CAT 2025 Slot 1 · Quant · Question 10

CAT 2025 Slot 1 previous year question on Time Speed and Distance, with the answer and a step-by-step solution.

Time Speed and DistanceArithmeticMultiple choiceMedium
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
  1. A
    96000
  2. B
    112000
  3. C
    76800
  4. D
    86400
Pick an option, then check.
Answer & solution

Answer: Option D

Work in metres and minutes throughout, since the data is given that way: the total is 224000 m in 180 minutes.

The times. They are in AP with first term 30 and sum 180. For four terms, 4\left( 30 \right)+6{d}_{t}=180, so {d}_{t}=10 and the times are 30,40,50,60 minutes.

The speeds. They are in AP with first term 960, say 960,

960+d,960+2d,960+3d m/min.

Distance is the sum of (speed \times time) over the four parts:

960\left( 30+40+50+60 \right)+d\left( 40+2\left( 50 \right)+3\left( 60 \right) \right)=224000.

That is 172800+320d=224000, so d=160.

The fourth speed is 960+480=1440 m/min over 60 minutes, giving 1440\times 60=86400 metres.

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