Question

A car travels from $P$ to $Q$ at a constant speed. If its speed were increased by $10$ km/hr , it would have taken one hour lesser to cover the distance. It would have taken further $45$ minutes lesser if the speed was further increased by $10$ km/hr. What is the distance between the two cities?

• A. $420$ km
• B. $540$ km
• C. $600$ km
• D. $650$ km

Answer 1

The correct option is A $420$ km

Let $x$ be the speed in Km/hr and $h$ be the time taken in hrs.
$\therefore xh=D.......\left(1\right)$,
Where D in the distance in Km.
If its speed were increased by 10 km / hr It would have taken one hour lesser to cover the distance.
$\therefore$$(x+10)(h-1)=D........\left(2\right)$
From (1) and (2),
$\therefore 7x-70h=-70.......\left(3\right)$

It would have taken further 45 minutes lesser if the speed was further increased by 10 km / h.
$\therefore$$(x+20)(h-\frac{7}{4})=D........\left(4\right)$
From (1) and (4),
$\therefore 7x-80h=-140.......\left(5\right)$
Solving (4) and (5) we get,
$h=7hrsandx=60$Km/hr
$\therefore$Distance between two cities is$=xh=420Km$