A takes 8 hours more than the time taken by B to cover a distance of 160 km. If A doubles his speed, he takes 3 hours more than B to cover the same distance. The speed (in km/h) of is:

80

Let speed of A = A km/h

Speed of B = B km/h

According to question ,

\(\frac{160}{A}\) -  \(\frac{160}{B}\) = 8  ------(1)

\(\frac{160}{2A}\) -  \(\frac{160}{B}\) = 3

\(\frac{80}{A}\) -  \(\frac{160}{B}\) = 3   --------(2)  

Multiply equation (1) by \(\frac{1}{2}\)

\(\frac{80}{A}\) -  \(\frac{80}{B}\) = 4   -----(3)

\(\frac{80}{A}\) = 4 + \(\frac{80}{B}\)

Put in (2)

4 + \(\frac{80}{B}\) -  \(\frac{160}{B}\) = 3

On solving B = 80 km/h

So , Speed of B is 80 km/h