The average age of a class of 6 girls is x years. Four new girls join the class with ages x − 2, x + 2, x + 4 and x + 6 years. What is the new average age in years of the class?

Introduction / Context:
This question deals with average age and how it changes when new members join a group. The original group has a symbolic average of x years rather than a specific number, and the new members have ages given in terms of x as well. The task is to compute the new average in algebraic form. Problems like this are helpful for understanding averages in a general algebraic setting, which is useful for many aptitude and math examinations.

Given Data / Assumptions:

• The class initially has 6 girls, and their average age is x years.
• The total age of these 6 girls is therefore 6x years.
• Four new girls join with ages x − 2, x + 2, x + 4 and x + 6 years.
• We need to find the new average age of all 10 girls together.

Concept / Approach:
Average age is calculated as total age divided by the number of people. The initial total age can be obtained by multiplying the average by the number of girls. After new members join, the total age becomes the sum of the original total plus the ages of the new girls. The new average is the new total divided by the new group size. Since everything is expressed in terms of x, we carry out the algebra carefully and simplify the expression to a neat form.

Step-by-Step Solution:
Step 1: Compute the initial total age of the 6 girls as 6 × x = 6x years. Step 2: Add the ages of the four new girls: (x − 2) + (x + 2) + (x + 4) + (x + 6). Step 3: Simplify this sum to get 4x + 10 years. Step 4: The new total age of all 10 girls is 6x + (4x + 10) = 10x + 10 years. Step 5: The new number of girls is 10, so the new average age is (10x + 10) ÷ 10 = x + 1. Step 6: Therefore, the new average age of the class is x + 1 years.

Verification / Alternative check:
To confirm, choose a simple value for x, for example x = 10. Initially, the total age of 6 girls is 60 and the average is 10. The new girls have ages 8, 12, 14 and 16, whose sum is 50. The new total becomes 60 + 50 = 110 and the new average is 110 ÷ 10 = 11. This is x + 1 when x is 10, confirming that the formula x + 1 is consistent for this test case. Because the relationship is linear and the computation was symbolic, the result holds for all valid values of x.

Why Other Options Are Wrong:
Option x + 2: This would require a new total age of 10x + 20, which does not match the algebraic sum of the actual ages.
Option 2.5x: This grows too rapidly with x compared to the correct linear expression and does not fit simple test values.
Option x + 2.5: This suggests an extra 1.5 years added compared to the true new average, and fails when checked with sample values of x.
Option x: This would mean no change in average despite adding older and younger girls, which is inconsistent with the computed total.

Common Pitfalls:
Learners sometimes forget to include all terms correctly when summing the new girls ages or make algebraic slips like misadding constants. Another common mistake is to divide by the wrong number of girls, for example by 6 instead of 10. Keeping track of the group size after the join and carefully simplifying the algebraic expressions step by step prevents such errors.

Final Answer:
The new average age of the class is x + 1 years.