**Problem Analysis:**

- Akishat starts moving with a velocity of 2 m/s.
- Hariom starts moving after some time.
- Both Akishat and Hariom reach their destination, which is 1000 m away.
- We need to find the ratio of the initial velocities of Akishat and Hariom, given that the ratio of their accelerations is 20:3.

**Solution:**

Let's break down the problem into smaller steps to find a solution.

**Step 1: Find the time taken by Akishat to reach the destination.**

We can use the formula:

\[ \text{Distance} = \text{Initial Velocity} \times \text{Time} + \frac{1}{2} \times \text{Acceleration} \times \text{Time}^2 \]

In this case, the acceleration is zero because Akishat is moving with a constant velocity. So, the equation becomes:

\[ 1000 = 2 \times \text{Time} \]

Simplifying the equation, we get:

\[ \text{Time} = \frac{1000}{2} = 500 \text{ seconds} \]

**Step 2: Find the time taken by Hariom to reach the destination.**

Since Hariom starts moving after some time, we need to find the time delay between Akishat and Hariom.

Let's assume the time delay is \( t \) seconds. So, Akishat has been moving for \( 500 + t \) seconds when Hariom starts.

Using the formula from Step 1, we can find the distance covered by Akishat during this time:

\[ \text{Distance} = 2 \times (500 + t) \]

Now, let's find the time taken by Hariom to cover the remaining distance (1000 m - distance covered by Akishat):

\[ \text{Time} = \frac{\text{Distance}}{\text{Velocity}} = \frac{1000 - 2 \times (500 + t)}{\text{Velocity}} \]

**Step 3: Find the ratio of the initial velocities.**

We are given that the ratio of accelerations is 20:3. Since the initial velocities are not given, we need to find the ratio of the initial velocities.

We know that acceleration is the rate of change of velocity. So, the ratio of accelerations is equal to the ratio of the change in velocities.

Let's assume the initial velocities of Akishat and Hariom are \( u_1 \) and \( u_2 \) respectively.

The change in velocity for Akishat is \( 2 - u_1 \) and the change in velocity for Hariom is \( \text{Velocity} - u_2 \).

So, we have the equation:

\[ \frac{2 - u_1}{\text{Acceleration of Akishat}} = \frac{\text{Velocity} - u_2}{\text{Acceleration of Hariom}} \]

Substituting the given ratio of accelerations (20:3), we get:

\[ \frac{2 - u_1}{20} = \frac{\text{Velocity} - u_2}{3} \]

Simplifying the equation, we get:

\[ 3(2 - u_1) = 20(\text{