2025 CSAT — Q9

Team Y scores the same $N$ runs in $10\%$ fewer overs than $20$, i.e. in $18$ overs, so Y’s run rate is $\dfrac{N}{18}$ runs/over.

Now raise Y’s rate by $50\%$: the new rate is $1.5 \times \dfrac{N}{18} = \dfrac{N}{12}$ runs/over. In $12$ overs at this rate Y scores

So the third condition says ”$N$ runs in $12$ overs” — which is automatically true for every $N$. It is an identity, not an equation: it imposes no constraint on $N$, so $N$ is not pinned down by the data.

Answer: (d) Cannot be determined.

This is a trap of structure, not arithmetic. The examiner gives three relations that look like a solvable system, but the third one ($1.5 \times \tfrac{N}{18} \times 12$) algebraically reduces to $N = N$ — it carries zero information. The gold habit on “find the value” items is to track degrees of freedom: here every condition is consistent for any $N$, so the correct exam answer is the option the over-eager solver never picks — “cannot be determined.” The three numeric distractors exist precisely to reward anyone who forces a number out of an underdetermined system. Spotting the vacuous condition is the whole question.