Question

A man covers a distance of $200$ km travelling with a uniform speed of $x$ km per hour. The distance could have been covered in $2$ hours less, had the speed been $(x+5)$ km per hour. Calculate the value of $x$.

• A. $20$
• B. $24$
• C. $28$
• D. $32$

Answer 1

The correct option is A $20$

Speed of the car $=x$ km /hr
Time taken $=t$ hrs
$xt=200$

$\therefore t=\frac{200}{x}$

Now, $(x+5)(t-2)=200$

$(x+5)(\frac{200}{x}-2)=200$

$(x+5)(200-2x)=200x$
$200x-2x^2+1000-10x=200x$
$x^2+5x-500=0$
$x^2+25x-20x-500=0$
$(x+25)(x-20)=0$
$x=-25,x=20$
Speed cannot be negative value, hence, $x=20$ km/hr