Percentage Mad
Weekly Problem 43 - 2013
What is 20% of 30% of 40% of £50?
What is 20% of 30% of 40% of £50?
Age
11 to 14
Challenge level
Problem
What is $20\%$ of $30\%$ of $40\%$ of $ £50$?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: $ £1.20$
Finding the percentages
$20\%\text{ of } 30\%\text{ of }\underbrace{ 40\%\text{ of } £50}_{ £20}$
$=20\%\text{ of } \underbrace{30\%\text{ of } £20}_{ £6}$
$=60\text{p} + 60\text{p} = £1.20$
Using fractions
$20\%\times30\%\times40\%\times £50\\
=\frac1{5}\times\frac3{10}\times\frac2{5}\times £50\\
= £\frac{3\times2}{5\times10\times5}\times10\times5\\
= £\frac{3\times2}5\\
= £\frac 65\\
= £1.20$
Using decimals
$20\%$ of $30\%$ of $40\%$ of $ £50$ can be written as $0.2 \times 0.3 \times 0.4 \times 50 = 0.06 \times 20 = 1.2$, so the answer is $ £1.20$