Working out percentage in reverse

Question

Trying to brush up my appalling maths and came unstuck on this example:

"If I earned $11 yesterday, and that's a 96% drop, how much do I normally earn?"

I started approaching this as follows:

If $\$11 = 96%$ drop, it means $\$11 = 4\%$ of the total

therefore:

$\$11 \cdot \frac{10}{4} = \$27.5\ (10\%) \cdot 100 = \$275 (100\%)$

Is that the easiest way to arrive at that figure?

Thanks,

Osu

Answer 1

Yes you are correct, a $96\%$ drop means you take $x - .96x = .04x$ therefore:

$$ 11 = (1 - .96)x = .04x \rightarrow x = \frac{11}{.04} = 11\times\frac{1}{\frac{4}{100}} = 11\times\frac{1}{\frac{1}{25}} = 11\times\frac{25}{1} = 275 $$