Let's break down the problem step by step:

• The total cost of eatables is ₹96.
• Initially, let the total number of friends be $x$.
• The initial contribution per person is $\frac{96}{x}$.
• However, 4 people did not turn up, so the number of people who actually went is $x - 4$.
• The new contribution per person is $\frac{96}{x - 4}$.
• Each person now pays ₹4 extra, which gives us the equation: $\frac{96}{x - 4} = \frac{96}{x} + 4$

Now, let's solve the equation:

$\frac{96}{x - 4} - \frac{96}{x} = 4$

First, find a common denominator for the left side:

$\frac{96(x) - 96(x - 4)}{x(x - 4)} = 4$

Simplifying the numerator:

$\frac{96x - 96x + 384}{x(x - 4)} = 4$ $\frac{384}{x(x - 4)} = 4$

Now, multiply both sides by $x(x - 4)$:

$384 = 4x(x - 4)$

Divide both sides by 4:

$96 = x(x - 4)$

Expand the right side:

$96 = x^2 - 4x$

Rearrange it to form a quadratic equation:

$x^2 - 4x - 96 = 0$

Solve using the quadratic formula:

$x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(-96)}}{2(1)}$ $x = \frac{4 \pm \sqrt{16 + 384}}{2}$ $x = \frac{4 \pm \sqrt{400}}{2}$ $x = \frac{4 \pm 20}{2}$

This gives two possible solutions:

$x = \frac{4 + 20}{2} = 12 \quad \text{or} \quad x = \frac{4 - 20}{2} = -8$

Since $x$ must be positive, the total number of friends initially was $x = 12$.

Thus, 12 friends were originally supposed to go on the picnic, but after 4 did not turn up, 8 friends went on the picnic.

Would you like a detailed explanation of any part, or do you have further questions?

Here are 5 related questions you can try:

1. If 3 people didn’t turn up, how much more would each friend have to pay?
2. What if the total amount spent was ₹120 instead of ₹96?
3. How would the equation change if 5 people didn’t show up instead of 4?
4. What if the friends initially planned to spend ₹96, but the cost increased to ₹120 at the picnic?
5. What would the equation look like if 6 people dropped out instead of 4?

Tip: In problems like these, setting up an equation based on the changes (like an increase in cost per person) is a key strategy to solving them systematically!