CUET CUET Mathematics 2024 - Arun's speed of swimming in still water is 5 ~km / hr. He swims between two points in a river and returns back to the same starting point. He took 20 minutes more to cover the distance upstream than downstream. If the speed of the stream is 2 ~km / hr, then the distance between the two points is : | PYQs + Solutions

CUET Mathematics 2024

Arithmetic

Time, Speed & Distance

Easy

Arun's speed of swimming in still water is $5 \mathrm{~km} / \mathrm{hr}$ . He swims between two points in a river and returns back to the same starting point. He took $20$ minutes more to cover the distance upstream than downstream. If the speed of the stream is $2 \mathrm{~km} / \mathrm{hr}$ , then the distance between the two points is :

3 \mathrm{~km}

1.5 \mathrm{~km}

1.75 \mathrm{~km}

1 \mathrm{~km}

Correct Option: 3

We are given:

- Arun's speed in still water = 5 km/hr

\newline

- Speed of stream = 2 km/hr

\newline

- Time difference between upstream and downstream = 20 minutes =

\frac{1}{3}

hour

Let the distance between the two points be

D

km (one-way).

- Downstream speed

= 5 + 2 = 7

km/hr

\newline

- Upstream speed

=5 - 2 = 3

km/hr

Time taken downstream =

\frac{D}{7}

hours

\newline

Time taken upstream =

\frac{D}{3}

hours

We’re told upstream takes 20 minutes (i.e.,

\frac{1}{3}

hr) more than downstream:

\dfrac{D}{3} - \dfrac{D}{7} = \dfrac{1}{3}

\Rightarrow D\left(\frac{1}{3} - \frac{1}{7}\right) = \frac{1}{3}

\Rightarrow D\left(\frac{7 - 3}{21}\right) = \frac{1}{3}

\Rightarrow D \cdot \frac{4}{21} = \frac{1}{3}

\Rightarrow D = \frac{1}{3} \cdot \frac{21}{4} = \frac{7}{4} = 1.75

hours.