In a class, average height of all students is `a` cms. Among them, average height of 10 students is 'b' cms and the average height of the remaining students is 'c' cms. Find the number of students in the class. (Here `a gt c` and `b gt c`)

Options

A. `(a(b-c))/(a-c)`
B. `(b-c)/(a-c)`
C. `(b-c)/(10(a-c))`
D. `(10(b-c))/(a-c)`

Answer

To find the number of students in the class, we can use the information provided about the average heights. Let's break down the solution step by step.

### Step 1: Define Variables
Let:
- \( n \) = total number of students in the class
- \( a \) = average height of all students (in cms)
- \( b \) = average height of 10 students (in cms)
- \( c \) = average height of the remaining students (in cms)

### Step 2: Calculate Total Heights
From the average height, we can express the total heights:
- Total height of all students = \( n \times a \)
- Total height of 10 students = \( 10 \times b \)
- Total height of remaining students = \( (n - 10) \times c \)

### Step 3: Set Up the Equation
Since the total height of all students is the sum of the total height of the 10 students and the total height of the remaining students, we can write:
\[ n \times a = 10 \times b + (n - 10) \times c \]

### Step 4: Expand the Equation
Expanding the right side gives:
\[ n \times a = 10b + n \times c - 10c \]

### Step 5: Rearrange the Equation
Rearranging the equation to isolate \( n \):
\[ n \times a - n \times c = 10b - 10c \]
\[ n(a - c) = 10(b - c) \]

### Step 6: Solve for \( n \)
Now, we can solve for \( n \):
\[ n = \frac{10(b - c)}{a - c} \]

### Conclusion
Thus, the number of students in the class is:
\[ n = \frac{10(b - c)}{a - c} \]