If Rahul rows 15 km upstream in 3 hours and 21 km downstream in 3 hours, then the speed of the stream is

Answer: Option C

Explanation:

Please remember,
If a is rate downstream and b is rate upstream
Rate in still water = 1/2(a+b)
Rate of current = 1/2(a-b)

=> Rate in still water = 1/2(20+10) = 15 kmph
=> Rate of current = 1/2(20-10) = 5 kmph

Answer: Option B

Explanation:

Friends first we should analyse quickly that what we need to calculate and what values we require to get it.

So here we need to get speed of current, for that we will need speed downstream and speed upstream, because we know
Speed of current = 1/2(a-b) [important]

Let the speed upstream = x kmph
Then speed downstream is = 3x kmph [as per question]

$$\begin{aligned} \text{speed in still water = } \frac{1}{2}(a+b) \\ => \frac{1}{2}(3x+x) \\ => 2x \\ \text{ as per question we know, }\\ 2x = 9\frac{1}{3} \\ => 2x = \frac{28}{3} => x = \frac{14}{3} \\ \end{aligned}$$
So,
Speed upstream = 14/3 km/hr, Speed downstream 14 km/hr.
Speed of the current $$\begin{aligned} =\frac{1}{2}[14 - \frac{14}{3}]\\ = \frac{14}{3} = 4 \frac{2}{3} kmph \end{aligned}$$

Answer: Option A

Explanation:

First of all, we know that
speed of current = 1/2(speed downstream - speed upstream) [important]

So we need to calculate speed downstream and speed upstream first.

Speed = Distance / Time [important]

$$\begin{aligned} \text {Speed upstream =}\\ (\frac{15}{3\frac{3}{4}}) km/hr \\ = 15 \times \frac{4}{15} = 4 km/hr \\ \text{Speed Downstream = } (\frac{5}{2\frac{1}{2}}) km/hr \\ = 5 \times \frac{2}{5} = 2 km/hr \\ \text {So speed of current = } \frac{1}{2}(4-2) \\ = 1 km/hr \end{aligned}$$

Answer: Option A

Explanation:

$$\begin{aligned} \text{Speed Upstream} = \frac{3}{\frac{20}{60}} = 9 km/hr \\ \text{Speed Downstream} = \frac{3}{\frac{18}{60}} = 10 km/hr \\ \text{Rate of current will be} \\ \frac{10-9}{2} = \frac{1}{2} km/hr \end{aligned}$$

Answer: Option A

Explanation:

It is very important to check, if the boat speed given is in still water or with water or against water. Because if we neglect it we will not reach on right answer. I just mentioned here because mostly mistakes in this chapter are of this kind only.

Lets see the question now.
Speed downstream = (16 + 5) = 21 kmph

Time = distance/speed = 84/21 = 4 hours