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

Let's solve the problem step by step.

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

### Step 2: Express the Future Ages
Five years from now:
- Shruti's age will be \( x + 5 \) years.
- Divya's age will be \( 2x + 5 \) years.

### Step 3: Set Up the Equation Using the Given Ratio
According to the problem, five years hence, the ratio of their ages will be \( 9:5 \). Therefore, we can set up the equation:

\[
\frac{2x + 5}{x + 5} = \frac{9}{5}
\]

### Step 4: Cross-Multiply and Solve for \( x \)
Cross-multiply to get:

\[
5(2x + 5) = 9(x + 5)
\]

Expand both sides:

\[
10x + 25 = 9x + 45
\]

Now, subtract \( 9x \) from both sides:

\[
x + 25 = 45
\]

Subtract 25 from both sides:

\[
x = 20
\]

### Step 5: Find the Difference in Their Ages
Shruti's current age \( x = 20 \) years, so Divya's current age is \( 2x = 40 \) years.

The difference between their ages is:

\[
40 - 20 = 20 \text{ years}
\]

### Final Answer
The difference between their ages is **20 years**.

Would you like more details or have any questions?

### Related Questions

1. What would the ages of Shruti and Divya be after 10 years?
2. If the ratio of their ages 5 years ago was 7:2, what are their current ages?
3. How old will Shruti be when Divya is 60 years old?
4. What is the sum of their ages 15 years from now?
5. If Divya were 5 years younger, what would be the new ratio of their ages?
6. What would their age ratio be 20 years from now?
7. How old was Shruti when Divya was 30 years old?
8. If Shruti was 10 years younger, what would be the difference in their ages now?

**Tip:** Always verify your solution by plugging the values back into the original problem statement.

Learn how to solve an age problem involving Divya and Shruti, where Divya is twice as old as Shruti. Explore the step-by-step solution to find their current ages and calculate the difference between them. Suitable for students in Grades 7-9.

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