Question

Ranjan, on her birthday, distributed 540
oranges equally among the students. If there
would have been 30 students more, each
would have received 3 oranges less. Find the
number of students.​

Answer 1

To Determine :-

• The no . of student

Evaluation :-

• let x be the number of students

Now Rs. 540 is distributed equally among x students .

so , each of them gets

$\implies{\sf{\large { Rs.\:\:\: \dfrac{549}{x+30}\: }}}$

Now if there would have 30 students more than each of them gets .

$\implies{\sf{\large { Rs.\:\:\: \dfrac{540}{x+30}\: }}}$

$\bf\blue{so,~by~the~given~condition}$

⠀

$\implies{\sf{\large { \:\:\: \dfrac{540-540}{x(x+30)}\: }}}$ = 3

⠀

$\implies{\sf{\large { \:\:\: \dfrac{540x+16200-549x}{x(x+30)}\: }}}$

⠀

$\implies{\sf{\large { \:\:\: \dfrac{16200}{x(x+30)}\: }}}$

⠀

$\longmapsto\tt{x^2+30x=5400\:}$

$\longmapsto\tt{x^2 + 90x - 60x - 5400 = 0\:}$

$\longmapsto\tt{x(x+90) - 60(x+90)=0\:}$

$\longmapsto\tt{(x+90) (x-60) = 0\:}$

$\longmapsto\tt{x=-90, 60\:}$

$\:\:\:\:\:\bold{\underline{\sf{\red{Since~number~of~student~can't~be~negative}}}}$

$\longmapsto\tt{x=60\:}$