In a T20 cricket match, three players X, Y and Z scored a total of 37 runs. The ratio of number of runs…

In a T20 cricket match, three players X, Y and Z scored a total of 37 runs. The ratio of number of runs scored by X to the number of runs scored by Y is equal to ratio of number of runs scored by Y to number of runs scored by Z. Value-I = Runs scored by X Value-II = Runs scored by Y Value-III = Runs scored by Z Which one of the following is correct?
  1. Value-I < Value-II < Value-III
  2. Value-III < Value-II < Value-I
  3. Value-I < Value-III < Value-II
  4. Cannot be determined due to insufficient data

Solution

The condition $\dfrac{X}{Y} = \dfrac{Y}{Z}$ means $Y^2 = XZ$, with $X+Y+Z = 37$. This single equation with the geometric-progression condition admits multiple solution triples (the common ratio is not fixed), so the ordering of X, Y, Z is not uniquely determined. Hence the relationship cannot be determined - answer (d).

Asked in: CSAT 2025

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