Let's break down this age word problem step by step to find the mother's present age using the given ratio and the age difference information.

Understanding the Age Problem and Ratio

The problem gives us two main pieces of information about Leela and her mother:

1. The ratio of their present ages is 3 : 8. This means for every 3 years Leela is old, her mother is 8 years old at present.
2. The mother was 25 years old when Leela was born. This tells us the constant age difference between the mother and Leela. The mother is always 25 years older than Leela.

Setting up the Equation for Present Ages

We can represent the present ages using the given ratio. Let the common ratio factor be \(x\).

• Leela's present age = \(3x\) years
• Mother's present age = \(8x\) years

Now, we use the second piece of information: the mother is 25 years older than Leela. This age difference remains constant throughout their lives.

So, Mother's present age - Leela's present age = 25 years.

Substituting our expressions for their present ages:

\(8x - 3x = 25\)

Solving for the Unknown Factor \(x\)

Now we solve the equation for \(x\):

\(5x = 25\)

To find \(x\), divide both sides by 5:

\(x = \frac{25}{5}\)

\(x = 5\)

Calculating the Mother's Present Age

We found that the ratio factor \(x\) is 5. The mother's present age is represented by \(8x\).

Mother's present age = \(8 \times x = 8 \times 5 = 40\)

So, the mother's present age is 40 years.

Verifying the Solution

Let's check if the calculated ages satisfy both conditions:

• Leela's present age = \(3x = 3 \times 5 = 15\) years.
• Mother's present age = \(8x = 8 \times 5 = 40\) years.

Condition 1: Ratio of present ages = Leela : Mother = 15 : 40. Dividing both by 5, we get 3 : 8. This matches the given ratio.

Condition 2: Age difference = Mother's age - Leela's age = 40 - 15 = 25 years. This matches the given information that the mother was 25 when Leela was born.

Both conditions are satisfied, confirming our solution is correct.

Revision Table: Age Ratio Problem

Additional Information: Solving Age Word Problems

Age word problems often involve ratios, differences, sums, or ages at different points in time (past, present, future). Here are some tips for solving them:

• Read the problem carefully to identify the unknowns and the given relationships.
• Define variables to represent the unknown ages, usually starting with the present age.
• Write down the relationships between the ages as equations. Remember that age difference is constant, but ratios and sums change over time.
• Solve the equation(s) to find the value of the variable(s).
• Use the variable's value to calculate the specific ages asked for in the question.
• Always check your answer by plugging the calculated ages back into the original problem statement to ensure all conditions are met.
• If the problem involves past or future ages, calculate those based on the present ages (e.g., age 5 years ago = present age - 5; age 10 years from now = present age + 10).