Cricket run rate - team X total runs
Question
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?
Options
72
144
216
Cannot be determined
Explanation
Team X scores N runs in 20 overs. Team Y tied the score in 10\% fewer overs: 20 - 2 = 18 overs. Team Y's standard run rate is therefore N/18. If Y's run rate were 50\% higher, the new run rate would be 1.5 × N/18 = N/12. At this new run rate, the time taken to score N runs is N \div (N/12) = 12 overs. Notice that the variable ⟨MATH⟩N⟨/MATH⟩ perfectly cancels out of the equation. The statement "the scores would have been tied in 12 overs" is a mathematical tautology that holds true for absolutely any value of N. Therefore, N cannot be found.
Answer: (d).
Question details
Year
2025
Paper
CSAT
Question
Q29
Section
Numerical Ability
Sub-topic
Ratio & Proportion
Type
Arithmetic word problem
Difficulty
Hard
Source hint
Ratio application
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