When Usha was 45 years old, her daughter was 2 times her son's age. Usha would be twice her daughter's age when her son was 21 years old. How old would Usha be when her son was 7 years old?

	Usha	Daughter	Son
Before	45	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	21

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

Difference in Usha's and her daughter's ages at first
45 - 2 u = 2 p - 1 p
45 - 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 - 21
1 u + 21 = 1 p --- (2)

Make p the same.

(1) = (2)
45 - 2 u = 1 u + 21
1 u + 2 u = 45 - 21
3 u = 24

1 u = 24 ÷ 3 = 8

Age difference between Usha and her son
= 45 - 1 u
= 45 - 8
= 37

Usha's age when her son was 7 years old
= 37 + 7
= 44

Answer(s): 44