How to solve percentage difference problem?

Question

I am trying to figure out how to solve percentage difference problem?

Adam, Tom and Carl are selling lemonade and customers are giving likes. Adams received 40% more likes than Carl. Tom got 20% fewer likes than Carl. By what percentage did Adam get more likes than Tom?

I am thinking Adam likes are at 140%, Tom likes are at 80%, so Adam got 140 - 80 = 60% more likes than Tom.

Is that correct?

Answer 1

Say, Adam, Tom and Carl has $a, t$ and $c$ amount of likes.

Then we can make some equations from the question.

$$a=1.4c$$

$$t=0.8c$$

Then to find percentage that Adam got more than Tom,

\begin{align} \frac{a}{t}&=\frac{1.4c}{0.8c} \\ &=1.75 \end{align}

So the answer is $75\%$.

Answer 2

markup and margin shows for tom to be at the same number of likes as Carl, he needed ${1\over 1-0.2}-1 = 0.25=25\%$ more, which then needs 40% more of that value to get to Adam. This means he needs $$(1+0.25)\cdot (1+0.4)= 1+0.25+0.4+0.1=1.75$$ or 75% more than what he has.