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?
Cannot be determined
To solve the problem, we need to analyze the information given:
- Team X scored a total of \(N\) runs in 20 overs.
- Team Y tied the score in 10% less overs than Team X.
- Had Team Y’s average run rate been 50% higher, the scores would have been tied in 12 overs.
Let's understand and calculate the given conditions:
- Over Calculation for Team Y:
Team Y tied the score in 10% less time than Team X.- 10% of 20 overs is calculated as \(\frac{10}{100} \times 20 = 2\) overs.
- Therefore, Team Y used \(20 - 2 = 18\) overs to tie the score with Team X.
- Run Rate Analysis for Team Y:
Team Y’s run rate becomes 50% higher in another scenario leading to tying the score in 12 overs.- Let Team Y's initial run rate be \(r\).
- The current scenario for score tie in 18 overs implies: \(18 \times r = N\).
- If the run rate was 50% higher, the new run rate \(= 1.5r\).
- Increased run rate scenario gives: \(12 \times 1.5r = N\).
- Comparing the Two Situations:
We have:- \(18r = N\)
- \(18r = 12 \cdot 1.5r\) (from the condition in step 2)
- Since both equations represent the same \(N\), solving them we see both give the same value of \(N\).
Conclusion:
Based on the above analysis, we cannot directly calculate the exact number of runs scored by Team X. Thus, the most appropriate choice from the options given is "Cannot be determined."
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