To solve this problem, we need the total number of trees in the garden. Let's break this into steps:

1. Assume the total number of trees in the garden is $N$.
2. $25\%$ of the trees are apple trees, so the number of apple trees is: $\text{Apple trees} = 0.25 \times N$
3. $62.5\%$ of the trees are lemon trees, so the number of lemon trees is: $\text{Lemon trees} = 0.625 \times N$
4. The remaining percentage will be for mango trees: $100\% - (25\% + 62.5\%) = 12.5\%$ Hence, the number of mango trees is: $\text{Mango trees} = 0.125 \times N$

The final answer depends on $N$. If you provide the total number of trees, I can calculate the exact number of each type.

Would you like to provide the total number, or should I explain further? Here are some follow-up questions for you:

1. What is the total number of trees in the garden?
2. Should I proceed with calculations assuming $N = 100$ (a standard assumption)?
3. Do you need percentages explained in more detail?
4. Would you like this calculation expressed in a different format (e.g., as fractions)?
5. Is there a specific step you would like clarified in more depth?

Tip: Percentages can always be converted to decimals for calculations (e.g., $25\% = 0.25$).