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 present ages is 25 years.

• A. If the data in statement (1) alone is sufficient to answer the question, but the data in statement (2) alone is not sufficient.
• B. If the data in statement (2) alone is sufficient to answer the question, but the data in statement (1) alone is not sufficient.
• 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.
• E. If the data in neither statement (1) nor statement (2) is sufficient to answer the question, and more data is needed.

Hint:

Set father = 6x and son = x, then check whether each statement by itself gives you a single equation you can solve for x.

Answer 1

The Correct Option is D

Let father's present age be \(6x\) and son's present age be \(x\), matching the given ratio 6 : 1.

Statement (1): After 5 years, father is \(6x+5\) and son 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 \(x = 5\). This pins down the son's age exactly as 5 years, so statement (1) alone is sufficient.

Statement (2): The difference of present ages is 25, so \(6x - x = 25\), giving \(5x = 25\) and \(x = 5\). Again, the son's age comes out to exactly 5 years, so statement (2) alone is also sufficient.

Since each statement independently determines the son's present age (both, in fact, give the same value of 5 years), either statement alone answers the question. The correct choice is option (4).