The ages of two persons differ by 20 years. If 5 years ago, the older one be 5 times as old as the younger… · ABC26GN1824
Subject: General Aptitude · Chapter: Problems on Ages · Exam: M.A.T. 2004
The ages of two persons differ by 20 years. If 5 years ago, the older one be 5 times as old as the younger one, then their present ages are
(a)25 years, 5 years
(b)30 years, 10 years
(c)35 years, 15 years
(d)50 years, 30 years
Answer
Answer (as printed): B
Explanation
Let their present ages be $x$ years and $(x-20)$ years. $$\begin{aligned} & (x-5)=5[(x-20)-5] \\ & \Rightarrow(x-5)=5(x-25) \\ & \Rightarrow(x-5)=5 x-125 \\ & \Rightarrow 4 x=120 \\ & \Rightarrow x=30 \end{aligned}$$ ∴ Their present ages are 30 years and 10 years.
Explanation as extracted from the printed page; notation may be imperfect.