The following question is a ratio question and tests your ability to express one term in terms of another, given the ratio between the two terms.
Question
Sum of the ages of three friends is 98 years. If the ratio of the ages of the oldest to the middle is 5 : 3 and that of the middle to the youngest is 5 : 3, how old is the oldest?
1. 49 years
2. 50 years
3. 30 years
4. 32 years
5. 42 years
The correct answer is 50 years. i.e., Choice (2).
Explanatory Answer
One of the easiest approach to solve this question is outlined below
Let A be the oldest, B the middle one and C the youngest amongst the three friends.
Ratio of the ages of A and B, A : B :: 5 : 3
i.e., A/B = 5/3
Therefore, A = (5/3) B
Ratio of the ages of B and C, B : C :: 5 : 3
i.e, B/C = 5/3.
Hence, C = (3/5)B
We also know that A + B + C = 98
Rewriting the equation in terms of B, we get (5/3)B + B + (3/5)B = 98.
Taking 15 as the common denominator and adding we get (25B + 15B + 9B)/15 = 98
Or (49/15)B = 98
Or B = (98*15)/49 = 30.
Hence, age of A = (5/3)B = (5/3)*30 = 50 years.
Various alternative formats of the same question exist. Some oft repeated questions are given at the Ratio Proportion Practice Question Set.
