Question

A mother’s age is 5 times her daughter’s age and after 5 years the sum of their ages will be 76 years. What is the present age of the daughter?

• A. 11 years
• B. 16 years
• C. 21 years
• D. 26 years

Hint:

In age problems, always define variables clearly and convert word conditions into equations step by step for accuracy.

Answer 1

The Correct Option is A

Step 1: Assume the present age of the daughter.
Let the present age of the daughter be \( x \) years.
Then, the present age of the mother will be \( 5x \) years.
Step 2: Form the equation using the given condition.
After 5 years, the daughter’s age will be \( x + 5 \) years.
After 5 years, the mother’s age will be \( 5x + 5 \) years.
According to the question, the sum of their ages after 5 years is 76 years.
\[ (x + 5) + (5x + 5) = 76 \]
Step 3: Solve the equation.
\[ 6x + 10 = 76 \]
\[ 6x = 66 \]
\[ x = 11 \]
Step 4: Conclusion.
The present age of the daughter is 11 years.