A packet of chocolates contains pieces of milk, dark and orange chocolates. 25% of the chocolates are dark chocolates. The ratio of the number of dark chocolates to the number of milk chocolates is 5 : 7. There are 78 pieces of dark and orange chocolates. What is the total number of pieces of chocolates in the packet?

1. Find the percentage of milk chocolates using the given ratio

The ratio of dark to milk chocolates is $5 : 7$. Since dark chocolates make up $25\%$ of the total, $5 \text{ units} = 25\%$.
$1 \text{ unit} = 25\% \div 5 = 5\%$.
Percentage of milk chocolates = $7 \times 5\% = 35\%$.

2. Find the percentage of orange chocolates

Percentage of orange chocolates = $100\% - 25\% - 35\% = 40\%$.

3. Find the total percentage of dark and orange chocolates

Percentage of dark and orange chocolates = $25\% + 40\% = 65\%$.

4. Calculate the total number of chocolates

We are given that there are $78$ pieces of dark and orange chocolates.
$65\% \rightarrow 78$
$1\% \rightarrow \frac{78}{65} = 1.2$
$100\% \rightarrow 1.2 \times 100 = 120$
The total number of chocolates is $120$.