Question

A man covered a certain distance at some speed. Had he moved $3$ $kmph$ faster he would taken $40$ minutes less. If he had moved $2$ $kmph$ slower, he would have taken $40$ minutes more. The distance in $km$ is:

• A. $35$
• B. $36\frac{2}{3}$
• C. $37\frac{1}{2}$
• D. $40$

Answer 1

Answer: (D)

$40$

Let distance$=x$ km and usual rate$=ykm/hr$

Then, $\frac{x}{4}-\frac{x}{y+3}=\frac{40}{60}\Rightarrow 2y(y+3)=9x.............\left(1\right)$

And $\frac{x}{y-2}-\frac{x}{y}=\frac{40}{60}\Rightarrow y(y-2)=3x.............\left(2\right)$

On dividing (1) by (2), we get

$\frac{2(y+3)}{y-2}=3$

$\Rightarrow 2y+6=3y-6$

$x=40$.