Define the "ages", "other ages" and "older ages" or "younger ages" of three people. Then find the ages of three people if the ratio of their ages is 3:4:5 and the difference between the eldest and youngest is 8 years.

Given ratios:
Peter : John = 3 : 4
John : Mary = 5 : 6

To combine these, we need a common value for John's share. The least common multiple (LCM) of 4 and 5 is 20.

Adjust the first ratio:
Multiply (3 : 4) by 5:
Peter : John = $(3 \times 5) : (4 \times 5) = 15 : 20$

Adjust the second ratio:
Multiply (5 : 6) by 4:
John : Mary = $(5 \times 4) : (6 \times 4) = 20 : 24$

So, the combined ratio for Peter : John : Mary is $15 : 20 : 24$.

We are given that Mary's share is N120.00.
From the combined ratio, Mary's share corresponds to 24 parts.

$$24 \text{ parts} = \text{N}120.00$$

To find the value of 1 part:

$$1 \text{ part} = \frac{\text{N}120.00}{24} = \text{N}5.00$$

Peter's share = 15 parts

$$\text{Peter's share} = 15 \times \text{N}5.00 = \text{N}75.00$$

John's share = 20 parts

$$\text{John's share} = 20 \times \text{N}5.00 = \text{N}100.00$$

The sum of their shares is the total of Peter's, John's, and Mary's shares.

$$\text{Sum of shares} = \text{Peter's share} + \text{John's share} + \text{Mary's share}$$ $$\text{Sum of shares} = \text{N}75.00 + \text{N}100.00 + \text{N}120.00$$ $$\text{Sum of shares} = \text{N}295.00$$

Alternatively, sum of ratio parts = $15 + 20 + 24 = 59$ parts.

$$\text{Sum of shares} = 59 \times \text{N}5.00 = \text{N}295.00$$

The sum of their shares is:

$$\text{N}295.00$$