A36
B28
C54
D40
Answer:
B. 28
Read Explanation:
Understanding the Concept of Average
The fundamental formula for average is: Average = (Sum of quantities) / (Number of quantities).
Conversely, the sum of quantities can be found by: Sum of quantities = Average × Number of quantities. This derived formula is extremely useful for solving average-related problems quickly in competitive exams.
When dealing with ages, remember that everyone in a group ages simultaneously. If 'X' years pass, each person's age increases by 'X' years, and the total sum of their ages increases by 'X multiplied by the number of people'.
Step-by-Step Calculation
1. Calculate the Sum of Ages of A and B Four Years Ago:
Given that the average age of A and B four years ago was 18 years.
Number of people = 2 (A and B).
Sum of their ages four years ago = 18 years/person × 2 people = 36 years.
2. Calculate the Current Sum of Ages of A and B:
Since 4 years have passed, each person's age has increased by 4 years.
Total increase in their combined age over 4 years = 4 years/person × 2 people = 8 years.
Current sum of ages of A and B = (Sum of ages four years ago) + (Total increase) = 36 years + 8 years = 44 years.
3. Calculate the Current Sum of Ages of A, B, and C:
Given that the current average age of A, B, and C is 24 years.
Number of people = 3 (A, B, and C).
Current sum of ages of A, B, and C = 24 years/person × 3 people = 72 years.
4. Determine C's Current Age:
C's current age can be found by subtracting the current sum of A and B's ages from the current sum of A, B, and C's ages.
C's current age = (Current sum of A, B, C) - (Current sum of A, B) = 72 years - 44 years = 28 years.