Five years ago, the age of Kavita was one-third of the present age of her mother. After 5 years, the sum of their ages will be 75 years. What is Kavita's present age?
20 years
Let Kavita's present age be \(k\) and her mother's present age be \(m\).
Five years ago Kavita's age was \(k - 5\), and this equalled one-third of the mother's present age: \(k - 5 = \frac{m}{3}\), so \(m = 3(k - 5)\).
After 5 years the sum of their ages is \((k + 5) + (m + 5) = 75\), which gives \(k + m = 65\).
Substitute \(m = 3(k - 5)\): \(k + 3k - 15 = 65\), so \(4k = 80\).
Therefore \(k = 20\) years.
Hence, Kavita's present age is \(20\) years.
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