Divya is twice as old as Shruti .five year hence the ration of their ages would be 9:5 what is the difference in their ages 

Let's solve this problem step by step.

### Step 1: Define the variables
Let Shruti's current age be \( x \) years.  
Then, Divya's current age is \( 2x \) years (since Divya is twice as old as Shruti).

### Step 2: Consider the situation 5 years hence
Five years from now, Shruti's age will be \( x + 5 \) years, and Divya's age will be \( 2x + 5 \) years.

### Step 3: Set up the ratio equation
According to the problem, the ratio of their ages in five years will be \( 9:5 \). Therefore, we can write:
\[
\frac{2x + 5}{x + 5} = \frac{9}{5}
\]

### Step 4: Solve the equation
Now, we cross-multiply to solve for \( x \):
\[
5(2x + 5) = 9(x + 5)
\]
Expanding both sides:
\[
10x + 25 = 9x + 45
\]

Subtract \( 9x \) from both sides:
\[
x + 25 = 45
\]

Subtract 25 from both sides:
\[
x = 20
\]

### Step 5: Calculate Divya's age
If Shruti is \( 20 \) years old, then Divya, being twice as old, is:
\[
2x = 2(20) = 40 \text{ years old}
\]

### Step 6: Find the difference in their ages
The difference in their ages is:
\[
40 - 20 = 20 \text{ years}
\]

### Final Answer:
The difference in their ages is \( \boxed{20} \) years.

---

Would you like more details, or do you have any specific questions? Here are some related topics you might explore:

1. How to solve age-related algebra problems?
2. What is the importance of ratios in solving problems?
3. How do linear equations apply in real-life situations?
4. What are other methods to solve for ages in word problems?
5. How to check the consistency of a solution in algebra?
6. How to set up equations based on word problems?
7. What are some tips for solving ratio problems efficiently?
8. How to understand the relationship between variables in an equation?

**Tip:** Always verify your final answer by substituting it back into the original problem. This ensures the solution is correct and consistent.

Learn how to solve the age problem where Divya is twice as old as Shruti and in five years, their ages will have a ratio of 9:5. Follow a detailed step-by-step solution involving age-related algebra, ratio equations, and linear equations. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation