A mother is five times older than her daughter at present. After 5 years, she will be three times older than her daughter. What is the mother present age in years?

Introduction / Context:
This is a standard mother daughter age relationship problem. At the present time, one age is a multiple of the other, and in the future the same relation changes to a different multiple. The question asks for the present age of the mother. Such problems are common in aptitude exams and help strengthen skills in handling linear equations with simple multiples and a fixed time shift.

Given Data / Assumptions:

• At present, the mother is five times as old as her daughter.
• After 5 years, the mother will be three times as old as her daughter.
• We need to find the current age of the mother.
• Both ages increase by 5 years over the given period.

Concept / Approach:
We use a variable for the daughter present age and express the mother present age as a multiple of that variable. Then we form expressions for their ages after 5 years and use the future three times relationship to create an equation. Solving this linear equation gives the daughter age, and multiplying appropriately gives the mother age. This method is very direct and highlights the importance of reading the word times as a multiplier in the algebraic equation.

Step-by-Step Solution:
Step 1: Let the present age of the daughter be x years. Step 2: The mother is five times older, so her present age is 5x years. Step 3: After 5 years, the daughter will be x + 5 years old and the mother will be 5x + 5 years old. Step 4: The condition after 5 years says 5x + 5 is three times x + 5, so 5x + 5 = 3 × (x + 5). Step 5: Solve this linear equation to get x = 5 years. Therefore, the mother present age is 5x = 25 years. Step 6: Thus, the required present age of the mother is 25 years.

Verification / Alternative check:
Using the found ages, the daughter is 5 years old and the mother is 25 years old at present. This clearly matches the statement that the mother is five times older than her daughter now, because 25 = 5 × 5. After 5 years, their ages will be 10 and 30 respectively. At that time, 30 is three times 10, confirming the second condition. Both conditions are satisfied, so the computed mother age is correct.

Why Other Options Are Wrong:
Option 20 years: If the mother were 20, the daughter present age would have to be 4, and after 5 years they would be 25 and 9, which does not give a three times relation.
Option 22 years and 29 years: These values do not satisfy both the five times and three times conditions when you attempt to back calculate the daughter age.
Option 30 years: This would give a different ratio now and in the future which does not align with the problem statements.

Common Pitfalls:
One common confusion is the phrase five times older, which some learners misread as five years older. Here it clearly means five times the daughter age. Another mistake is forgetting to add 5 years to both ages when using the future condition. Carefully distinguishing multiples from differences and tracking the time shift prevent such errors.

Final Answer:
The mother present age is 25 years.