A number of friends decided to go on a picnic and planned to spend Rs.960 on food. Four of them, however, did not turn up. As a consequence, the remaining ones had to contribute Rs.40 each extra. The number of those who attended the picnic was:

Options

A. 8
B. 12
C. 16
D. 24

Explanation

To solve the problem step by step, let's denote the number of friends who initially planned to go on the picnic as \( x \).

### Step 1: Establish the total expenditure and individual contribution
The total expenditure for food is Rs. 960. Therefore, if all \( x \) friends had turned up, the contribution of each friend would be:
\[ \text{Contribution per friend} = \frac{960}{x} \]

### Step 2: Account for the friends who did not turn up
Since 4 friends did not turn up, the number of friends who actually attended the picnic is \( x - 4 \). The contribution per friend for those who attended would then be:
\[ \text{Contribution per friend (attendees)} = \frac{960}{x - 4} \]

### Step 3: Set up the equation based on the extra contribution
According to the problem, the remaining friends had to contribute Rs. 40 each extra. Therefore, we can set up the following equation:
\[ \frac{960}{x - 4} = \frac{960}{x} + 40 \]

### Step 4: Solve the equation
To solve this equation, we first eliminate the fractions by multiplying through by \( x(x - 4) \):
\[ 960x = 960(x - 4) + 40x(x - 4) \]

Expanding both sides:
\[ 960x = 960x - 3840 + 40x^2 - 160x \]

Now, simplify the equation:
\[ 0 = -3840 + 40x^2 - 160x \]
\[ 40x^2 - 160x - 3840 = 0 \]

### Step 5: Simplify the quadratic equation
We can simplify this equation by dividing all terms by 40:
\[ x^2 - 4x - 96 = 0 \]

### Step 6: Factor the quadratic equation
Next, we can factor the quadratic equation:
\[ (x - 12)(x + 8) = 0 \]

### Step 7: Solve for \( x \)
Setting each factor to zero gives us:
\[ x - 12 = 0 \quad \Rightarrow \quad x = 12 \]
\[ x + 8 = 0 \quad \Rightarrow \quad x = -8 \quad (\text{not a valid solution since } x \text{ cannot be negative}) \]

Thus, the number of friends who initially planned to go on the picnic is \( x = 12 \).

### Step 8: Find the number of friends who attended
Since 4 friends did not turn up, the number of friends who attended the picnic is:
\[ x - 4 = 12 - 4 = 8 \]

### Final Answer
The number of friends who attended the picnic is **8**.

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