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

The speed of a boat in still water is 8 km/hr. If it can travel 20 km down stream at the same time as it can travel 12 km upstream, the rate of stream (in km/hr) is

Answer:

Explanation:

Let rate of stream $=x$ km/hr

Speed of boat in still water $=8$ km/hr 

Upstream speed $=(8-x)$ km/hr

Downstream speed $=(8+x)$ km/hr

Given, $\frac{20}{( 8 + x )}$ $=\frac{12}{( 8-x )}$

$\Rightarrow 160-20x$ $=96+12x$

$\Rightarrow 32x$ $=64$ $\Rightarrow x$ = 2 km/hr.

A person can row a boat $d$ km upstream and the same distance downstream in 5 hours 15 minutes. Also, he can row the boat $2d $ km upstream in 7 hours. How long will it take to row the same distance $2d$ km downstream?

Answer:

Explanation:

Let the speeds of boat and stream be $x$ and $y$ km/hr respectively.

Then, Rate downstream $=(x+y)$ km/hr and Rate upstream $=(x-y)$ km/hr

Given $\frac{d}{(x+y)} +\frac{d}{( x-y )}$ $=5$ hrs $15$ minutes $=\frac{21}{4}$ hours

and $\frac{2d}{(x-y)}$ $= 7$ $=\frac{d}{(x-y)}$ $\frac{7}{2}$

$\Rightarrow\frac{d}{(x+y)}$ $=\frac{21}{4}-\frac{7}{2}$ $=\frac{7}{4}$

$\Rightarrow\frac{2d}{(x+y)}$ $=\frac{7}{2}$

Hence, he takes $\frac{7}{2}$ hours to row $2d$ km distance downstream.

A boat takes half time in moving a certain distance downstream than upstream. What is the ratio between rate in still water and rate of current?

Answer:

Explanation:

Let the speed of boat in still water be $=x$ km/hr and that of current $=y$ km/hr

Rate upstream $=(x-y)$ km/hr and Rate downstream $=(x+y)$ km/hr

Let distance covered in each case be $d$ km

$\frac{2d}{( x+y )}$ $=\frac{d}{( x-y )}$

$\Rightarrow 2x-2y$ $=x+y$

$\Rightarrow x=3y$ $\Rightarrow\frac{x}{y}$ $=\frac{3}{1}$ = 3 : 1.

The speed of a motor boat to that of the current of water is 36 : 5. The boat goes along with the current in 5 hours 10 minutes. It will come back in

Answer:

Explanation:

Let speed of motor boat $= 36x$ km/hr

Speed of current $= 5x$ km/hr

The boat goes along with the current in $\frac{31}{6}$ hrs (5 hrs 10 mins)

Distance $=\left({\frac{31}{6}}\times (36x + 5x)\right)$ $=\frac{(41x\times 31)}{6}$

Rate upstream $=36x-5x$ $=31x$

Time taken $=\left(\frac{41x\times\frac{31}{6}}{31x}\right)$ $=\frac{41}{6}$ hrs = 6 hrs 50 minutes.

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