Question

A man can row three quarters of a kilometres against the stream in $11\dfrac{1}{4}$ minutes and return in $7\dfrac{1}{2}$ minutes. The speed of the man in still water is
(a) 2 km/hr
(b) 3 km/hr
(c) 4 km/hr
(d) 5 km/hr

Answer 1

Hint:Here, distance is given i.e. three quarter which is equal to $\dfrac{3}{4}$ . Also, time taken for upstream and downstream is given which we have to convert in hours as we need answers in kmph. We will use a formula for finding speed in upstream and downstream as $\dfrac{\text{Distance}}{\text{Time}}$. Speed of the man in still water will get by $\dfrac{1}{2}\left( \text{speed of upstream + speed of downstream} \right)$ .

Complete step-by-step answer:
Now, first we will take three quarter km which is equal to 0.75km.
Here, if the boat is flowing in the opposite direction to the stream, then it is called upstream.
Similarly, if the boat is flowing in the same direction to the direction, then it is called downstream.
So, in the question against the stream is given which is upstream and the return word indicates downstream.
We also know that $1\text{hour}=60\text{minutes}$ or we can say that $1\text{minute}=\dfrac{1}{60}\text{hour}$
Time taken upstream is given in mixed fraction form. So, after converting in fraction form, we get $\dfrac{45}{4}=11.25$ minutes. On converting it to hours, we get $=\dfrac{11.25}{60}=0.1875$ hour.
Similarly, doing it downstream we get, $\dfrac{15}{2}=7.5$ minutes. On converting it to hours, we get $\dfrac{15}{2}=\dfrac{7.5}{60}=0.125$ hour.
 Now, finding speed of upstream $=\dfrac{\text{Distance}}{\text{Time}}$
$=\dfrac{0.75}{0.1875}\text{ km/hr}$
$=4\text{ km/hr}$
Now, finding speed of downstream $=\dfrac{\text{Distance}}{\text{Time}}$
$=\dfrac{0.75}{0.125}\text{ km/hr}$
$=6\text{ km/hr}$
Now, to find speed of man in still water by using formula $\dfrac{1}{2}\left( \text{speed of upstream + speed of downstream} \right)$
$\Rightarrow \dfrac{1}{2}\left( 4+6 \right)\text{km/hr}$
$\Rightarrow \dfrac{1}{2}\left( 10 \right)\text{km/hr}$
$\Rightarrow 5\text{km/hr}$
Hence, option (d) is correct.

Note: Students might get confused by the formula of upstream downstream and speed in still water. So, the correct formula should be known and also sometimes make mistakes by not seeing the option given in an hour and in question minutes are given. Also, mistakes can happen by taking $11\dfrac{1}{4}$ minutes as downstream instead of upstream and vice versa for downstream.
Formula for upstream $=\left( u-v \right)km/hr$
(Where u is speed of boat in still water and v is speed of stream)
Formula for downstream $=\left( u+v \right)km/hr$
Speed of boat in still water $=\dfrac{1}{2}\left( \text{downstream speed+upstream speed} \right)$