A number of friends decided to go on a picnic and planned to spend Rs 108 on eatables. Three of them however did not turn up. As a consequence each one of the remaining had to contribute Rs 3 extra. The number of them who attended the picnic was :

Options

A. 15
B. 12
C. 9
D. 6

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the Variables
Let \( X \) be the total number of friends who initially planned to go on the picnic.

### Step 2: Calculate the Contribution per Person
If all \( X \) friends had gone, the contribution per person would be:
\[ \text{Contribution per person} = \frac{108}{X} \]

### Step 3: Determine the Number of Friends Who Actually Attended
Since 3 friends did not turn up, the number of friends who actually attended the picnic is:
\[ \text{Number of friends who attended} = X - 3 \]

### Step 4: Calculate the New Contribution per Person
With \( X - 3 \) friends attending, the new contribution per person becomes:
\[ \text{New contribution per person} = \frac{108}{X - 3} \]

### Step 5: Set Up the Equation
According to the problem, the new contribution per person is Rs 3 more than the original contribution. Therefore, we can set up the equation:
\[ \frac{108}{X - 3} = \frac{108}{X} + 3 \]

### Step 6: Solve the Equation
To solve the equation, first, eliminate the fractions by multiplying through by \( X(X - 3) \):
\[ 108X = 108(X - 3) + 3X(X - 3) \]
Expanding both sides gives:
\[ 108X = 108X - 324 + 3X^2 - 9X \]
Now, simplify this equation:
\[ 0 = 3X^2 - 9X - 324 \]
Dividing the entire equation by 3:
\[ 0 = X^2 - 3X - 108 \]

### Step 7: Factor or Use the Quadratic Formula
Now we can factor or use the quadratic formula to find \( X \). The quadratic formula is:
\[ X = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Here, \( a = 1, b = -3, c = -108 \):
\[ X = \frac{-(-3) \pm \sqrt{(-3)^2 - 4 \cdot 1 \cdot (-108)}}{2 \cdot 1} \]
Calculating the discriminant:
\[ X = \frac{3 \pm \sqrt{9 + 432}}{2} \]
\[ X = \frac{3 \pm \sqrt{441}}{2} \]
\[ X = \frac{3 \pm 21}{2} \]
This gives us two possible solutions:
\[ X = \frac{24}{2} = 12 \quad \text{and} \quad X = \frac{-18}{2} = -9 \]
Since the number of friends cannot be negative, we have:
\[ X = 12 \]

### Step 8: Calculate the Number of Friends Who Attended
The number of friends who actually attended the picnic is:
\[ X - 3 = 12 - 3 = 9 \]

### Final Answer
The number of friends who attended the picnic is **9**.