The question below is followed by two statements numbered I and II. Choose the option that describes whether the statements are sufficient to answer the question.
What is the present age of Farhan?
I. The sum of the present ages of Farhan and his father is 56 years.
II. Four years ago, Farhan’s father was three times as old as Farhan was then.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → The question can be answered by using both statements together, but not by using either statement alone.
Let the present ages of Farhan and his father be \(F\) and \(P\) years. Two unknowns need two independent facts.
Statement I alone:
\(F+P=56\): one equation in two unknowns: not sufficient
Statement II alone:
\(P-4=3(F-4)\), so \(P=3F-8\): one equation in two unknowns: not sufficient
Both together:
\(F+(3F-8)=56\)
\(4F=64\), so \(F=16\) and \(P=40\)
Check: four years ago they were 12 and 36, and \(36=3\times12\)
Farhan is 16 years old: sufficient together