Find the present ages of Aarav, Aayush and Ahana (in years).

Question

The present ages of Aarav, Aayush and Ahana in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56.
Find the present ages of Aarav, Aayush and Ahana (in years).

Answer 1

Now their ages are in the ratio of 4:7:9
Let the common multiple be x
Therefore their ages are
4x, 7x and 9x

8 years ago, their ages were 4x-8, 7x-8, 9x-8

Therefore adding them,
(4x-8) + (7x-8) + (9x-8) = 56

20x = 56+24 = 80

Hence x = 4

Therefore their present ages are:
4x = 16
7x = 28
9x = 36

Answer 2

present ratio of their ages are 4:7:9,
so present sum of thier ages is 80,
let their ages are 4x,7x & 9x
4x+7x+9x=56+24=80
20x=80
x=4
so their ages are 16,28 &36

Answer 3

It was eight yours ago when the sum was 56. so
3 x 8 +56 = the sum of their current age. (80)
the ratiois 4:7:9 so
80 / (4+7+9) =4
Aarav: 4 x4 =16
Aayush: 7x 4= 28
Ahana: 9x 4= 36

Answer 4

We can write the following equations:
(Aa - 8) + (Aay - 8) + ( Aha -8) = 56 or Aa + Aay + Aha = 80 (1)
Aha/Aay = 9/7 (2)
Aay/Aa = 7/4 (3)

Solving the system of three equations, yields : Aa = 16, Aay = 28 , Aha = 36