Answer:
6 years and 15 years of age
Step-by-step explanation:
Given the ratio of their ages is 2 : 5 = 2x : 5x ( x is a multiplier )
Then in 9 years their ages are 2x + 9 and 5x + 9 in the ratio 5 : 8
By proportion
[tex]\frac{2x+9}{5x+9}[/tex] = [tex]\frac{5}{8}[/tex] ( cross- multiply )
5(5x + 9) = 8(2x + 9) ← distribute parenthesis on both sides
25x + 45 = 16x + 72 ( subtract 16x from both sides )
9x + 45 = 72 ( subtract 45 from both sides )
9x = 27 ( divide both sides by 9 )
x = 3
Thus
Rohit's age = 2x = 2( 3) = 6
James' age = 5x = 5(3) = 15
6 : 15 = 2 : 5
