To cover a distance of 450 km train A takes 1\(\frac{4}{5}\) hours more than train B.  If the speed of train A is doubled, it would take 1\(\frac{1}{5}\) hours less than train B.  What is the speed (in km/h) of train A?

75

Let, speed of train A = S_A

Speed of train B = S_B

According to 1st condition, 

\(\frac{450}{S_A}\) - \(\frac{450}{S_B}\) = \(\frac{9}{5}\)

\(\frac{1}{S_A}\) - \(\frac{1}{S_B}\) = \(\frac{9}{5 × 450}\) = \(\frac{1}{5 × 50}\) ..... (i)

According to 2nd condition, 

\(\frac{450}{S_B}\) - \(\frac{450}{2S_A}\) = \(\frac{6}{5}\)

\(\frac{1}{S_B}\) - \(\frac{1}{2S_A}\) = \(\frac{6}{5 × 450}\) = \(\frac{1}{5 × 75}\) ..... (ii)

adding equation (i) and (ii)

⇒ \(\frac{1}{S_A}\) - \(\frac{1}{S_B}\) + \(\frac{1}{S_B}\) - \(\frac{1}{2S_A}\) = \(\frac{1}{5 × 50}\) + \(\frac{1}{5 × 75}\)

⇒ \(\frac{1}{2S_A}\) = \(\frac{1}{5}\) [\(\frac{1}{50}\) + \(\frac{1}{75}\)]

⇒ \(\frac{1}{2S_A}\) = \(\frac{1}{5}\) [\(\frac{2 + 3}{150}\)]

⇒ \(\frac{1}{2S_A}\) = \(\frac{1}{150}\)

S_A= 75 km/h