In a class of 50 students, the average marks are 70 percent. The average of the first 25 students is 60 percent and the average of the next 24 students is 80 percent. What percentage of marks did the last student obtain?

Introduction / Context:
This question is about averages and total sums. The overall average of the class is given, along with separate averages for two groups of students. We must use this information to deduce the marks of a single remaining student. This type of problem shows how averages can be manipulated to find missing values.

Given Data / Assumptions:
Total number of students = 50. Average marks of entire class = 70 percent. Average of first 25 students = 60 percent. Average of next 24 students = 80 percent. Marks of the last (50th) student are unknown.

Concept / Approach:
Average is defined as total sum divided by number of observations. Thus total marks of the class equal 50 multiplied by 70. Similarly, we can compute total marks of the first 25 students and the next 24 students separately. Subtracting these subtotals from the grand total gives the marks of the last student. Finally, we can interpret that value as a percentage since all averages are given in percent format.

Step-by-Step Solution:
Total marks of all 50 students = 50 * 70 = 3500 (in percentage points units). Total marks of first 25 students = 25 * 60 = 1500. Total marks of next 24 students = 24 * 80 = 1920. Combined marks of first 49 students = 1500 + 1920 = 3420. Let marks of 50th student be M. Then 3420 + M = 3500. So M = 3500 - 3420 = 80. Thus the last student scored 80 percent.

Verification / Alternative check:
Recalculate the overall average to confirm. Adding the marks of first 49 students which are 3420 and the last student which is 80 gives 3500. Dividing by 50 returns 70 which matches the given class average. This confirms the calculation is consistent.

Why Other Options Are Wrong:
If the last student had 90 percent, total marks would be 3420 + 90 = 3510 and average would be 3510 / 50 = 70.2, not 70. If marks were 60 percent, total would be 3480 and average 69.6. Marks of 70 percent would give average 69.8. A value of 75 percent would also produce an incorrect overall average. Only 80 percent maintains the class average at exactly 70 percent.

Common Pitfalls:
Some learners mistakenly average the three given percentages directly instead of using total sums weighted by student counts. Another error is to divide by 49 instead of 50 when recomputing averages. It is crucial to remember that averages must be handled through totals, not by naive averaging of averages.

Final Answer:
The last student of the class obtained 80 percent marks.