CAT 2025 Question Paper | Quant Slot 2

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 19 : 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

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Video Explanation

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Explanatory Answer

Sneha's speed = 6 km/h, distance = 14 km,
time difference = 48 minutes = \(\frac{4}{5}\) hours.

Let river speed be \(S\) km/h.

\[ \frac{14}{6-S}-\frac{14}{6+S}=\frac{4}{5} \]
\[ \frac{14[(6+S)-(6-S)]}{36-S^2}=\frac{4}{5} \]
\[ \frac{28S}{36-S^2}=\frac{4}{5} \]
\(35S=36-S^2\)
\(S^2+35S-36=0\)
\((S+36)(S-1)=0\Rightarrow S=1\) km/h

Rita's speed = 5 km/h, total time = 100 minutes = \(\frac{5}{3}\) hours.
Downstream speed = \(5+1=6\) km/h
Upstream speed = \(5-1=4\) km/h

\[ \frac{d}{6}+\frac{d}{4}=\frac{5}{3} \]
\[ \frac{2d+3d}{12}=\frac{5}{3} \Rightarrow\frac{5d}{12}=\frac{5}{3} \Rightarrow d=4\text{ km} \]

Total Distance = \(d+d=4+4=8\) km

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The answer is '8'

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