Sixteen children are divided into two groups A and B of 10 and 6 children respectively. The average percentage of marks obtained by the children of group A is 75, and the average percentage of marks of all the 16 children together is 76. What is the average percentage of marks of the children in group B?

Introduction:
This problem is about averages of subgroups within a larger group. We know the overall average of all children and the average of one subgroup. From this information we can find the total marks, subtract the marks of group A and then compute the average for group B. This is a standard type of question in aptitude tests dealing with averages and weighted sums.

Given Data / Assumptions:
- Total number of children = 16. - Group A has 10 children. - Group B has 6 children. - Average marks of group A = 75 percent. - Average marks of all 16 children together = 76 percent. - We need the average marks of group B.

Concept / Approach:
Average is defined as total marks divided by number of children. We use this definition twice: once to compute the total marks of all 16 children and once to compute the total marks of group A. The marks of group B are obtained by subtracting the sum for group A from the overall sum. Finally, dividing by the number of children in group B gives the required average in that group.

Step-by-Step Solution:
Step 1: Total marks of all 16 children = 16 * 76 = 1216. Step 2: Total marks of group A = 10 * 75 = 750. Step 3: Total marks of group B = total marks of all children minus total marks of group A. Step 4: So, marks of group B = 1216 - 750 = 466. Step 5: Number of children in group B = 6. Step 6: Average marks of group B = 466 / 6. Step 7: Simplify 466 / 6 by dividing numerator and denominator by 2: 466 / 6 = 233 / 3. Step 8: As a mixed fraction this is 77 and two thirds, which is approximately 77.67 percent.

Verification / Alternative Check:
We can check by computing the combined average using this group B average. Group A contributes 750 marks and group B contributes 466 marks, total 1216 marks. Dividing by 16 gives 1216 / 16 = 76, which matches the given overall average. This confirms that the value 233 / 3 for group B is correct.

Why Other Options Are Wrong:
Option 76: This is the average of all 16 children, not of group B alone. Option 77 and option 80 are simple round numbers but they do not satisfy the condition that the combined average is 76. Option 243/4 corresponds to 60.75 percent, which is far from the required higher average for group B.

Common Pitfalls:
Many students mistakenly average the two given averages 75 and 76 directly, without taking into account the different group sizes. Another error is to forget that the overall average is influenced more by the larger group. Working with total marks rather than directly with averages helps avoid these mistakes.

Final Answer:
The average marks of the children in group B is 233/3 percent.