After 10 years, Ajay will be two times as old as Bhushan is today. Five years ago, Chandru was younger than Bhushan by 10 years. After 5 years, Ajay will be seven times as old as Chandru was five years ago. What is the sum of the current ages of Ajay, Bhushan and Chandru? (All ages are in years)

Let's define the current ages of Ajay, Bhushan, and Chandru as \( A \), \( B \), and \( C \) respectively. We are given the following information:

1. **After 10 years, Ajay will be two times as old as Bhushan is today.**
   \[
   A + 10 = 2B
   \]
   Rearranging, we get:
   \[
   A = 2B - 10
   \]

2. **Five years ago, Chandru was younger than Bhushan by 10 years.**
   \[
   C - 5 = B - 5 - 10
   \]
   Simplifying, we get:
   \[
   C = B - 10
   \]

3. **After 5 years, Ajay will be seven times as old as Chandru was five years ago.**
   \[
   A + 5 = 7(C - 5)
   \]
   Substituting \( C = B - 10 \) into the equation:
   \[
   A + 5 = 7(B - 10 - 5)
   \]
   Simplifying:
   \[
   A + 5 = 7(B - 15)
   \]
   Expanding and simplifying further:
   \[
   A + 5 = 7B - 105
   \]
   \[
   A = 7B - 110
   \]

### Step 1: Solve the system of equations
We now have two equations involving \( A \) and \( B \):

1. \( A = 2B - 10 \)
2. \( A = 7B - 110 \)

Equating the two expressions for \( A \):
\[
2B - 10 = 7B - 110
\]
Subtract \( 2B \) from both sides:
\[
-10 = 5B - 110
\]
Add 110 to both sides:
\[
100 = 5B
\]
Divide by 5:
\[
B = 20
\]

### Step 2: Calculate \( A \) and \( C \)
Using \( B = 20 \) in the equation \( A = 2B - 10 \):
\[
A = 2(20) - 10 = 40 - 10 = 30
\]

Using \( B = 20 \) in the equation \( C = B - 10 \):
\[
C = 20 - 10 = 10
\]

### Step 3: Find the sum of their ages
The sum of the current ages of Ajay, Bhushan, and Chandru is:
\[
A + B + C = 30 + 20 + 10 = 60
\]

Thus, the sum of their current ages is **60 years**.

Would you like more details or have any questions? Here are some related questions:

1. What other methods could be used to solve this problem?
2. How can we verify that the solution is correct?
3. What if the conditions were slightly different? How would that change the solution?
4. How do you solve problems with more than three variables?
5. Why is it important to check the consistency of your equations?

**Tip:** When solving word problems, breaking down the problem step by step and translating the words into equations can help make the problem more manageable.

Learn how to solve an age problem involving Ajay, Bhushan, and Chandru with a detailed step-by-step solution. This problem covers linear equations and age-related formulas, focusing on logical deduction and equation solving. Suitable for students in Grades 7-9.

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