1. My age is a two-digit number

=> So my name is not Sarah because Sarah is 6 years old - a one-digit number

I am half of the age of my sister - my sister is 24 years old.

=> So my age is: 24 : 2 = 12 (years old)

=> My name is Mia.

2. There are no tens in my age.

=> So my name is not Lucy, Mia, or Ranjit because they have tens of their ages.

I am half of my sister's age.

=> So my age is: 12 : 2 = 6 (years old)

=> My name is Sarah.

3. My age has five tens in it.

=> So my name is not Lucy, Mia, or Sarah because they don't have five tens in their ages.

I am 30 years older than my eldest daughter - 24 years old

=> So my age is: 24 + 30 = 54 (years old)

=> My name is Ranjit.

4. My age has the same number of tens as double 10 

=> Her tens is: 10 x 2 = 20

My age is half of 48

=> So my age is: 48 : 2 = 24 (years old)

=> My name is Lucy