The average marks obtained in a class of 50 students is 70%. The average of first 25 in 60% and average of next 24 students is 80%. What is the marks obtained by the last student?

Options

A. 0.9
B. 0.6
C. 0.8
D. 0.7

Answer

To solve the problem step by step, we will calculate the total marks obtained by the students in the class and then find the marks obtained by the last student.

### Step 1: Calculate the total marks of all 50 students
The average marks of the class of 50 students is 70%.

Total marks = Average marks × Number of students
Total marks = 70% × 50
Total marks = (70/100) × 50 = 35

### Step 2: Calculate the total marks of the first 25 students
The average marks of the first 25 students is 60%.

Total marks of first 25 students = Average marks × Number of students
Total marks = 60% × 25
Total marks = (60/100) × 25 = 15

### Step 3: Calculate the total marks of the next 24 students
The average marks of the next 24 students is 80%.

Total marks of next 24 students = Average marks × Number of students
Total marks = 80% × 24
Total marks = (80/100) × 24 = 19.2

### Step 4: Calculate the total marks of the last student
Now, we can find the marks obtained by the last student.

Let the marks obtained by the last student be \( x \).

From the total marks of all students, we can write the equation:
Total marks of all students = Total marks of first 25 students + Total marks of next 24 students + Marks of last student

So, we have:
35 = 15 + 19.2 + x

### Step 5: Solve for \( x \)
Now, we can solve for \( x \):
35 = 15 + 19.2 + x
35 = 34.2 + x
x = 35 - 34.2
x = 0.8

Thus, the marks obtained by the last student is **0.8**.