Arithmetic aptitude :: Boats and Streams :: General Questions

• Boats and Streams - General Questions
• Boats and Streams - Data Sufficiency 1
• Boats and Streams - Data Sufficiency 2
• Boats and Streams - Important Formulas and Facts

Still water : The speed of water in the river is zero.

Stream water : The water in the river is flowing or moving.

Speed of Boat and Stream :

Assume the man's rate of rowing in still water $=x$ km/hr Speed of stream $= y$ km/hr

(a) Down stream rate $=(x+y)$ km/hr

(i.e.) direction of rowing and direction of flow is same.

(b) Up stream rate $=(x-y)$ km/hr

(i.e.) direction of rowing and direction of stream are opposite. Speed of still water and stream : Assume, speed downstream $=a$ km/hr

Speed upstream $=b$ km/hr

Then, speed in still water $=\frac{1}{2}(a + b)$ km/hr

Rate of stream $=\frac{1}{2}(a - b)$ km/hr

A man can row 18 kmph in still water. It takes him thrice as long to row up as to row down the river. Find the rate of stream.

Answer:

Explanation:

Let man's rate upstream be $x$ kmph.

Then, his rate downstream $=3x$ kmph.

$\therefore$ Rate in still water $=\frac{1}{2}(3x+x)$ kmph $= 2x$ kmph.

So, $2x=18$ or $x=9$.

$\therefore$ Rate upstream $= 9$ km/hr, Rate downstream $=27$ km/hr.

Hence, rate of stream $= \frac{1}{2}(27-9)$ km/hr = 9 km/hr.

A man can row upstream at 7 kmph and downstream at 10 kmph. Find man's rate in still water and the rate of current.

Answer:

Explanation:

Rate in still water $=\frac{1}{2} (10+ 7)$ km/hr $=8.5$ km/hr.

Rate of current $=\left(\frac{1}{2}(10-7)\right)$ km/hr = 1.5 km/hr.

A man takes 3 hours 45 minutes to row a boat 15 km downstream of a river and 2 hours 30 minutes to cover a distance of 5 km upstream. Find the speed of the river current in km/hr.

Answer:

Explanation:

Rate downstream $=\frac{15}{\left(3\frac{3}{4}\right)}$ km/hr

$=15\times\frac{4}{15}$ km/hr $=4$ km/hr.

Rate upstream $=\left(\frac{5}{2\frac{1}{2}}\right)$  km/hr

$=\left(5\times\frac{2}{5}\right)$ $=2$ km/hr

Speed of current $=\frac{1}{2}(4-2)$ km/hr = 1 km/hr.

A man swimming in a stream which flows 1.5 kmph, finds that in a given time he can swim twice as fast with the stream as he can against it. At what rate does he swim ?

Answer:

Explanation:

Rate of stream $=1.5$ km/hr

Let speed of man in still water $=x$ km/hr and Distance $=d$

Upstream speed $=(x-1.5)$ km/hr Downstream speed $=(x+1.5)$ km/hr

Given, $\frac{2d}{(x+1.5)}$ $=\frac{d}{(x-1.5)}$

$\Rightarrow 2x-3$ $=x+1.5$ $\Rightarrow x$ = 4.5 km/hr.

A boat covers 24 km upstream and 36 km downstream in 6 hours while it covers 36 km upstream and 24 km downstream in $6 \frac{1}{2}$ hours. The velocity of the current is :

Answer:

Explanation:

Let rate upstream $=x$ kmph and rate downstream $=y$ kmph.

Then, $\frac{24}{x}+\frac{36}{y}$ $=6$ ....(i)

and $\frac{36}{x}+\frac{24}{y}$ $=\frac{13}{2}$ ...(ii)

Adding (i) and (ii), we get : $60\left(\frac{1}{x}+\frac{1}{y}\right)$ $=\frac{25}{2}$

or $\frac{1}{x}+\frac{1}{y}$ $=\frac{5}{24}$ ....iii)

Subtracting (i) from (ii), we get : $12\left(\frac{1}{x}-\frac{1}{y}\right)$ $=\frac{1}{2}$

or $\frac{1}{x}-\frac{1}{y}$ $=\frac{1}{24}$ .....iv)

Adding (iii) and (iv), we get : $\frac{2}{x}$ $=\frac{6}{24}$ or $x=8$

So $\frac{1}{8}+\frac{1}{y}$ $=\frac{5}{24}$

$\frac{1}{y}$ $=\frac{5}{24}-\frac{1}{8}$ $=\frac{1}{12}$ $\Leftrightarrow y=12$

Speed upstream = 8 kmph, Speed downstream = 12 kmph.

Hence, rate of current $= \frac{1}{2}(12-8)$ kmph = 2 kmph.

• Boats and Streams - General Questions
• Boats and Streams - Data Sufficiency 1
• Boats and Streams - Data Sufficiency 2