1. If only 1st statment taken into consideration:
$$y=0.30x$$ (Where y= distance from Madras to Trivandrum and x= distance from Calcutta to Madras)
Nothing absolute can be said about average speed from Madras to Trivendrum.
2. If only 2nd statement taken into consideration:
$$frac{y}{t_y} = 2frac{x}{t_x}$$ ( Where tx and ty are time taken for calcutta to madras and madras to trivendrum respectively.)
And nothing absolute can be said about average speed from Madras to Trivendrum.
3. Now when both statements taken into consideration:
We will have $$y=0.30x$$;  $$frac{y}{t_y} = 2frac{x}{t_x}$$ and $$frac{x+y}{t_x+t_y}$$ = 40 (Given)
After solving above three equations we can find a unique value for average speed from Madras to Trivendrum i.e. 
 $$frac{y}{t_y} = frac{920}{13}$$
Hence answer will be C.