Explanation

Let S = a+b+c+d. Then a+b+c = 5d gives S = 6d; b+c+d = 7a gives S = 8a; c+d+a = 3b gives S = 4b. So d = S/6, a = S/8, b = S/4, and c = S(1 − 1/6 − 1/8 − 1/4) = 11S/24. The ratio a:b:c:d = 3:6:11:4. Hence option C.