The ages of two brothers are in the ratio 2 to 3 but in eight years the ratio of their ages will be 3 to 4 what is the age of the older brother 16, 18, 24

  24

Step-by-step explanation:

Let x represent the age of the older brother now. Then 2/3x is the age of the younger brother now. In 8 years, the ratio of their ages will be ...

  (2/3x +8)/(x +8) = 3/4

  4(2/3x +8) = 3(x +8) . . . . . multiply by 4(x+8)

  8/3x +32 = 3x +24 . . . . . . eliminate parentheses

  8 = 1/3x . . . . . . . . . . . . . . . subtract 8/3x +24

  24 = x . . . . . multiply by 3

The older brother is 24.

Alternate solution

In terms of "ratio units" adding 8 years increases the numbers in the ratio 2 : 3 by one to 3 : 4. So, each ratio unit must stand for 8 years, and the "3" in 2 : 3 means the older brother is 3·8 years = 24 years old.

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step-by-step explanation:

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