In an English test, Alvin scored 28 out of 40 marks. In a Mathematics test, he scored 36 out of 60 marks.

(a) In which test did Alvin score better?

(b) What was the percentage difference between Alvin's scores for both tests?

a) 28/40*100 = 70%

36/60*100 = 60%
He did better on 28/40
b) He did 10% better on the first test

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To compare Alvin's scores in the English and Mathematics tests, we need to calculate the percentages of marks he scored in each test.

To find the percentage score for a test, use the formula:

Percentage score = (Marks obtained / Total marks) * 100

(a) To determine which test Alvin scored better in, we compare the percentage scores he obtained in each test.

For the English test:
Marks obtained = 28
Total marks = 40

English test percentage score = (28 / 40) * 100 = 70%

For the Mathematics test:
Marks obtained = 36
Total marks = 60

Mathematics test percentage score = (36 / 60) * 100 = 60%

Comparing the two percentage scores, Alvin scored better in the English test with a score of 70%, compared to his score of 60% in the Mathematics test. Therefore, Alvin scored better in the English test.

(b) To find the percentage difference between Alvin's scores in both tests, we use the formula:

Percentage difference = |(Score in Test A - Score in Test B) / ((Score in Test A + Score in Test B) / 2)| * 100

In this case, Test A corresponds to the English test and Test B corresponds to the Mathematics test.

Percentage difference = |(70 - 60) / ((70 + 60) / 2)| * 100

Calculating this:

Percentage difference = |10 / 65| * 100 = 15.38%

Therefore, the percentage difference between Alvin's scores in both tests is approximately 15.38%.