| Answer : 64-year old Grand Mother |
As per the hint the number of sons and the number of sons to each one of the son are consecutive numbers.
Grand mother's age is a product of two consecutive numbers + number of sons , which lies between 50 to 70.
It is possible only with the numbers 7 & 8
7 x 8 = 56 +8 = 64 , with in the given range.
Let us try some other numbers.
6 x 7 = 42 + 7 = 49, not in the range.
8 x 9 = 72 + 9 = 81 , again not in the range.
Given below a small pictorial diagram.