NinetynineCAT 2025 Slot 1 QA Q10 Time, Speed & Distance
Question 10 of the Quantitative Ability (QA) section, CAT 2025 Slot 1, with CAT's official answer and a worked solution.
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
- A96000
- B112000
- C76800
- D86400
Answer: (D) 86400 Time, Speed & Distance MCQ
Solution
- First part: \(960\) m/min \(= 57.6\) km/h for \(0.5\) h, so 28.8 km.
- Times are in AP with 4 terms summing to 3 h and first term \(\frac12\): \(2 + 6d = 3 \Rightarrow d = \frac16\), giving times \(\frac12, \frac23, \frac56, 1\).
- Speeds are \(57.6 + je\) for \(j = 0..3\). Distance \(= 57.6 \times 3 + e\left(\frac23 + \frac53 + 3\right) = 172.8 + \frac{16e}{3} = 224 \Rightarrow e = 9.6\).
- Fourth part: speed \(57.6 + 28.8 = 86.4\) km/h for 1 h, which is 86.4 km = 86400 m.