CAT 2025 Question Paper | Quant Slot 1

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 10 : Shruti travels a distance of 224 km in four parts for a total travel time of 3 hours. Her speeds in these four parts follow an arithmetic progression, and the corresponding time taken to cover these four parts follow another arithmetic progression. If she travels at a speed of 960 meters per minute for 30 minutes to cover the first part, then the distance, in meters, she travels in the fourth part is

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Video Explanation

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Explanatory Answer

Let the times for the four parts be \(t_1,t_2,t_3,t_4\) in arithmetic progression.

First time: \(t_1=30\) minutes
Common difference for time: \(d_t\)

Total Time \(=t_1+t_2+t_3+t_4=180\)
\(30+(30+d_t)+(30+2d_t)+(30+3d_t)=180\)
\(120+6d_t=180\)
\(6d_t=60\Rightarrow d_t=10\) minutes

The times taken for each part are:
\(t_1=30\) minutes
\(t_2=40\) minutes
\(t_3=50\) minutes
\(t_4=60\) minutes

Let the speeds for the four parts be \(v_1,v_2,v_3,v_4\) in arithmetic progression.

First speed: \(v_1=960\text{ m/min}\)
Common difference for speed: \(d_v\)

The speeds are:
\(v_1=960\)
\(v_2=960+d_v\)
\(v_3=960+2d_v\)
\(v_4=960+3d_v\)

Total Distance \(=v_1\times t_1+v_2\times t_2+v_3\times t_3+v_4\times t_4=224,000\) meters

\(224,000=28,800+38,400+40d_v+48,000+100d_v+57,600+180d_v\)
\(224,000=172,800+320d_v\)
\(d_v=\frac{51,200}{320}=160\text{ m/min}\)

Distance in Part 4 (\(d_4\)):
\(d_4=v_4\times t_4=1,440\text{ m/min}\times60\text{ minutes}=86,400\text{ meters}\)

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The answer is '86400'

Choice 4 is the correct answer.

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