Weighted average of two classes: Two classes have average marks of 25 and 40 respectively. When the students of both classes are combined, the overall average becomes 30 marks. If the second class has 30 students, determine how many students are in the first class (show the weighted-average setup clearly).

Introduction / Context: This problem tests the weighted-average concept. When two groups with different averages are combined, the overall average is a weighted mean, where each group average is weighted by its group size. We use this to back-calculate the unknown number of students.

Given Data / Assumptions:

• Average of class 1 = 25.
• Average of class 2 = 40.
• Overall (combined) average = 30.
• Class 2 has 30 students; class 1 size is unknown (say x).

Concept / Approach: Weighted average formula: overall average = (sum of totals from each class) / (total students). If A1, A2 are averages and n1, n2 are sizes, then overall = (A1*n1 + A2*n2) / (n1 + n2). Solve for n1 when other values are known.

Step-by-Step Solution:

Verification / Alternative check: Totals: class 1 = 25*60 = 1500; class 2 = 40*30 = 1200. Combined = 2700 over 90 students → 2700/90 = 30, as required.

Why Other Options Are Wrong: 45, 70, 80, and 40 do not satisfy the weighted-average equation when substituted; only 60 produces an overall average of 30.

Common Pitfalls: Mixing simple average with weighted average; forgetting to divide by total students x + 30; or incorrectly moving terms while solving the linear equation.

Final Answer: 60