Desmond's gcse maths exam is next week. as part of his revision he attempted 31
questions on his least favourite topic of percentages. he got 21 questions fully right on the first attempt. two days later he tried all 31 questions again and this time got
29 correct.
what is the percentage improvement in desmond's results?

The easiest way (for me) to count it is to find how much 1 percent is. We know that 31 is 100%, so 1% will be 100 / 31, which is (after rounding to the hundredths) 3,23.

At the first attempt he gave 21 correct answers, so he made 21 * 3,23 = 67,83%.

At the second attempt he gave 29 correct anserws, so he made 29 * 3,23 = 93,67%.

The difference between 97,67% and 67,83% is 25,84% - and that's his improvement :)