The present age of Mr. Sanyal is three times the age of his son. Six years hence, the ratio of their ages will be $5 : 2$. What is the present age of Mr. Sanyal?

Concept & Logic Translating a "times" relationship into a ratio ($3 : 1$) allows you to set up an algebraic fraction involving the future timeline shift. Equating the modified expressions to the future ratio yields the variable multiplier. $$ \frac{3x + 6}{x + 6} = \frac{5}{2} $$ Step-by-Step Solution * **Given:** Mr. Sanyal is currently 3 times as old as his son. * **Given:** Six years hence (in the future), their age ratio will be $5 : 2$. * **Calculation:** Let the son's present age be $x$. Mr. Sanyal's present age is $3x$. * Set up the equation for 6 years in the future: $(3x + 6) / (x + 6) = 5 / 2$. * Cross-multiply to eliminate the fractions: $2(3x + 6) = 5(x + 6)$. * Expand the terms: $6x + 12 = 5x + 30$. * Isolate $x$: $6x - 5x = 30 - 12 \Rightarrow x = 18$. * The son's present age is 18 years. * Mr. Sanyal's present age is $3x = 3(18) = 54$ years. Exam Strategy & Shortcut Use the **Ratio Check Method** via options. Mr. Sanyal's present age must be a multiple of 3 (since he is 3 times his son's age). Options: (a) 48, (b) 50, (c) 54, (d) 60. Option 50 is eliminated immediately. Six years hence, his age must be divisible by 5 (from the $5 : 2$ ratio). Test (a): Present = 48. Future = $48 + 6 = 54$. Not divisible by 5. (Eliminate) Test (c): Present = 54. Future = $54 + 6 = 60$. Divisible by 5. Let's verify (c): If Mr. Sanyal is 54, the son is 18. In 6 years, they are 60 and 24. Ratio: $60 / 24 = 5 / 2$. It matches perfectly. Common Pitfall A common mistake is solving for $x$ (18) and selecting an option too early if 18 were present as a trap. Always trace back to exactly *whose* age the question is asking for—in this case, Mr. Sanyal's age, which is $3x$. Final Answer **Therefore, the correct answer is 54 years.**