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.