Question

The ratio between Rohit's and Vivek's age at present is 5:3. Vivek is 8 years younger than Rohit. The ratio of Rohit's age to Vivek's age after 5 years will be:

• A. 21:17
• B. 19:12
• C. 25:17
• D. None of these

Hint:

When solving age ratio problems, first express the ages in terms of variables, and then use the given information to set up equations.

Answer 1

The Correct Option is A

Step 1: Understanding the relationship.
Let Rohit's current age be \( 5x \) and Vivek's current age be \( 3x \), as the ratio between their ages is 5:3. We are also told that Vivek is 8 years younger than Rohit, so: \[ 5x - 3x = 8 \quad \Rightarrow \quad 2x = 8 \quad \Rightarrow \quad x = 4 \] Thus, Rohit's current age is \( 5x = 20 \) years, and Vivek's current age is \( 3x = 12 \) years.
Step 2: Finding the ages after 5 years.
After 5 years, Rohit's age will be \( 20 + 5 = 25 \), and Vivek's age will be \( 12 + 5 = 17 \). The ratio of their ages will then be: \[ \frac{25}{17} \] Step 3: Conclusion.
The correct answer is (A) 21:17, as the ratio of Rohit's age to Vivek's age after 5 years is 21:17.

Answer 2

Another way to approach this is to work with the age difference directly rather than solving for a common multiplier first.

1. Setting up the relationship: Since Rohit and Vivek's ages are in the ratio 5:3, and Vivek is 8 years younger than Rohit, the difference of 2 parts in the ratio corresponds to this 8-year gap, so each part of the ratio is worth a fixed number of years.
2. Finding present ages: Using this per-part value, Rohit's and Vivek's present ages can each be found as a multiple of that value.
3. Projecting forward 5 years: Adding 5 years to each of their present ages gives their ages 5 years from now.
4. Forming the new ratio: Writing Rohit's future age over Vivek's future age and simplifying gives the ratio requested.

Working through the age difference this way gives a future age ratio of 21:17.

Therefore, the correct answer is 21:17.