Question

The ages of a son and his father was in the ratio \(2:5\) seventeen years ago. If the present age of the son is \(35\) years, the age of the father \(5\) years hence is

• A. \(62\) years
• B. \(65\) years
• C. \(67\) years
• D. \(68\) years

Hint:

For age ratio problems, convert the given present age to the same time period mentioned in the ratio.

Answer 1

The Correct Option is C

Concept:
In age problems, first convert present ages into past ages using the given time.

Step 1: Find son's age \(17\) years ago. Present age of son is \[ 35 \] So son's age \(17\) years ago was \[ 35-17=18 \]

Step 2: Use the ratio. Seventeen years ago, the ratio of son's age to father's age was \[ 2:5 \] So, \[ 2\text{ parts}=18 \] \[ 1\text{ part}=9 \] Father's age \(17\) years ago: \[ 5\text{ parts}=5\times 9=45 \]

Step 3: Find father's present age. \[ 45+17=62 \]

Step 4: Find father's age \(5\) years hence. \[ 62+5=67 \]

Step 5: Final answer. \[ \boxed{67\text{ years}} \]