NinetynineCAT 2025 Slot 2 QA Q19 Time, Speed & Distance
Question 19 of the Quantitative Ability (QA) section, CAT 2025 Slot 2, with CAT's official answer and a worked solution.
Rita and Sneha can row a boat at 5 km/h and 6 km/h in still water, respectively. In a river flowing with a constant velocity, Sneha takes 48 minutes more to row 14 km upstream than to row the same distance downstream. If Rita starts from a certain location in the river, and returns downstream to the same location, taking a total of 100 minutes, then the total distance, in km, Rita will cover is
TITA: type in the answer. There are no options and no negative marking.
Answer: 8 Time, Speed & Distance TITA
Solution
- Sneha, stream speed \(v\): \(\frac{14}{6-v} - \frac{14}{6+v} = \frac{48}{60} \Rightarrow \frac{28v}{36 - v^2} = 0.8\).
- \(v^2 + 35v - 36 = 0 \Rightarrow v = 1\) km/h.
- Rita: upstream 4 km/h, downstream 6 km/h. Going \(d\) upstream and back: \(\frac d4 + \frac d6 = \frac{100}{60} \Rightarrow \frac{5d}{12} = \frac53 \Rightarrow d = 4\).
- Total distance \(= 2d = 8\) km.