Question

Five years ago, the average age of A, B, C and D was 45 years. By including X in the present lot their present average changes to 49 years.
What is the present age of X?

• A. 45 years
• B. 40 years
• C. 48 years
• D. 9 years

Answer 1

The Correct Option is A

To find the present age of X, we need to follow these steps: 

1. Calculate the total age of A, B, C, and D five years ago:
   The average age of A, B, C, and D five years ago was 45 years. Therefore, their total age five years ago was: \(\text{Total age five years ago} = \text{Average} \times \text{Number of people} = 45 \times 4 = 180 \text{ years}.\)
2. Determine their present total age:
   The age of each person increases by 5 years over 5 years. Since there are 4 people, the total increase in age is: \(5 \times 4 = 20 \text{ years}.\)
   Therefore, their present total age is: \(180 + 20 = 200 \text{ years}.\)
3. Include X in the group and calculate the new average:
   With X included, the present average age of A, B, C, D, and X is 49 years for 5 people.
   Therefore, the total current age of A, B, C, D, and X is: \(49 \times 5 = 245 \text{ years}.\)
4. Find the present age of X:
   The total present age of A, B, C, and D is 200 years. Hence, the age of X can be calculated as: \(\text{Age of X} = 245 - 200 = 45 \text{ years}.\)

Therefore, the present age of X is 45 years.