Arithmetic

Time, Speed & Distance

Medium

Aman takes half the time in rowing a certain distance downstream than upstream.
Statement (I): Ratio of the speed of the boat in still water to the speed of the water current is 2: 1.
Statement (II): If the speed of the boat in still water is 6 km per hour, then the speed of the water current is 2 km per hour.
Choose the most appropriate answer from the options given below.

Both Statement (I) and Statement (II) are true.

Both Statement (I) and Statement (II) are false.

Statement (I) is true but Statement (II) is false.

Statement (I) is false but Statement (II) is true.

✅ Correct Option: 4

Let's use standard notations:

Let speed of boat in still water = $u$ km/hr
Let speed of water current = $v$ km/hr

Given that time taken downstream is half of upstream time:

Time upstream = $\frac{\text{Distance}}{u-v}$
Time downstream = $\frac{\text{Distance}}{u+v}$
According to question: $\frac{\text{Distance}}{u+v} = \frac{1}{2} \times \frac{\text{Distance}}{u-v}$
Therefore: $\frac{\text{Distance}}{u+v} = \frac{\text{Distance}}{2(u-v)}$
Simplifying: $2(u-v) = u+v$
Further: $2u-2v = u+v$
Finally: $u = 3v$

This means ratio of boat speed to current speed is $3:1$ , not $2:1$

Therefore Statement (I) is false.

From Statement (II):

If $u = 6$ km/hr and $v = 2$ km/hr
Then ratio $u:v = 6:2 = 3:1$
This satisfies our derived equation $u = 3v$

Therefore Statement (II) is true.

JIPMAT 2022

Given below are two statements based on the following:

A motor boat can travel 30 km upstream and 28 km downstream in 7 hours. It can travel 21 km upstream and return in 5 hours.

Statement I: Speed of the boat in still water is 12 km per hour.

Statement II: Speed of the stream is 4 km per hour.

In the light of the above statements, choose the correct answer from the options given below:

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