5 years ago Gita was three times the age of his cousin Dilip. If Dilip is 8 years younger than Gita. How old is Gita now?
Let's let G = Gita's age now, and D = Dilip's age now
5 years ago, Gita was G-5 and Dilip was D-5
5 years ago, Gita was three times Dilip's age, which was D-5, so
G-5 = 3(D-5), or
G - 5 = 3D - 15, and
G = 3D - 15 + 5, or
G = 3D - 10
Now (this year), Gita is 8 years older than Dilip, or
G = D + 8, or
D = G - 8
Let's substitute D = G - 8 into the first equation:
G = 3(G-8) - 10, or
G = 3G - 24 - 10, or
G -3G = -34 and
-2G = -34, or
2G = 34, so
G = 17, Gita's current age.
Dilip is 8 years younger, so he is 17-8 = 9
Five years ago, Gita was 17-5 = 12, and Dilip was 9-5 = 4, so five years ago Gita was three times older than Dilip.