Tanya is 6 times younger than her great-grandfather. If a zero is placed between the digits of her age, it will read as the age of her great-grandfather. How old is Tanya?

Tanya is 18 years old.

Step-by-step explanation:

In order to determine this, we assume the following

x =  tens digit of the age of Tanya, and also the hundreds digit of Tanya's great-grandfather age

y = units digit of the age of Tanya, and also the units digit of Tanya's great-grandfather age

Therefore, we have:

10x + y = (1 / 6) * (100x + y)

Multiply both sides by 6, we have:

[10x + y] * 6 = [(1 / 6) * (100x + y)] * 6

60x + 6y = 100x + y

Collect the like terms, we have:

6y - y = 100x - 60x

5y = 40x

Divide through by 5, we have:

y = 8x

That is,

8x = y

Note that x and y has to be single digits. This can only be obtained only when x = 1 and y = 8. And given how x and y is defined above, we have:

The age of Tanya = 18

This can be verified as follows:

18 = 108 / 6

18 * 6 = 108

108 = 108

Therefore, Tanya is 18 years old.