Question

Three numbers are in the ratio 3:7:9. If 5 is subtracted from the second, the resulting numbers are in AP. Find the original numbers.

Answer 1

so let the three numbers are 3x , 7x , 9x

so according to question
3x , 7x - 5 , 9x are AP

2(7x - 5) = 9x + 3x 

⇒ 14x - 10 = 12x

⇒ 2x = 10 

⇒ x = 5 

so the original numbers are 

3 x 5 = 15
7 x 5 = 35 
9 x 5 = 45 

Answer 2

so let the three numbers are 3x , 7x , 9x

so according to question
3x , 7x - 5 , 9x are AP

2(7x - 5) = 9x + 3x 

⇒ 14x - 10 = 12x

 2x=10
x=5
the real numbers are
3 x 5 = 15
7 x 5 = 35 
9 x 5 = 45
the original numbers are 15 35 45