Let's break down the problem and form the necessary equations based on the information provided in the image.

Given Information:

1. The sum of the ages of Reeta and her father Ranjeet is 55 years.
2. After 10 years, Reeta's age will be double that of her father.

Let:

• $R$ be Ranjeet's current age.
• $r$ be Reeta's current age.

(a) First Equation:

From the first piece of information:

• The sum of their ages is 55 years. $R + r = 55$ This is the first equation.

(b) Second Equation:

From the second piece of information:

• After 10 years, Reeta's age will be double that of her father.
• In 10 years, Ranjeet's age will be $R + 10$ and Reeta's age will be $r + 10$.
• According to the condition, $r + 10 = 2(R + 10)$.

Expanding and simplifying: $r + 10 = 2R + 20$ $r = 2R + 10$ This is the second equation.

(c) Present Ages:

Now, let's solve these two equations simultaneously:

1. $R + r = 55$
2. $r = 2R + 10$

Substitute the second equation into the first: $R + (2R + 10) = 55$ $3R + 10 = 55$ $3R = 45$ $R = 15$

Now, substitute $R = 15$ back into the second equation: $r = 2(15) + 10 = 30 + 10 = 40$

Answers:

• Ranjeet's current age: 15 years.
• Reeta's current age: 40 years.

Would you like to know more details, or do you have any other questions?

Here are five related questions you might find interesting:

1. What will be the sum of their ages after 5 years?
2. How old was Ranjeet when Reeta was born?
3. What was the ratio of their ages 5 years ago?
4. If their ages were halved, what would be the new sum of their ages?
5. How many years ago was Reeta's age equal to Ranjeet's current age?

Tip: When solving simultaneous equations, substitution and elimination methods are key strategies to simplify and find solutions effectively.