Arithmetic

Time, Speed & Distance

Easy

applied

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
- Speed of stream = 2 km/hr
- 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 $= 5 + 2 = 7$ $= 5 + 2 = 7$ km/hr
- Upstream speed $=5 - 2 = 3$ km/hr

Time taken downstream = $\frac{D}{7}$ hours

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.

2026: 29 May Shift 1

The speed of a boat in still water is 12 km/hr. It takes twice as long to go upstream to a point as to return downstream to the starting point, then the speed of the stream is :

2025: 30 May Shift 1

Ravi's speed of rowing in still water is 6 km/hr. He rows between two points in a river and return to the same starting point. He took 30 minutes more to cover the distance upstream than downstream. If the speed of the stream is 3 km/hr, then the distance between the two points is:

2026: 25 May Shift 1

A boat goes downstream at a speed of 18 km/hr and upstream at a speed of 'm' km/hr. The boat travelled 90 km downstream in a river and then returned back taking altogether 12.5 hours. Then which of the following are true ?

A. $m = 12$

B. $m = 15$

C. Speed of water current is 3 km/hr

D. Speed of water current is 1.5 km/hr

Choose the correct answer from the options given below:

2025: 3 June Shift 1

A man rows 15 km upstream in 5 hours and 25 km downstream in 5 hours each time, then the speed of the stream is

2026: 19 May Shift 1

Usain Bolt runs a 100 m race and defeats his rival by 1 m. If Usain's speed was 9 m/s, the speed of the rival was :

2024: 16 May Shift 1

In a $700 \mathrm{~m}$ race, Amit reaches the finish point in $20$ seconds and Rahul reaches in $25$ seconds. Amit beats Rahul by a distance of :

Solution

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