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.

## Comments

let G = Gita's age now, and let D = Dilip's age now;

then 5 years ago, Gita's age was G - 5, and Dilip's age was D - 5;

so that, G - 5 = 3(D - 5);

also, D = G - 8;

in which case, D - 5 = G - 8 - 5 = G - 13;

in which case, G - 5 = 3(G - 13);

in which case, G - 5 = 3G - 3*13

or, G -5 = 3G - 39;

or, 3G - 39 = G - 5;

now, subtracting G from each of the equation ---> 2G - 39 = - 5

then, adding 39 to each side of the equation ---> 2G = 39 - 5 ---> 2G = 34

or, dividing each side of the equation by 2 ---> G = 34/2 ---> G = 17 (Gita's age now)