Question:medium

The ratio of the present ages of father and son is 6:1. What is the present age of the son?
Statement 1: The ratio of the ages of father and son after 5 years is 7:2
Statement 2: The difference of their ages is 25 years

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Write father and son's ages as \(6x\) and \(x\); each statement alone gives one equation that solves for \(x\).
Updated On: Jul 21, 2026
  • If the data in statement (1) alone is sufficient to answer the question
  • If the data in statement (2) alone is sufficient to answer the question
  • If the data in both the statements together are needed to answer the question
  • If either statement (1) alone or statement (2) alone is sufficient to answer the question
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The Correct Option is D

Solution and Explanation

Step 1: Understanding the Question.
Father and Son's present ages are in the ratio 6 to 1, but the actual numbers are unknown. We are asked to pin down the son's exact present age using the extra clues in the two statements.

Step 2: Key Formula or Approach.
Since the ratio fixes the ages as \(6x\) and \(x\) for the same unknown \(x\), any single additional equation connecting Father's age and Son's age (a future ratio, or a present-day difference) is enough to solve for \(x\), because it gives one equation in one unknown.

Step 3: Detailed Explanation.
Using statement (1): five years from now the ratio becomes 7 to 2, so \(2(6x+5)=7(x+5)\). Expanding gives \(12x+10=7x+35\), so \(5x=25\) and \(x=5\), meaning the son is 5 years old today.
Using statement (2) instead: the age gap is 25 years, and since Father is older, \(6x-x=25\), which directly gives \(5x=25\) and again \(x=5\).
Both routes land on the exact same son's age without needing the other statement.

Step 4: Final Answer.
The son's present age is 5 years, and either statement alone is enough to reach it. \[ \boxed{\text{Either statement alone is sufficient}} \]
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