CEMC Cayley, 2023

Solution 1

Suppose that the original number is 100.

When 100 is increased by 60%, the result is 160.

To return to the original value of 100, 160 must be decreased by
60.

This percentage is $\frac{60}{160} \times 100\% = \frac{3}{8} \times 100\% = 37.5\%$.

Solution 2

Suppose that the original number is $x$ for some $\text{x gt; 0}$.

When $x$ is increased by 60%, the
result is $1.6x$.

To return to the original value of $x$, $1.6x$ must be decreased by $0.6x$.

This percentage is $\frac{0.6x}{1.6x} \times 100\% = \frac{3}{8} \times 100\% = 37.5\%$.