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

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

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Let the number be 3x and 5x

3x + 8 : 5x + 8 = 2 : 3

(3x + 8)/(5x + 8) = 2/3

⇒ 2(5x + 8) = 3(3x + 8)

⇒ 10x + 16 = 9x + 24

⇒ 10x - 9x = 24 - 16

⇒ x = 8

∴ The number are 24 and 40.