Number is zeros in n is-

(n/5)+(n/25)+(n/125)...

if n=100
(100/5)+(100/25)=20+4=24

Logic is: Number of zeros means total number of 10. Total number of 10 means total number of 5 (because 2 is available in abundant ). To calculate the number of 5 we divide 100 by 5, first term of the above written expression. But four terms are there which have 2 five embed in them and they are 25,50,75,100 so total 4, which is second term of the above written equation.
Answer is B.

100! = 1*2*3*4*5*...10...15...20...25....100 = (5^n) * X, where X,n are integers

The Total number of zeroes = Total number of 5's in the product.

First method - Counting the number of 5's
5 - 1,
10 - 2,
15 - 3,
20 - 4
25(5*5) - 5,6
30 - 7,
35 - 8,
40 - 9,
45 - 10,
50(5*5*2) - 11,12,
55 - 13,
60 - 14,
65 - 15,
70 - 16,
75(5*5*3)- 17,18,
80 - 19,
85 - 20,
90 - 21,
95 - 22,
100(5*5*4) - 23,24

Total - 24

Second Method - Mentioned above by kul