Question

A number of friends decided to go on a picnic
and planned to spend 96 on eatables. Four of
them, however, did not turn up as a consequence,
the remaining ones had to contribute 4 each
extra. The number of those who attended the
picnic was
1. 8
2.12
3. 16
4. 24
​

Answer 1

Answer:

96 be the total amount for the eatables, and x number of friends who were attend the picnic. So each friend had to pay 96/x. The number of friends who did attend the picnic was (x-4) and each had to pay (96/x)+4. So 8 friends did attend the picnic.

Answer 2

$\bold{\boxed{ANSWER}}$

$\mathbb\blue{Let\: the\: total\: number\: of\: friend \: X}$

$\frac{96}{x - 4} - \frac{96}{x} = 4 \\ \\ four \: of \: them \: however \: did \: not \: turn \: up \\ \\ 96 | \frac{1}{x - 4} - \frac{1}{x} | = 4 \\ \frac{1}{x - 4} - \frac{1}{x} | = \frac{4}{96} \\ \frac{x - x - 4}{x(x - 4)} = \frac{1}{24} \\ \frac{ - 4}{ {x}^{2} - 4x} = \frac{1}{24} \\ \\ 24 \times 4 = {x}^{2} - 4x \\ \\ 96 = {x}^{2} - 4x \\ {x }^{2} - 4x - 96 = 0 \\ \ lcm \: of \: 96 | \\ 2 |96| \\ 2 |48| \\ 2 |24| \\ 2 |12 | \\ 2| 6| \\ 3 |3| \\ 1$

••• 2x2x2. x 2x2x3 •••

$2 \times 2 \times 2 \times = 8 \\ 2 \times 2 \times 3 = 12$

12-8=4

${ x}^{2} - 4x - 96 = 0 \\ {x}^{2} - 12x + 8x - 96 = 0 \\ x(x - 12) + 8(x - 12) = 0 \\ (x + 8)(x - 12) = 0 \\ x = 12 \: The \: total \: friend$

↪️No of friends attend in picnic =

12-4 =8.

↪️so 8 is the answer. ↩️