The age of Jaya 10 years ago is equal to Ritu present age. The sum of Jaya's age 8 years hence from today and Ritu age 12 years ago is 90 years then what was age of Neha 13 years ago from now if Neha is 9 years younger than Ritu?

Let \( J \) be Jaya's current age, \( R \) be Ritu's current age, and \( N \) be Neha's current age. We are given the following conditions:

1. **Jaya's age 10 years ago is equal to Ritu's present age**:
   \[
   J - 10 = R
   \]

2. **The sum of Jaya's age 8 years hence and Ritu's age 12 years ago is 90**:
   \[
   (J + 8) + (R - 12) = 90
   \]

3. **Neha is 9 years younger than Ritu**:
   \[
   N = R - 9
   \]

We need to find Neha's age 13 years ago, i.e., \( N - 13 \).

### Step 1: Solve the system of equations

From the first equation:
\[
J = R + 10
\]

Substitute this into the second equation:
\[
(J + 8) + (R - 12) = 90
\]
\[
(R + 10 + 8) + (R - 12) = 90
\]
\[
(R + 18) + (R - 12) = 90
\]
\[
2R + 6 = 90
\]
\[
2R = 84
\]
\[
R = 42
\]

### Step 2: Find Jaya's and Neha's current ages

Now that we know \( R = 42 \), substitute this into \( J = R + 10 \):
\[
J = 42 + 10 = 52
\]

Also, using \( N = R - 9 \):
\[
N = 42 - 9 = 33
\]

### Step 3: Find Neha's age 13 years ago

Now, Neha's age 13 years ago is:
\[
N - 13 = 33 - 13 = 20
\]

### Final Answer:
Neha's age 13 years ago was **20 years**.

Would you like more details or explanations?

Here are some related questions to expand your understanding:

1. If Ritu's age was doubled, how old would she be?
2. How old will Jaya be in 15 years from now?
3. What will Neha's age be in 5 years?
4. How much older is Jaya than Neha currently?
5. What is the total of all their current ages?

**Tip:** To solve age-related problems, forming equations based on the information given is key to finding the correct values.

The age of Jaya 10 years ago is equal to Ritu's present age. The sum of Jaya's age 8 years hence from today and Ritu's age 12 years ago is 90 years. What was the age of Neha 13 years ago if Neha is 9 years younger than Ritu?

Discover how to solve an age-related algebra problem involving Jaya, Ritu, and Neha. Learn to apply linear equations and solve for Neha's age 13 years ago. This problem is ideal for students in Grades 8-10.

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