In covering a distance, the speeds of A & B are in the ratio of 5 : 4. A takes 30 minutes less than B to reach the destination. Find the time taken by A to reach the destination.

Sure, let's solve this step by step:

Step 1: Let's assume the common distance they both cover is D km. The speeds of A and B are in the ratio 5:4. So, let's say the speed of A is 5x km/hr and the speed of B is 4x km/hr.

Step 2: We know that time is equal to distance divided by speed. So, the time taken by A to cover the distance D is D/(5x) hours and the time taken by B is D/(4x) hours.

Step 3: According to the problem, A takes 30 minutes less than B to reach the destination. We can write this as: D/(4x) - D/(5x) = 30/60 (since we need to convert minutes into hours)

Step 4: Simplifying the above equation, we get D/x = 300. This means that the distance D is 300x km.

Step 5: Now, we can find the time taken by A to reach the destination by substituting D = 300x into the time equation for A: Time_A = D/(5x) = 300x/(5x) = 60 hours.

So, A takes 60 hours to reach the destination.