UPSC Prelims 2025·CSAT·Quantitative Aptitude·Arithmetic

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?

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Last updated 8 Jul 2026, 4:39 pm IST
  1. A72
  2. B144
  3. C216
  4. DCannot be determinedCorrect

Explanation

To solve this problem, we need to analyze the information given about the run rates.

  1. Team X scored N runs in 20 overs.
  2. Team Y scored N runs in 10 percent less overs than Team X. Since 10 percent of 20 is 2, Team Y scored N runs in 18 overs.
  3. This means Team Y's actual run rate was N divided by 18.
  4. The problem states that if Team Y's run rate had been 50 percent higher, they would have scored the same N runs in 12 overs.
  5. A 50 percent increase of the rate N/18 is calculated as 1.5 multiplied by N/18, which simplifies to N/12.
  6. According to the formula, Distance or Total Runs equals Rate multiplied by Time. If we multiply this new rate of N/12 by the given time of 12 overs, we get N runs.

The equation becomes N equals N. This is a mathematical identity where the variable N cancels out on both sides. This signifies that the information provided describes the relationship between the overs and the rates correctly but does not provide any fixed numerical value for the total runs scored. Since N can be any number, the exact number of runs cannot be determined.

The correct answer is D.

Quantitative Aptitude: 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 (run
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