Ram travelled from a place Z to P at an average speed of 130 km/h. He travelled the first 75% of the distance in two- third of the time and the rest at an average speed of X km/h. The value of $\frac{X}{2}$ is:

48.75

Let total distance = A km/h 

Time= \(\frac{A}{130}\) hours

75% of Distance = \(\frac{3}{4}\) × A

Time taken by him to cover 75% of distance = \(\frac{A}{130}\)×\(\frac{2}{3}\)

= \(\frac{A}{195}\)

Time taken to cover this left distance = \(\frac{A}{130}\) - \(\frac{A}{195}\)

= \(\frac{A}{390}\)

Remaining distance = A - \(\frac{3A}{4}\) = \(\frac{A}{4}\)

According to question ,

X = \(\frac{A}{4}\) × \(\frac{A}{390}\)

X = 97.5

Now ,

\(\frac{X}{2}\) = 48.75km