In a class, each student likes either cricket or football 40% of the students like football. 80% of the students like cricket. The number of studnets who like only cricket is 40 more than the number of students who like only football. What is the strength of the class?

Options

A. 80
B. 100
C. 120
D. 150

Explanation

To solve the problem step by step, we will define variables and set up equations based on the information provided.

### Step 1: Define the Variables
Let the total number of students in the class be \( x \).

### Step 2: Set Up the Equations
From the problem, we know:
- 40% of the students like football:
\[ A + B = 0.4x \]
- 80% of the students like cricket:
\[ B + C = 0.8x \]
- The number of students who like only cricket (C) is 40 more than the number of students who like only football (A):
\[ C = A + 40 \]

### Step 3: Substitute the Third Equation into the First Two
Substituting \( C = A + 40 \) into the second equation:
\[ B + (A + 40) = 0.8x \]
This simplifies to:
\[ A + B + 40 = 0.8x \]
Now, we can express \( B \) in terms of \( A \):
\[ B = 0.8x - A - 40 \]

### Step 4: Substitute \( B \) into the First Equation
Now substitute \( B \) from the above equation into the first equation:
\[ A + (0.8x - A - 40) = 0.4x \]
This simplifies to:
\[ 0.8x - 40 = 0.4x \]
Rearranging gives:
\[ 0.8x - 0.4x = 40 \]
\[ 0.4x = 40 \]

### Step 5: Solve for \( x \)
Now, divide both sides by 0.4:
\[ x = \frac{40}{0.4} = 100 \]

### Conclusion
The strength of the class is \( 100 \) students.