**Given Information:**

- Average cost of 5 apples and 4 mangoes is 36.
- Average cost of 7 apples and 8 mangoes is 48.

**Let's solve the problem step by step:**

1. **Calculating the total cost of 5 apples and 4 mangoes:**

- Average cost of 5 apples and 4 mangoes = 36

To find the total cost, we need to multiply the average cost by the number of items.

- Total cost of 5 apples = 36 * 5 = 180
- Total cost of 4 mangoes = 36 * 4 = 144

Therefore, the total cost of 5 apples and 4 mangoes is 180 + 144 = 324.

2. **Calculating the total cost of 7 apples and 8 mangoes:**

- Average cost of 7 apples and 8 mangoes = 48

Similar to the previous step, we can calculate the total cost.

- Total cost of 7 apples = 48 * 7 = 336
- Total cost of 8 mangoes = 48 * 8 = 384

Therefore, the total cost of 7 apples and 8 mangoes is 336 + 384 = 720.

3. **Calculating the cost of each apple and each mango:**

Let's assume the cost of each apple is 'x' and the cost of each mango is 'y'.

- 5x + 4y = 324 (Equation 1)
- 7x + 8y = 720 (Equation 2)

4. **Solving the system of equations:**

To find the values of 'x' and 'y', we can solve the system of equations given above.

Multiplying Equation 1 by 2 and Equation 2 by 5 to eliminate 'y':

- 10x + 8y = 648 (Equation 3)
- 35x + 40y = 3600 (Equation 4)

Subtracting Equation 3 from Equation 4:

- 35x + 40y - 10x - 8y = 3600 - 648
- 25x + 32y = 2952 (Equation 5)

5. **Solving Equation 5 for 'y':**

Rearranging Equation 5:

- 32y = 2952 - 25x
- y = (2952 - 25x) / 32 (Equation 6)

Now we have the value of 'y' in terms of 'x'.

6. **Substituting the value of 'y' in Equation 1:**

- 5x + 4((2952 - 25x) / 32) = 324

Solving this equation will give us the value of 'x'.

7. **Calculating the total cost of 24 apples and mangoes:**

Once we have the values of 'x' and 'y', we can calculate the total cost of 24 apples and mangoes.

- Total cost of 24 apples = 24