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 Ishaan?
I. The sum of the present ages of Ishaan and his mother is 62 years.
II. Six years ago, Ishaan’s mother was four times as old as Ishaan 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 Ishaan and his mother be \(I\) and \(M\) years. Two unknowns need two independent facts.
Statement I alone:
\(I+M=62\): one equation in two unknowns: not sufficient
Statement II alone:
\(M-6=4(I-6)\), so \(M=4I-18\): one equation in two unknowns: not sufficient
Both together:
\(I+(4I-18)=62\)
\(5I=80\), so \(I=16\) and \(M=46\)
Check: six years ago they were 10 and 40, and \(40=4\times10\)
Ishaan is 16 years old: sufficient together