Copyright © University of Cambridge. All rights reserved.

'Valuable Percentages' printed from https://nrich.maths.org/

Show menu


Answer: the greatest is 30% of 30


Finding the values
50% of 10 = 10$\div$2 = 5                           

40% of 20 = 10$-$2 = 8 

30% of 30 = 3$\times$3 = 9        

20% of 40 = 4 + 4 = 8

10% of 50 = 50$\div$10 = 5

So 30% of 30 is the greatest


Using commutativity and strategy
$50\% \text{ of } 10 = \frac{50}{100}\times10 = \frac{10\times50}{100} = \frac{10}{100}\times50 = 10\%\text { of }50$

Similarly, $40\% \text{ of }20 = 20\%\text{ of }40$

So $30\%\text{ of }30$ is the only one without a partner - so it must be the greatest, because there is only one answer


This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.