Question

Some students planned for go for a picnic. The budget for food was Rupee 960. But four of them fail to go by 12 rupees. How many students went to the picnic.

Answer 1

Let the no.of students planned to go for tour be 'x'
$cost \: of \: each \: person = \frac{960}{x}$


By Qn,

$\frac{960}{x - 4} - \frac{960}{x} = 12$
ie

$960( \frac{1}{x - 4} - \frac{1}{x} ) = 12$
ie
$80( \frac{4}{ {x}^{2} - 4x } ) = 1$
ie

${x}^{2} - 4x = 320$
ie
${x}^{2} - 4x - 320 = 0$
ie

${x}^{2} - 20x + 16x - 320 = 0$
ie
$x(x - 20) + 16(x - 20) = 0$
ie

$(x + 16)(x - 20) = 0$
ie

$x = - 16(rejected) \: (or) \: x = 20$
Thus no. of persons went for the tour =x-4=16