X and Y start traveling in the same direction, from a particular point

\(Speed = \frac{Distance}{Time}\)

Question: Time of meeting = ?

To answer the question we need the speeds of X and Y alongwith the distance that they are travelling together

Statement 1:Y = 2X
We know the ratio of speeds but we don't know the speeds and distance hence
NOT SUFFICIENT

Statement 2: After 5 hours, Y is 10 miles ahead of X.
i.e. at relative speed the total distance change in 5 hours between X and Y = (Distance travelled by X in 45 mins+10)
but neither do we know the speed of x and Y nor do we know any relationship between their speeds hence
NOT SUFFICIENT

Combining the two statements

Now we know that the speed of Y is double the speed of X and
i.e. Relative speed = Y-X = 2X-X = X

(the distance travelled by Y in 5 hours) = (Distance of X in 5 hour and 45 mins) + 10
i.e. 5*Y = 5.75*X + 10
i.e. 5*(2X) = 5.75*X + 10
which gives us the value of X adn Y both i.e. their speeds

Now, Time of meeting = 5 hours - (time to travel 10 miles at their relative speeds)

since we know their speeds so we can canculate the time they will take to travel 10 miles at their relative speeds hence

SUFFICIENT

Answer: Option C