Question

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

• A. If the data in statement (1) alone is sufficient to answer the question
• B. If the data in statement (2) alone is sufficient to answer the question
• C. If the data in both the statements together are needed to answer the question
• D. If either statement (1) alone or statement (2) alone is sufficient to answer the question

Hint:

Write father and son's ages as \(6x\) and \(x\); each statement alone gives one equation that solves for \(x\).

Answer 1

The Correct Option is D

Step 1: Set up the ages using a common multiplier.
Since Father : Son = 6 : 1, let Father = \(6x\) and Son = \(x\) for some positive number \(x\). We need to find \(x\).

Step 2: Check statement (1) alone.
After 5 years, Father's age is \(6x+5\) and Son's age is \(x+5\), and their ratio is 7 : 2. So \[ \frac{6x+5}{x+5}=\frac{7}{2} \] Cross multiplying, \(2(6x+5)=7(x+5)\), which gives \(12x+10=7x+35\), so \(5x=25\) and \(x=5\). The son's present age is 5 years, a single clear value, so statement (1) alone is enough.

Step 3: Check statement (2) alone.
The difference in their ages is 25 years, so \(6x - x = 25\), that is \(5x=25\), giving \(x=5\). Again the son's age comes out to 5 years, using only statement (2).

Step 4: Final answer.
Both statements, used separately, lead to the same single value for the son's age, 5 years. \[ \boxed{\text{Either statement alone is sufficient}} \]