I got 30% on a 10-problem test, 70% on a 20-problem test and 80% on a 30-problem test. If the three tests are combined in one 60-problem test what percentage is my overall score?

Answer 1

30% on the 10 problem test = 30%*10=3
70% on the 20 problem test = 70%*20=14
80% on the 30 problem test = 80%*30=24
=> total right problem is 41.the percentage is 41*100/60=

Answer 2

That result is like adding
3/10 + 14/20 + 24/30 = 41/60

Wow, just adding the numerators and the denominators ! Unfortunately Math doesn't work like that

3/10 + 14/20 + 24/30
= 18/60 + 42/60 + 48/60
= 108/60 for 3 tests

so average = (108÷3)/60 = 36/60 = 60%

By simply adding the numerator and denominators you are "weighting" the tests.
This is a major topic in statistics.
There are also many on-line calculators to calculate marks weighed differently.
Here is one of them:
http://www.rapidtables.com/calc/grade/grade-calculator.htm

Notice also by simply averaging the 3 percentages we get 60% as well. That is because percentages all have the same denominator of 100, so the normally erroneous method of just adding the numerators and denominators does work.
i.e.
average of (30/100 + 70/100 + 80/100)
---> 180/300 = .6 or 60%

Without knowing what the weight factors are this question can't really be answered.

Answer 3

You can calculate like below:

30% on (10 problem test) = 30% x 10 = 3
70% on (20 problem test) = 70% x 20 = 14
80% on (30 problem test) = 80% x 30 = 24
Total of problems = 41
in (%) = 41 x 100/60= 68.33%

Also, you can calculate in this tool: gradecalculator.tech