CAT 2024 Question Paper | Quant Slot 3

CAT Questions

CAT 2024 Quant was dominated by Algebra followed by Arithmetic. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 15 A train travelled a certain distance at a uniform speed. Had the speed been 6 km per hour more, it would have needed 4 hours less. Had the speed been 6 km per hour less, it would have needed 6 hours more. The distance, in km, travelled by the train is

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Video Explanation

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Explanatory Answer

Distance = XT
From the table, we have: \[ \begin{array}{l} XT=(X+6)(T-4)=(X-6)(T+6) \\ \Rightarrow XT=XT+6 T-4 X-24 \\ 6 T-4 X=24 \\ 3 T-2 X=12 \ldots . . . . . . . .(1) \end{array} \] Also, \[ \begin{array}{l} X T=X T-6 T+6 X-36 \\ 6 X-6 T=36 \\ X-T=6 \quad \ldots \text { (2) } \end{array} \] Solving (1) & (2), \[ \begin{array}{ll} (1) \Rightarrow & 3 T-2 X=12 \\ 2 \times(2) \Rightarrow & -2 T+2 X=12 \end{array} \] Adding the equations, \[ \begin{array}{l} T=24 \\ \Rightarrow X=30 \end{array} \] Distance \(= XT =720 km\)

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The question is "A train travelled a certain distance at a uniform speed. Had the speed been 6 km per hour more, it would have needed 4 hours less. Had the speed been 6 km per hour less, it would have needed 6 hours more. The distance, in km, travelled by the train is "

Hence, the answer is '720'

Choice B is the correct answer.

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