = race length, x = margin A beats B by
Derive the speed ratio first from the margin \u2014 once you have S_A/S_B = L/(L\u2212x), use it to solve head-start, three-runner, and dead-heat follow-ups.
Beat by Time
S_A / S_B = T_B / T_A | Margin in time = T_B − T_A
Invert the time ratio to get the speed ratio when the problem gives finishing times instead of distance margins.
Head Start Equivalence
With x-metre head start: B covers L−x metres while A covers L metres
When B starts x metres ahead of A. B now needs L−x metres to finish. Compare distances using the established speed ratio to determine who wins.
Three-Runner Transitivity
If A beats B by x in L, and B beats C by y in L, then when A finishes: B has run L−x, and C has run (L−x) × (L−y)/L
In A vs B vs C problems. First find where B is when A finishes, then apply B's speed ratio to find where C is at that same moment.
Games of Skill (Points)
A gives B p points in a game of n → when A scores n, B scores n−p → S_A / S_B = n / (n−p)
In billiards or games problems. Treat 'points scored' exactly like 'distance covered'. Chain multiple game ratios the same way as three-runner race problems.
Relevant Exams
Races & Games is a guaranteed topic in SSC CGL Tier I (1 question) and appears in RRB NTPC. Common question types: three-runner transitivity, head start equivalence, and chaining game ratios across two rounds.