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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?

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?

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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)

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2 Answers

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.

 

Let Dilip's present age = x

Gita's present age = x + 8

5 yrs ago

3 (x-5) = (x+8)-5

3x - 15 = x + 3

2x = 18 , x = 9

Gita's present age = 17 yrs