# Two cars start at a point A at the same time. The first car goes with a uniform speed of 100 Km/hr and the second car starts at 80 for the first hour and increases the speed by 10 km/hr every hour. After how much time does the second car overtake the first car, assuming these are no stops in between.

$\begin{array}{1 1} 4\;hours \\ 5\;hours \\ 7\;hours \\ 9\;hours \end{array}$

$Explanation\;:\;Let\;number\;of\;hours\;be\;n\;distance\;covered\;by\;1^{st}\;car=100n$
$Distance\;covered\;by\;2^{nd}\;car=\frac{n}{2}\;[2*80+(n-1)10]$
$At\;n^{th}\;hour\;=>\;\frac{n}{2}\;[160+(n-1)10]=100n$
$(n-1)10=200-160=40$
$n-1=4$
$n=5\;hours.$