Question 1210597
The question is unclear, and I cannot find an interpretation that would yield a reasonable result (a whole number for all numbers of stamps involved in those transactions).
 
Liam and Noah shared a collection of 540 vintage stamps."
Apparently Noah has a number {{{N}}} of stamps, and Liam has a number {{{L}}} of stamps, and {{{L+N=540}}}
 
The third sentence seems clear, and we can translate it into an equation that leads us to
{{{highlight(x=(3/5)N)}}} for the number of stamps Noah sold.
The second sentence is a puzzle:
"Liam sold 2/5 fewer stamps than Noah." What could that mean?
A)	I would think it could mean that the difference {{{x-y}}} is {{{(2/5)x}}}
B)	It could mean that the number of stamps Liam sold is {{{y=(2/5)x}}}
C)	It could mean that while Noah sold {{{3/5}}} of his stamps,
the ratio of the number of stamps Liam sold to the number he originally had is
{{{3/5-2/5=1/5}}}
 
I tried all three approaches and failed to find a whole number for all numbers of stamps involved.
However, if you do not calculate all numbers involved, you can find that Noah could start with {{{N=324}}} stamps and Liam with {{{L=216}}} stamps, from  there on all the numbers of stamps would be fractional, but if Liam sells {{{1/5}}} of his stamps the non-integer numbers of remaining Liam's stamps and total stamps left are in exactly a {{{4/7}}} ratio.
 
The numbers of stamps left are {{{(4/5)L=4L/5}}} for Liam
and {{{(2/5)(540-L)=(1080-2L)/5}}} for Noah
The total unsold is
{{{4L/5+(1080-2L)/5=(1080+2L)/5}}}
The ratio of Liam's unsold to total unsold is {{{4L/5)/((1080+2L)/5)=4L/(1080+2L)}}}
All we have to do is solve {{{4L/(1080+2L)=4/7}}} without thinking about all the transactions.
{{{4L/(1080+2L)=4/7}}}-->{{{L/(1080+2L)=1/7}}}-->{{{7L/(1080+2L)=1}}}-->{{{7L=1080+2L)}}}-->{{{5L=1080)}}}-->{{{L=1080/5)}}}-->{{{highlight(L=216)}}}