In a kilometre race, by how many meters Chandu beats Chand? Statement I : In a…
2025
In a kilometre race, by how many meters Chandu beats Chand?
Statement I : In a kilometer race, Chandu beats Chandan by 100 meters.
Statement II : The respective ratio of the speed of Chandan and Chand is 4 : 3.
Statement III : In a kilometer race, Chandan beats Chand by 150 meters.
- A.
Either statements I and III together, or statements I and II together, are sufficient.
- B.
Only statement III is sufficient.
- C.
Only statements I and II together are sufficient.
- D.
Only statements I, II, and III together are sufficient.
Attempted by 1 students.
Show answer & explanation
Correct answer: A
Concept
In a "races and games" data-sufficiency problem with three runners, a statement is useful only if it supplies a speed (or distance-covered) ratio between two of the three runners. To compare two runners who never appear together in the same statement, their ratio must be built by chaining two statements through a runner common to both: if runner A's ratio to B is known, and B's ratio to C is known, then A's ratio to C follows by scaling both ratios to a common value of B.
Application
Check each statement and each pairing against the runners it actually links:
Statement I: Chandu beats Chandan by 100 m in a 1000 m race, so when Chandu covers 1000 m, Chandan covers 900 m -- speed ratio Chandu : Chandan = 10 : 9.
Statement II alone gives only Chandan : Chand = 4 : 3 -- Chandu is never mentioned, so alone it cannot compare Chandu and Chand.
Statement III alone gives only Chandan : Chand = 1000 : 850 = 20 : 17 (Chandan beats Chand by 150 m in a 1000 m race) -- again Chandu is never mentioned, so alone it cannot compare Chandu and Chand.
Combine Statement I with Statement II: scale Chandu : Chandan = 10 : 9 and Chandan : Chand = 4 : 3 to a common Chandan term (LCM of 9 and 4 is 36) -- Chandu : Chandan : Chand = 40 : 36 : 27, so Chandu : Chand = 40 : 27, a fully determinate ratio giving a margin of 325 m.
Combine Statement I with Statement III: scale Chandu : Chandan = 10 : 9 and Chandan : Chand = 20 : 17 to a common Chandan term (LCM of 9 and 20 is 180) -- Chandu : Chandan : Chand = 200 : 180 : 153, so Chandu : Chand = 200 : 153, again a fully determinate ratio, giving a margin of 235 m.
Cross-check
Any pairing that never includes Statement I -- that is, Statement II with Statement III -- only ever describes Chandan versus Chand and never brings Chandu into the comparison, so it cannot answer this question regardless of which Chandan : Chand figure is used. This confirms Statement I is the indispensable common link, and either external link (Statement II or Statement III) completes it independently.
Result
Either statements I and III together, or statements I and II together, are sufficient.