Competition problem — Algebra — Maths Olympiad Prep

Library / /12 of 60

Algebra Difficulty 3.8 AMC 10/12 Find the answer South Africa

When $a$ is increased by $20\%$ and $b$ is decreased by $20\%$ the resulting values are equal. The ratio of $a$ to $b$ is

Pick one

Solution

$120\%$ of $a$ is $\frac{6}{5}a$ while $80\%$ of $b$ is $\frac{4}{5}b$ .
We thus have $\frac{6}{5}a = \frac{4}{5}b$ from which it follows that $\frac{a}{b} = \frac{4}{5} \times \frac{5}{6} = \frac{2}{3}$

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: MathNet, licensed CC-BY-4.0. Statement and solution reproduced as published; topic and difficulty added by this site.