Subject: General Aptitude · Chapter: Problems on Ages · Exam: 2008 · Marks: · Difficulty:
The ratio between the ages of Ram and Mohan is 4 : 5 and that between the ages of Ram and Anil is 5 : 6. If the sum of the ages of the three is 69 years, what is Mohan's age?
(a)20 years
(b)24 years
(c)25 years
(d)30 years
Answer
Answer (as printed): C
Explanation
Ram's age : Mohan's age $=4: 5=1: \frac{5}{4}$. Ram's age : Anil's age $=5: 6=1: \frac{6}{5}$. Let Ram's age be $x$ years. Then, Mohan's age $=\frac{5 x}{4}$ years. And, Anil's age $=\frac{6 x}{5}$ years. $$\begin{aligned} & \therefore x+\frac{5 x}{4}+\frac{6 x}{5}=69 \\ & \Rightarrow 20 x+25 x+24 x=1380 \\ & \Rightarrow 69 x=1380 \\ & \Rightarrow x=20 \end{aligned}$$ Mohan's age $=\frac{5 x}{4}$ years $=\frac{5 \times 20}{4}$ years $=25$ years.
Explanation as extracted from the printed page; notation may be imperfect.