I have to give an overall percentage score to learners after they sit two tests.
The first test is scored from 16 and the second is scored from 48. The overall score, therefore, is taken from 64.
Let's say a learner scores 16 on the first test (100%) and 36 on the second (75%) then their overall score from 64 is 52 for an overall percentage of 81%.
Without knowing the initial scoring conditions, is there any way to derive that 81% from the individual percentages, 100% and 75%?
If you have done x% of one thing and y% of another thing, then you have completed z% overall, and it seems logical to me that z must have some relationship to x and y, but I cannot work it out.
Sorry if this is way more simple than I am making it out to be!
You're right that this doesn't work. What you're calculating is a weighted mean, meaning that for $n$ percentages ($p_1,p_2,\dots,p_n$) you have a set of $n$ corresponding weights ($w_1,w_2,\dots,w_n$) that sum to 1. The weighted mean is then calculated as $$ \sum_{k=1}^np_kw_k $$ Without knowing the weights, you can only calculate the mean (un-weighted), or end up with some equation with unknown weights such as $100w_1+75w_2$.
In almost all cases, the $n$th weight ($w_n$) will be the highest mark for the $n$th test divided by the sum of the highest marks for all tests. This only changes if you weight specific tests.