When Abi was 33 years old, her daughter was 2 times her son's age. Abi would be twice her daughter's age when her son was 27 years old. How old would Abi be when her son was 20 years old?

	Abi	Daughter	Son
Before	33	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	27

The difference in the ages between Abi and her daughter remains unchanged.

Difference in Abi's and her daughter's ages at first
33 - 2 u = 2 p - 1 p
33 - 2 u = 1 p --- (1)

The difference in the ages between her daughter and her son remains unchanged.

Difference in her daughter's and her son's ages at first
2 u - 1 u = 1 p - 27
1 u + 27 = 1 p --- (2)

Make p the same.

(1) = (2)
33 - 2 u = 1 u + 27
1 u + 2 u = 33 - 27
3 u = 6

1 u = 6 ÷ 3 = 2

Age difference between Abi and her son
= 33 - 1 u
= 33 - 2
= 31

Abi's age when her son was 20 years old
= 31 + 20
= 51

Answer(s): 51