4 years ago, the age of Shyam was seven times the age of his son, Rajat. After 8 years, Shyam’s age will be three times the age of Rajat. Find the present age of Shyam.
46 years
Let Shyam's present age be \(S\) years and Rajat's present age be \(R\) years.
4 years ago: \(S - 4 = 7(R - 4)\), which gives \(S = 7R - 24\).
After 8 years: \(S + 8 = 3(R + 8)\), which gives \(S = 3R + 16\).
Equating both: \(7R - 24 = 3R + 16\), so \(4R = 40\), hence \(R = 10\).
Then \(S = 7(10) - 24 = 46\).
Hence, Shyam's present age is 46 years.
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