Question

the sum of ages of 3 person is 150 years . 10 years ago their ages were in the ratio 7:8:9 , their present ages are

Answer 1

ten years ago, their ages were in the ratio 7:8:9, so you can assume their ages 10 years ago to be 7x, 8x and 9x respectively. 
as of now, their ages would be 7x + 10, 8x + 10 and 9x + 10 
the sum of these ages is 150, so: 
7x + 10 + 8x + 10 + 9x + 10 = 150 
or, 24x + 30 = 150 
or, 24x = 150 - 30 = 120 
or, x = 120/24 = 5 
so their present ages are 7*5 + 10, 8*5 + 10 and 9*5 + 10 
i.e. 45, 50 and 55 (a)

Answer 2

Given
SUM of 3 person age =150

10 year ago
The sum of person age =120 ( age of every single person increases or decreases with same rate)

10 year back sum of there age =150-30=120

Ratio of there age = 7:8:9

Sum of ratio =7+8+9=24

Value of 1 ratio =120/24=5

So age of first person was=7x5=35

Age of 2nd person was =8x5=40

Age age of 3rd person was =9x5=45

The present age of 1st=35+10=45yr

2nd=40+10=50yr

3rd=45+10=55

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