Question

An enterprise got a bonus and decided to share it in equal parts between the exemplary workers. It turned out, however, that there were 3 more exemplary workers than it had been assumed. In that case, each of them would have got 4 roubles less. The administration had found the possibility to increase the total sum of the bonus by 90 roubles and as a result each exemplary worker got 25 roubles. How many people got a bonus?

Answer 1

Lets initially the bonus is Rs 4 is it is distributed among x workers

share of each worker = $\frac{y}{x}$

but when there were 3 more worker sec. to question

$\frac{y}{x+3}=\frac{y}{x}-4$ ...(i)

Now Net Bonus = $y+90$

again acc. to question

$\frac{y+90}{x+3}=25$

$\Rightarrow y+90=25(x+3)$

$\Rightarrow y=25(x+3)-90$ ...(ii)

put value of y from eq. (ii) to eq. (i)

$\frac{25(x+3)-90}{x+3}=\frac{25(x+3)-90}{x}-4$

$\Rightarrow 25-\frac{90}{x+3}=\frac{25(x+3)-90}{x}-4$

$\Rightarrow 29=\frac{25(x+3)-90}{x}+\frac{90}{x+3}$

$\Rightarrow 29\left(x\right)(x+3)=25(x+3{)}^2-90(x+3)+90x$

$\Rightarrow 29x(x+3)=25(x^2+9+6x)-90x-270+90x$

$\Rightarrow 29x^2+87x=25x^2+225+150x-270$

$\Rightarrow (29x^2-25x^2)+(87x-150x)+(270-225)=0$

$\Rightarrow 4x^2-63x+45=0$

split method

$4x^2-60x-3x+45=0$

$\Rightarrow 4x(x-15)-3(x-15)=0$

$\Rightarrow (4x-3)(x-15)=0$

$x=15,x=\frac{3}{4}$

x is number of works it can't be $\frac{3}{4}$

$x+3=15+3=18$

so 18 people got Bonus.