CAT 2025 Slot 2 QA Question 7

Type-in-the-answer (no negative marking) · Arithmetic · Time, Speed & Distance · Try it, then check the answer and solution below.

CAT 2025 Slot 2QAArithmetic • Time, Speed & DistanceModerate

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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Official Convenor Answer Key: 8

Verified Solution:

### Core Concept When rowing in a river with a current, the effective speed depends on the direction.

Upstream: Speed = Still water speed - Current speed

Downstream: Speed = Still water speed + Current speed

The time taken to cover a distance is given by

\text{Time} = \frac{\text{Distance}}{\text{Speed}}

### Step-by-Step Solution

Determine the river's current speed (v):

Let the current speed be

v

km/h.

Sneha's upstream speed = 6 - v$ km/h.

Sneha's downstream speed = 6 + v$ km/h.

Time difference for 14 km:

\frac{14}{6 - v} - \frac{14}{6 + v} = \frac{48}{60} = 0.8 \text{ hours}

Simplify the equation:

14 \left( \frac{1}{6 - v} - \frac{1}{6 + v} \right) = 0.8

\[ 14 \left( \frac{(6 + v) - (

Answer and solution

Answer: 8

### Core Concept When rowing in a river with a current, the effective speed depends on the direction.

Upstream: Speed = Still water speed - Current speed

Downstream: Speed = Still water speed + Current speed

The time taken to cover a distance is given by

\text{Time} = \frac{\text{Distance}}{\text{Speed}}

### Step-by-Step Solution

Determine the river's current speed (v):

Let the current speed be

v

km/h.

Sneha's upstream speed = 6 - v$ km/h.

Sneha's downstream speed = 6 + v$ km/h.

Time difference for 14 km:

\frac{14}{6 - v} - \frac{14}{6 + v} = \frac{48}{60} = 0.8 \text{ hours}

Simplify the equation:

14 \left( \frac{1}{6 - v} - \frac{1}{6 + v} \right) = 0.8

\[ 14 \left( \frac{(6 + v) - (

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