Question

A man walks a distance of 48 km in a given time. If he walks 2 km/hr faster, he will perform the journey 4 his before. His normal rate of walking is _______.

• A. 3 km/hr
• B. 4 km/hr
• C. - 6 km/hr or 4 km/hr
• D. 5 km/hr

Answer 1

The correct option is B 4 km/hr

Let us assume that the man walks at a speed of $x$ $kmph$

Then the time taken by the man to complete the journey is $t=\frac{48}{x}$ ($\because time=\frac{distance}{speed}$)

Now in the second case, $t^{\prime }=t-3$ and $x^{\prime }=x+2$.

Then,

$t-4=\frac{48}{x+2}$

$\Rightarrow$ $t-\frac{48}{x+2}=4$

$\Rightarrow$ $\frac{48}{x}-\frac{48}{x+2}=4$

$\Rightarrow$ $\frac{96}{x(x+2)}=4$

$\Rightarrow$ $x^2+2x=24$

$\Rightarrow$ $x^2+2x-24=0$

$\Rightarrow$ $x^2-4x+6x-24=0$

$\Rightarrow$ $(x-4)(x+6)=0$

Speed cannot be a negative value and hence $x=4kmph$

$\therefore$ Option B is correct.