CAT 2024 Slot 3 QA Question 22: A train travelled a certain distance at a uniform speed. Had the speed been $6$ km per hour more, it would have needed $4$ hours less. Had the speed been $6$ km per hour less, it would have needed $6$

Question

A train travelled a certain distance at a uniform speed. Had the speed been $6$ km per hour more, it would have needed $4$ hours less. Had the speed been $6$ km per hour less, it would have needed $6$

Accepted Answer

Let the original speed be $v$ km/h and the original time be $t$ hours. Then the distance is $vt$.

Using the first condition:

$(v + 6)(t - 4) = vt$
$vt - 4v + 6t - 24 = vt$
$4v = 6t - 24$
$v = \dfrac{3}{2}(t - 4)$

Using the second condition:

$(v - 6)(t + 6) = vt$
$vt + 6v - 6t - 36 = vt$
$v = t +

A train travelled a certain distance at a uniform speed. Had the speed been 666 km per hour more, it would have needed 444 hours less. Had the speed been 666 km per hour less, it would have needed 666 hours more. The distance, in km, travelled by the train is

A train travelled a certain distance at a uniform speed. Had the speed been $6$ km per hour more, it would have needed $4$ hours less. Had the speed been $6$ km per hour less, it would have needed $6$ hours more. The distance, in km, travelled by the train is