Question

$480$ sweets were equally distributed among a certain number of children .Had their been $4$ more children each child would have got $6$ less sweets. Find the original number of children.

Answer 1

Let, $x=$ total sweets ,

$y=$ children

According to question ,

$\frac{x}{y+4}=\frac{x}{y}-6$

$\frac{480}{y+4}$$=\frac{480}{y}-6$

$480y=480(y+4)-6y(y^2+4y)$.

$480y=480y+1920-6y^2-24y$

$6y^2+4y-320=0$

$y=\frac{-4\pm \sqrt{16+1280}}{2}$

$y=\frac{-4\pm 36}{2}$

$y=16,-20$

$y>0\Rightarrow y=16$ .

$\therefore \frac{x}{y}=30$