If we are interested in a part of a part of something, i.e. 20% of 80% of something, we can multiply those percentages together to find out how much the part is.

If we are looking at percentage increase and there is more than one increase, then it is a little bit more difficult. So, if we are considering a 20% increase, we should think of this as 120% of the original amount. Then we can follow the same approach and if there is , more than one increase, just multiply the percentages together (e.g. to calculate the overall increase of a 30% increase followed by a 40% increase we should take 130% x 140% and subtract the original 100% from our answer).

Let’s try some of each of those two types with the teacher and then do the exercise.

Compound Percentages Exercise

1. I start off with a certain amount of money.  I give 80% of it to my sister.  She gives 30% of what she receives to her friend.  How much of my money does she give to her friend?

2. 75% of my friends like skiing.  Of my skiing friends, 10% of them like yoga.  What percentage of my friends like yoga?

3. My height increased by 20% last year.  I have grown another 10% taller this year.  How much taller am I now that I was 2 years ago?

4. My friend eats 10% more food than me.  Her friend eats 15% more food than her.  How much more food does her friend eat than me?

5. In year 8 I worked 15% harder than in year 7 and improved my results by one grade.  In year 9 I worked 35% harder than in year 8 and improved my results by another grade.  Then in year 10 I worked 45% harder than in year 9 and improved my results by a further grade.  How much harder was I working in year 10 than in year 7?

Answers(1.) 24% (2.) 7.5% (3.) 32% (4.) 26.5% (5.) 125%