Question

A boat goes $15km$ upstream and $22km$ down stream in $15$ hours. In $14$ hours it can go $45$ upstream and $55km$ down stream. The speed of the boat in still water in $km/hr$ is

• A. $3$
• B. $7$
• C. $6$
• D. $8$

Answer 1

Answer: (D)

$8$

Let speed of boat in still water(in $km/hr$) $=x$ and speed of stream(in $km/hr$) $=y$

Time required by the boat to travel $d$ kilometers upstream is $\frac{d}{x-y}$.

Time required by the boat to travel $d$ kilometers downstream is $\frac{d}{x+y}$.
According to the given condition,

$\frac{22}{x+y}+\frac{15}{x-y}=5$

And
$\frac{55}{x+y}+\frac{45}{x-y}=14$
Here only $x$ is to be found so option method cannot be used using substitution method
Let $\frac{1}{x+y}=u,\frac{1}{x-y}=v$
$22u+15v-5=0$
$55u+45v-14=0$
Then, by cross multiplication
$\frac{u}{-15\times 14-\left(45\right)\times -5}=\frac{v}{-5\times 55-22\times (-14)}$
$=\frac{1}{22\times 45-55\left(15\right)}$
$\frac{u}{-210+225}=\frac{v}{-275+308}=\frac{1}{990-825}$
$\frac{u}{15}=\frac{v}{33}=\frac{1}{165}$
$u=\frac{1}{11},v=\frac{1}{5}$
$x+y=11$, $x-y=5$

Add both the equations.
$\Rightarrow$ $2x=16$

$⟹x=8$