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 ?
- (a) 72
- (b) 144
- (c) 216
- (d) Cannot be determined ✓ UPSC's answer
Why the answer is (d)
• Team X scored N runs in 20 overs, so its run rate is N/20.
• Team Y tied the score in 10% less overs than 20, which is 18 overs, so Team Y's actual run rate is N/18.
• If Team Y's run rate were 50% higher, it would be 1.5 * (N/18) = N/12.
• At this hypothetical run rate, scoring N runs would take N / (N/12) = 12 overs, which matches the condition given in the problem.
• Since the condition holds true for any value of N, the specific number of runs cannot be uniquely determined from the given information.
Why the other options are wrong
- (a) 72
- 72 is a specific value that satisfies the condition but is not the only possible solution.
- (b) 144
- 144 is a specific value that satisfies the condition but is not the only possible solution.
- (c) 216
- 216 is a specific value that satisfies the condition but is not the only possible solution.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2025, held on 25 May 2025. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.