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UPSC Prelims 2025 CSAT, question 9

Topic: Arithmetic

Q9

Team XX scored a total of NN runs in 20 overs. Team YY tied the score in 10% less overs. Had team YY'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 XX ?

  1. (a) 72
  2. (b) 144
  3. (c) 216
  4. (d) Cannot be determinedCorrect answer

Solution.

Answer: (d) Cannot be determined

  1. Team XX scored NN runs in 2020 overs, and Team YY tied the score NN in 10%10\% fewer overs, which is 20×0.9=1820 \times 0.9 = 18 overs, so Team YY's actual average run rate was N18\frac{N}{18} runs per over.
  2. Increasing Team YY's run rate by 50%50\% gives 32×N18=N12\frac{3}{2} \times \frac{N}{18} = \frac{N}{12} runs per over, which ties the score NN in NN/12=12\frac{N}{N/12} = 12 overs for any positive value of NN.
  3. Because NN cancels out identically from both conditions, the value of NN cannot be determined.