Problems on Ages
Problems on Ages Formulas
Basic Concepts
The problems on ages generally involve relationships between the ages of different people at different points in time.
Common Formulas
Present Age
Let the present age of person A be \( x \) years and person B be \( y \) years.
Future Age
If after \( n \) years, person A will be \( x + n \) years old and person B will be \( y + n \) years old.
\[ \text{Future Age of A} = x + n \] \[ \text{Future Age of B} = y + n \]Past Age
If \( n \) years ago, person A was \( x - n \) years old and person B was \( y - n \) years old.
\[ \text{Past Age of A} = x - n \] \[ \text{Past Age of B} = y - n \]Age Difference
The difference in ages between two people remains constant over time.
Sum of Ages
If the sum of the ages of two people is given, let the sum be \( S \).
Average Age
If there are \( n \) people with ages \( A_1, A_2, A_3, \ldots, A_n \), the average age is given by:
Examples
Example 1: Age Difference
If the present age of A is 30 years and B is 20 years, the age difference is:
\[ \text{Age Difference} = |30 - 20| = 10 \text{ years} \]Example 2: Sum of Ages
If the sum of the ages of A and B is 50 years, and A is 30 years old, then B's age is:
\[ x + y = 50 \implies 30 + y = 50 \implies y = 50 - 30 = 20 \text{ years} \]Example 3: Average Age
If there are 3 people with ages 25, 30, and 35 years, the average age is:
\[ \text{Average Age} = \frac{25 + 30 + 35}{3} = \frac{90}{3} = 30 \text{ years} \]Master This Topic with Smart Practice
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