X is one-fourth the age of Z and two-third the age of Y. What is the ratio of the ages of X, Y and Z respectively?

X is one-fourth the age of Z and two-third the age of Y.

Let Z’s age be 4x.

Since X is one-fourth of Z’s age:

X = $$\frac {1}{4}$$​ × 4x = x

X is also two-thirds of Y’s age:

x = $$\frac {2}{3}$$​ × Y

Y = $$\frac {3}{2}$$​ × x

Express all ages in terms of X

X’s age: x

Y’s age: $$\frac {3}{2}$$​ × x = 1.5x

Z’s age: 4x

Convert to a ratio:

To make the values integers, multiply everything by 2:

x : 1.5x : 4x $$\rightarrow$$​  2 : 3 : 8

Thus, correct option is (c).