If the last two digits of the child's birthyear form a number x, then the child has stated that (s)he is x years old. Or, in other words x more years has passed since the child's birth.
In that case, the last two digits of the year would be 2*x (or, for x > 50, 2*x - 100) Since the actual year in which the statement was made is 1932, we have 2*x = 32 for x = 16
(the child's age) or 2*x - 100 = 32 for x = 66 (the grandmother's age)
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