Question
Four years ago, the ratio of ages of a brother and
sister was 5:6 respectively. 3 years from now, the age of the sister will be twice that of the brother. If the sum of their current age is 47 years, find the current age of the brother.Solution
Four years ago,  let the age of the brother = 5x years. Then, the age of the sister = 5x × (6/5) = 6x years. Present age of the brother = (5x + 4) years. Present age of the sister = 47 - (5x + 4) = (43 - 5x) years. 3 years hence, age of the sister = 6x + 4 + 3 = (6x + 7) years, age of the brother = (43 - 5x + 3) = (46 - 5x) years.  According to the question,  2 × (46 - 5x) = 6x + 7. 92-10x =6x+7 16x =85 Solving, we get x = 5.3 Thus, the current age of the brother = 5x + 4 =5 ×5.3+4= 30.5 years.
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