Question

The sum of present ages of Anish, Ajay and Anvit is 75 years. If 5 years ago the ratio of their ages was 3 : 4 : 5, What is the present age of Ajay?

• A. \(65 \text{ years} \)
• B. \(28 \text{ years} \)
• C. \(32 \text{ years} \)
• D. \(25 \text{ years} \)

Hint:

Always be careful with the timeline! If a ratio is given for "5 years ago," translate the total sum to that same time period before dividing by the ratio parts.

Answer 1

The Correct Option is B

Concept: In age-related problems involving ratios from a different time period, it is often easiest to calculate the sum of ages for that specific time period first. If the present sum is \(S\), the sum \(n\) years ago for \(k\) people is \(S - (n \times k)\).
Step 1: Calculate the sum of ages 5 years ago.
Present sum = 75 years.
Number of people = 3 (Anish, Ajay, Anvit).
Sum 5 years ago = \(75 - (3 \times 5) = 75 - 15 = 60 \text{ years}\).

Step 2: Use the ratio to find Ajay's age 5 years ago.
The ratio 5 years ago was \(3 : 4 : 5\).
Sum of ratio parts = \(3 + 4 + 5 = 12\).
Ajay's share 5 years ago = \(\frac{4}{12} \times 60 = \frac{1}{3} \times 60 = 20 \text{ years}\).

Step 3: Find Ajay's present age.
Present age = Age 5 years ago + 5
Present age = \(20 + 5 = 25 \text{ years}\).