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Q29·CSAT · Prelims 2025

Cricket run rate - team X total runs

NumericalRatio & ProportionArithmetic word problemHard

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

a

72

b

144

c

216

d

Cannot be determined

Answer

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.

In algebra-based word problems, if tracking the variable leads to a self-evident truth where the variable cancels out (12=12), the original value cannot be determined.

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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