
The ratio of the ages of Rahul and Ravi is 3: 4. After 6 years, the new ratio of their ages will be 4: 5. What is the age of Ravi at present?


Let the present ages of Rahul and Ravi be \(3x\) and \(4x\) respectively, according to the ratio of their ages \(3:4\).

After 6 years, their ages will be:
- Rahul: \(3x + 6\)
- Ravi: \(4x + 6\)

According to the problem, the new ratio of their ages will be \(4:5\). Therefore, we can set up the equation:

\[
\frac{3x + 6}{4x + 6} = \frac{4}{5}
\]

Cross-multiplying gives:

\[
5(3x + 6) = 4(4x + 6)
\]

Expanding both sides:

\[
15x + 30 = 16x + 24
\]

Rearranging the equation:

\[
15x - 16x = 24 - 30
\]
\[
-x = -6
\]
\[
x = 6
\]

Now, substituting \(x\) back to find Ravi's age:

\[
\text{Ravi's age} = 4x = 4 \times 6 = 24
\]

Thus, Ravi's present age is **24 years**.

If you have any questions or need further details, feel free to ask! Here are some related questions you might find interesting:

1. How would you set up a similar problem if the ratio were different?
2. Can you calculate the age of Rahul with the information provided?
3. What if the ratio of their ages changed after a different number of years?
4. How can we apply this concept to other real-life situations, like comparing ages of multiple people?
5. What other methods can be used to solve ratio problems? 

**Tip:** Always verify ratios by plugging the values back into the original ratio after solving for variables.

The ratio of the ages of Rahul and Ravi is 3: 4. After 6 years, the new ratio of their ages will be 4: 5. What is the age of Ravi at present?

Discover how to find Ravi's present age given the age ratio with Rahul and future age ratios. This step-by-step solution involves algebraic methods and understanding of ratios. Suitable for Grades 6-8.

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