Question

X and Y are two towns. A man goes from town X to town Y at an average speed of $30$ km per hour and returns at an average speed of $20$ km per hour. Find the distance between the two towns if a man takes $10$ hours on the whole.

• A. $40$ km
• B. $120$ km
• C. $110$ km
• D. $50$ km

Answer 1

Answer: (B)

$120$ km

$speed=\frac{distance}{time}$

Let the distance from X to Y be $dkm$

Let the time taken from X to Y at a speed of $30km/hr$ be $t_1$

Therefore,

$\Rightarrow 30=\frac{d}{t_1}$

$\Rightarrow d=30t_1$

And, Let the time taken from Y to X at a speed of $20km/hr$ be $t_2$

Therefore,

$\Rightarrow 20=\frac{d}{t_2}$

$\Rightarrow d=20\left(t_2\right)$

Therefore, $30\left(t_1\right)=20\left(t_2\right)$

$\Rightarrow \frac{t_1}{t_2}=\frac{20}{30}$

$\Rightarrow t_1=\frac{2}{3}{t}_2$ ..............(i)

Now, the total time taken is $10hrs$

Therefore, $10=t_1+t_2$ .................(ii)

Substituting equation i in ii, we get

$\Rightarrow 10=\frac{2}{3}{t}_2+t_2$

$\Rightarrow 5t_2=30$

$\Rightarrow t_2=6$

Substituting $t_2=6$ in $20=\frac{d}{t_2}$ we get

$20=\frac{d}{6}$

$d=120km$