Team X scored a total of N runs in 20 overs. Team Y tied the score in 10% less overs. Had team Y’s average run rate (runs per over) been 50% higher, the scores would have been tied in 12 overs. How many runs were scored by team X?
Answer & explanation
Answer: (d) Cannot be determined
The '12 overs' condition follows automatically from the first one: a run rate 1.5 times N/18 is N/12, which reaches N in exactly 12 overs whatever N is. With no independent equation, N cannot be found.
- 10% fewer than 20 overs is 18 overs, so team Y's run rate was N/18 runs per over.
- A 50% higher run rate is 1.5 × N/18 = N/12 runs per over.
- At N/12 runs per over, N runs take N ÷ (N/12) = 12 overs — for every value of N.
- The last condition is always true and gives no new information, so N cannot be determined.
- Check: N = 72 and N = 144 both satisfy every condition, so the data cannot pick one value.
Remember · Test whether a second condition is independent; if it reduces to an identity, the value cannot be determined.
Question and answer: UPSC's official GS Paper II (2025, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·