2. Two numbers are in the ratio of 3 : 5. If 8 is added
to each number, the ratio becomes 2 : 3. Find the number

 x/y = 3/5

=> x = (3/5)y   (1)

(x + 8)/(y + 8) = 2/3

=> 3*(x + 8) = 2*(y + 8)

=> 3x + 24 = 2y + 16

=> 3x - 2y = -8   (2)

From (1) and (2), we have:

=> 3*(3/5)y - 2y = -8

=> (-1/5)y = -8

=> y = 40

=> x = (3/5)*y = (3/5)*40 = 24

=> Solution: x = 24, y = 40

Hope this helps!

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