How do you find by what percent a number is more or less than another number.

Question

Lets say by what percent 50 is less than 100?

1. (100-50/100)*100
2. (100-50/50)*100

over here which of the following options are right 1 or 2? and why?

By what percent 100 is more than 50?

1. (100-50/100)*100
2. (100-50/50)*100

over here which of the following options are right 1 or 2? and why?

Answer 1

If $x$ and $y$ are positive numbers, \begin{equation} 100 \times \frac{y}{x} \end{equation} is the percentage of $x$ into $y$. For example \begin{equation} 100\times \frac{99}{60} = 165 \end{equation} hence 99 is 165% of 60. Similarly \begin{equation} 100\times \frac{45}{60} = 75 \end{equation} hence 45 is 75% of 60. In order to get by what percentage $y$ is larger or smaller than $x$, simply remove 100, so \begin{equation} 100\times\frac{y}{x} - 100 \end{equation} For example 99 is $165 -100 = 65\%$ more than 60, and 45 is $75 - 100 = -25\%$ more than 60, that is to say 25% less than 60.