CAT 2024 Question Paper | Quant Slot 1

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 :Two places A and B are 45 kms apart and connected by a straight road. Anil goes from A to B while Sunil goes from B to A. Starting at the same time, they cross each other in exactly 1 hour 30 minutes. If Anil reaches B exactly 1 hour 15 minutes after Sunil reaches A, the speed of Anil, in km per hour, is

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Video Explanation

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Explanatory Answer

Ratio of the distances, \(90 / T =( T +75) / 90\) \[ \begin{array}{l} T^2+75 T=8100 \\ T^2+75 T-8100=0 \\ (T+135)(T-60)=0 \\ T=60 \text { mins } \end{array} \] So, Anil takes \(90+60+75=225 mins =3 hr 45 min=3(3 / 4)=15 / 4 hr\)
Speed of Anil in Km/hr \(=45 /(15 / 4)=45 * 4 / 15=12 km / hr\)

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The question is "Two places A and B are 45 kms apart and connected by a straight road. Anil goes from A to B while Sunil goes from B to A. Starting at the same time, they cross each other in exactly 1 hour 30 minutes. If Anil reaches B exactly 1 hour 15 minutes after Sunil reaches A, the speed of Anil, in km per hour, is "

Hence, the answer is '12'

Choice C is the correct answer.

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