Let number of white balls be W and number of black balls be B

There are 27 more white balls than black balls
W = B + 27
Total number of balls = W + B = B + 27 + B = 2B + 27

probability of randomly selecting a white ball = (B+27)/ 2B + 27 = 4/5
Solving it, B = 9, W= 36 and total number of balls = 36 + 9 = 45

Let x white balls must be added to the box so that the probability of randomly drawing a white ball is 7/8
Number of white balls be (36 + x)
Total number of balls = (45 + x)
probability of randomly drawing a white ball = (36 + x) / (45 + x) = 7/8
Solving it, x = 27

IMO C