CAT 2025 Question Paper | Quant Slot 3

CAT Questions

CAT 2025 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 6 : Rahul starts on his journey at 5 pm at a constant speed so that he reaches his destination at 11 pm the same day. However, on his way, he stops for 20 minutes, and after that, increases his speed by 3 km per hour to reach on time. If he had stopped for 10 minutes more, he would have had to increase his speed by 5 km per hour to reach on time. His initial speed, in km per hour, was

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Video Explanation

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Explanatory Answer

Rahul's total journey time is \(6\) hours.
Let his initial speed be \(v\) km/h and the remaining distance after the stop be \(d\) km.

Since his original journey takes 6 hours, total distance is \(6v\).

Scenario 1: He stops for 20 minutes \(=\frac{1}{3}\) hour and increases speed by 3 km/h.
Remaining travel time is: \[ 6-\frac{1}{3}=\frac{17}{3} \]
Therefore: \[ \frac{6v-d}{v}+\frac{d}{v+3}=\frac{17}{3} \]

Scenario 2: He stops for 30 minutes \(=\frac{1}{2}\) hour and increases speed by 5 km/h.
Remaining travel time is: \[ 6-\frac{1}{2}=\frac{11}{2} \]
Therefore: \[ \frac{6v-d}{v}+\frac{d}{v+5}=\frac{11}{2} \]

Solving the two equations gives:
\(v=15\) km/h and \(d=30\) km.

Rahul's initial speed was \(15\) km/h.

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The answer is '15'

Choice 4 is the correct answer.

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