Question 306207
Let A,B,C,D be your numbers in increasing value. 
{{{(A+B+C+D)/4=24}}}
{{{(A+B+C)/3=20}}}
{{{(B+C+D)/3=30}}}
Let's substitute,
{{{Z=B+C}}}
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1.{{{A+Z+D=96}}}
2.{{{A+Z=60}}}
3.{{{Z+D=90}}}
From eq. 2,
{{{A+Z=60}}}
{{{A=60-Z}}}
From eq. 3,
{{{Z+D=90}}}
{{{D=90-Z}}}
Substitute these into eq. 1,
{{{A+Z+D=96}}}
{{{(60-Z)+Z+(90-Z)=96}}}
{{{150-Z=96}}}
{{{Z=54}}}
So then
{{{B+C=54}}}
We're looking for {{{(B+C)/2}}}
{{{(B+C)/2=27}}}
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c) is the correct answer.