Some friends decided to go on picnic and the amount fixed for expenditure was kept ₹ 768 . Due to non-arrival of four friends, the friends who participated in picnic beared an additional amount of ₹ 16 per friend. How many friends participated in picnic?

Correct option is A

Given:
Total expenditure fixed = ₹768
Number of absent friends = 4
Additional amount borne per present friend = ₹16
Formula Used:
$$\frac{Total\ Amount}{Actual\ Number} - \frac{Total\ Amount}{Planned\ Number}$$​ = Additional Amount
Solution:
Let the original planned number of friends be x.
The planned share per friend = $$\frac{768}{x}$$​​
The actual number of friends who participated = x - 4
The actual share per friend = $$\frac{768}{x - 4}$$​​
According to the given condition:
$$\frac{768}{x - 4} - \frac{768}{x}$$​= 16
​$$\frac{48}{x - 4} - \frac{48}{x} = 1$$​​
48x - 48(x - 4) = x(x - 4)
48x - 48x + 192 = x^2 - 4x
​$$x^2 - 4x - 192 = 0$$​​
​$$x^2 - 16x + 12x - 192 = 0$$​​
x(x - 16) + 12(x - 16) = 0
(x - 16)(x + 12) = 0
Since the number of friends cannot be negative, x = 16.
The number of friends who participated = 16 - 4 = 12.
Final Answer
So the correct answer is (a)