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 streamer goes downstream from one port to another in 4 hours. It covers the same distance upstream in 5 hours. If the speed of stream is 2 km/h, the distance between the two ports is 

Answer:

Explanation:

Let the distance between the two ports be $=x$ km

Let the speed of streamer in still water  $=y$ km/h

$\frac{x}{y+2}$ $=4$

$\Rightarrow x$ $=4y+8$ -------------------(1)

$\frac{x}{y-2}$ $=5$

$\Rightarrow x$ $=5y-10$ -------------------(2)

Solving (1) & (2)

$y$ $= 18$

$x$ = 80 km

There is a road beside a river. Two friends started from a place A, moved to a temple situated at another place B and then returned to A again. One of them moves on a cycle at a speed of 12 km/hr, while the other sails on a boat at a speed oi 10 km/hr. If the river flows at the speed of 4 km/hr, which of the two friends wit return to place A first ?

Answer:

Explanation:

Clearly, the cyclist moves both ways at a speed of 12 km/hr. So, average speed of the cyclist = 12 km/hr.

The boat sailor moves downstream at $(10 + 4)$ $=14$ km/hr

and upstream at $(10 - 4)$ $=6$ km/hr

So, average speed of the boat sailor $=\frac{2\times 14\times 6}{14+6}$ km/hr

$=\frac{42}{5}$ $=8.4$ km/hr.

Since the average speed of the cyclist is greater, he will return to A first.

A man can row 40 km upstream and 55 km downstream in 13 hours. Also, he can row 30 km upstream and 44 km downstream in 10 hours. Find the speed of the man in still water and the speed of the current.

Answer:

Explanation:

Let rate upstream $=x$ km/hr and rate downstream $=y$ km/hr.

Then, $\frac{40}{x}$ $+\frac{55}{y}$ $= 13$   ...(i)

and $\frac{30}{x}$ $+\frac{44}{y}$ $=10$      ...(ii)

Multiplying (ii) by 4 and (i) by 3 and subtracting, we get : $\frac{11}{y}$ $=1$ or $y$ $=11$.

Substituting $y=11$ in (i), we get : $x=5$.

$\therefore$ Rate in still water $=\frac{1}{2} (11+5)$ kmph = 8 kmph.

Rate of current $=\frac{1}{2} (11-5)$ kmph = 3 kmph. 

In a stream running at 2 kmph, a motorboat goes 6 km upstream and back again to the starting point in 33 minutes. Find the speed of the motorboat in still water.

Answer:

Explanation:

Let the speed of the motorboat in still water be $x$ kmph.

Then, speed downstream $=(x+2)$ kmph; Speed upstream $=(x-2)$ kmph.

$\therefore$ $\frac{6}{x+2}$ $+ \frac{6}{x-2}$ $=\frac{33}{60}$

$\Leftrightarrow$ $11x^{2}- 242x$ $+2x-44$ $=0$ $\Leftrightarrow$ $(x-22)(11x+2)=0$ $\Leftrightarrow x=22$. Hence, speed of

motorboat in still water = 22 kmph.

A man can row $7\frac{1}{2}$ kmph in still water. If in a river running at 1.5 km an hour, it takes him 50 minutes to row to a place and back, how far off is the place ?

Answer:

Explanation:

Speed downstream $=(7.5+1.5)$ kmph $=9$ kmph,

Speed upstream $=(7.5-1.5)$ kmph $=6$ kmph. 

Let the required distance be $x$ km.

Then, $\frac{x}{9}+\frac{x}{6}$ $=\frac{50}{60}$

$\Leftrightarrow 2x+3x$ $=\left(\frac{5}{6}\times 18\right) $

$\Leftrightarrow 5x$ $=15$ $\Leftrightarrow x= 3$

Hence, the required distance is 3 km.

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