# Algebra word problem : magician

A magician is playing mind tricks with the audience. He asks one member of the crowd to think of two numbers, write them on pieces of paper and throw them into his hat. Meanwhile, the magician also thinks of a number and drops it into the hat. He then waves his wand and a shiny paper comes out of the hat. The numbers the member of the audience picked are both less than the number the magician dropped into the hat. The first number is 40 percent less than the magician's number, while the second number is 50 percent less than the same. The shiny paper has the percentage comparison of the two numbers from the audience member. What is the percentage on the shiny paper?

I took the numbers as $$x$$, $$0.6x$$ and $$0.5x$$, but by that logic we get the answer as 120.

You seem to have done everything correctly other than the fact that you need to find the percentage difference of both numbers given by the audience and not there percentage ratio. So rather than doing, $$\frac{0.6}{0.5}*100\%=120\%$$ do $$\frac{0.6-0.5}{0.5}*100\%=20\%$$.