ibm - if 200 chocolates were distributed among 100 people in such a manner that each man received 1 chocolate each woman received 4 chocolates and each child received 6 chocolates find which of the following is a possible value for the number of children - skillgun

x be the number of children
y be the number of women
z be the number of men.
Given that, total number of people = 100
i.e., x+ y + z = 100 …(1)
Each man received 1, each woman received 4 and each child received 6 chocolates
6x + 4y + z = 200 ...(2)
Here, we have 2 equations and 3 unknowns.
Eliminate z by subtracting 1 from 2, we have 5x + 3y = 100.
Y = (100 - 5x) / 3.
From the given option,
If x = 12 then y = (100 - 5(12)) / 3 = 13.33
If x = 16 then y = (100 - 5(16)) / 3 = 6.67
If x = 8 then y = (100 - 5(8)) / 3 = 20
If x = 0 then y = (100 - 5(12)) / 3 = 33.33.
In all of these, the only integer value is 20. So the only possible solution would be x = 8 and y = 20.