The present ages of two sisters are in the ratio \(5:7\). After 4 years, their ages will be in the ratio \(6:8\). Find the present age of the younger sister.
20 years
Let the present ages be \(5x\) and \(7x\) years.
After 4 years the ratio is \(\dfrac{5x+4}{7x+4} = \dfrac{6}{8} = \dfrac{3}{4}\).
Cross-multiply: \(4(5x+4) = 3(7x+4)\).
Expand: \(20x + 16 = 21x + 12\).
Solve: \(21x - 20x = 16 - 12 \Rightarrow x = 4\).
Younger sister's present age \(= 5x = 5\times4 = 20\) years.
Hence, the present age of the younger sister is 20 years.
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