Question

A and B are 25 Km apart, if they travel in opposite directions they meet after one hour, if they travel in the same direction they meet after 5 hours. If A travels faster than B then the speed of A is,
 $ \left( a \right) $ 10 Km/hr.
 $ \left( b \right) $ 12.5 Km/hr.
 $ \left( c \right) $ 15 Km/hr.
 $ \left( d \right) $ 20 Km/hr.

Answer 1

Hint: In this particular question use the concept of the relative velocity, if two objects travel in opposite directions then their relative velocity is the addition of their respective velocity opposite case when they move in the same direction, so use these concepts to reach the solution of the question.

Complete step-by-step answer:
Given data:
A and B are 25 Km apart.
Let the velocity of A be u km/hr. and the velocity of B be v km/hr.
It is given that the velocity of A is greater than B.
Therefore, u > v
Now according to the theory of relativity when two objects travel in opposite directions then their relative velocity is the addition of their respective velocity.
So when A, and B moves in opposite directions their relative velocity = (u + v) Km/hr.
Now it is given that they meet after 1 hour when they travel in the opposite direction.
Noe as we know that, velocity = $ \dfrac{{{\text{distance}}}}{{{\text{time}}}} $
 $ \Rightarrow u + v = \dfrac{{25}}{1} = 25 $ .............. (1)
Now according to the theory of relativity when two objects travel in the same direction then their relative velocity is the difference of their respective velocity.
So when A, and B move in the same direction their relative velocity = (u - v) Km/hr.
Now it is given that they meet after 5 hour when they travel in the same direction.
Noe as we know that, velocity = $ \dfrac{{{\text{distance}}}}{{{\text{time}}}} $
 $ \Rightarrow u - v = \dfrac{{25}}{5} = 5 $ .............. (2)
Now add equation (1) and (2) we have,
 $ \Rightarrow u + v + u - v = 25 + 5 $
 $ \Rightarrow 2u = 30 $
 $ \Rightarrow u = \dfrac{{30}}{2} = 15 $ Km/hr.
So the speed of A is 15 Km/hr.
Hence option (C) is the correct answer.

Note: Whenever we face such types of question the key concept involved here is relative velocity, so according to the theory of relativity first find out the sum and addition of the velocities as above, then add them and simplify we will get the required speed of A, always remember that velocity is the ratio of the distance to time.