As we have a value for A, let us convert B.
B = mean of 4a − 5c, b − 24, 8c − a,and 3d + 2b = (4a-5c+b-24+8c-a+3d+2b)/4=(3a+3b+3c+3d-24)/4=3(a+b+c+d-8)/4=3(a+b+c+d)/4-(3*8/4).
Now from initial statement (a+b+c+d)/4=7, so B=3*7-3*8/4=21-6=15
Now A is also 15.
Thus both are equal

C

(a+b+c+d)/4 = 7
a+b+c+d = 28 ------------(1)

(4a − 5c + b − 24 + 8c − a + 3d + 2b)/4 = X
3a + 3b + 3c + 3d - 24 = 4X
a + b + c + d - 8 = 4X/3
28 - 8 = 4X/3 ---------- (from (1) a+b+c+d = 28)
20 = 4X/3
X = 15

So answer is C

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