Question

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

• A. $40$ km
• B. $28$ km
• C. $42$ km
• D. $48$ km

Answer 1

The correct option is A $40$ km

Let distance be $x$ Kmph and speed $y$ kmph
Now, according to question,
$\frac{x}{y}-\frac{x}{y+3}=\frac{40}{60.}$

$\frac{3x}{y(y+3)}=\frac{2}{3}$ ...................................(i)

$\frac{x}{y-2}-\frac{x}{y}=\frac{40}{60}$

Divide (i) by (ii)

$\frac{2x}{y(y-2)}=\frac{2}{3}$ .........................(ii)

Divide (i) and (ii)

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

$3y^2-6y=2y^2+6y$

$y^2-12y=0$

$y=0,y=12$

From (i)

Substitute value of $y=12$ in (i)

$\frac{3x}{12(12+3}=\frac{2}{3}$

$x=40$ kmph.