Question : The speed of Ashu is 15 km/hr more than the speed of Vishu. They start moving in the same direction at the same time, but initially, Vishu is ahead of Ashu by a certain distance. If Ashu crosses Vishu 6 hours after they start moving, what is the initial distance between them?
Option 1: 45 km
Option 2: 60 km
Option 3: 90 km
Option 4: 80 km
Correct Answer: 90 km
Solution :
Let the speed of Vishu be = $x$ km/hr
The speed of Ashu will be = $x$ + 15 km/hr
Also, let the initial distance covered by Vishu be $d$ km.
It is given that Vishu initially is ahead of Ashu by a certain distance. Let this distance be a km. So, the distance covered by Vishu before Ashu overtakes him in 6 hours is '$a$' km.
$\because$ Distance = Speed $\times$ Time
$a$ = $x$ $\times$ 6 = 6$x$
Also, Ashu will have to cover the initial distance plus the extra distance travelled by Vishu in that time. So, the distance covered by Ashu before he overtakes is '$a$ + $d$' km.
⇒ $a + d = 6(x+15)$
⇒ 6$x$ + d = 6$x$ + 90
⇒ $d$ = 90 km
$\therefore$ The initial distance between them is 90 km.
Hence, the correct answer is 90 km.
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