Question

A sum of Rs 600 was distributed equally among a certain number of children. If there were 40 more children, each would have received 50 paisa less. Find the original number of children.

Answer 1

$\sf\large\underline{Let:}$

• $\rm{The\: orginal\: Number\:of\: children=x}$

$\sf\large\underline{To\:Find:}$

• $\rm{The\: orginal\: Number\:of\: children=?}$

$\sf\underline{Given\:here:}$

A sum of Rs 600 was distributed equally among a certain number of children. If there were 40 more children, each would have received 50 paisa less]

$\sf\large\underline{Solution:}$

$\rm{\implies Money\:got\:_{each\: children}=\frac{Total\: amount}{No\:of\: children}}$

$\rm{\implies Money\:got\:_{each\: children}=\dfrac{600}{x}}$

Now, calculate each children got after increasing 40 children]

$\rm{\implies Money\:got\:_{each\: children}=\dfrac{600}{x+40}}$

$\sf\underline{According\:to\:the\: above\: information:}$

$\rm{\implies \dfrac{600}{x}-\dfrac{600}{x+40}=\dfrac{50}{100}}$

$\rm{\implies \dfrac{600x+24000-600x}{x(x+40)}=\dfrac{50}{100}}$

$\rm{\implies \dfrac{24000}{x^2+40x}=\dfrac{1}{2}}$

$\rm{\implies x^2+40x=48000}$

$\rm{\implies x^2+40x-48000=0}$

• Splitting the middle term here]

$\rm{\implies x^2+240x-200x-48000=0}$

$\rm{\implies x(x+240)-200(x+240)=0}$

$\rm{\implies (x+240)(x-200)=0}$

$\rm{\implies \therefore\:x=-240\:and\:200}$

Here, negative value can't be Number of children so we take x=200

$\sf\large{Hence,}$

$\rm{\implies Number\:_{orginal\: children}=200}$

Answer 2

SOLUTION :-

=> Let the number of children be "R".

=>It is given that, Rs.600 is divided amongst 'R' children's.

=>So, money received by each children = Rs. 600/R.

=> If there were 40 children more, then

=>Money received by each children = Rs. 600/R+40

=>From the given information,

=>600/R + 600/R + 40 = 50/100

=>600R + 24000 - 600R / R(R + 40) = 50/100

=> 24000/R² + 40R = 1/2

=>R² + 40R = 48000

[Spit the middle term]

=>R² + 40R - 48000 = 0

=>R(R +240) - 200(R + 240) = 0

=>(R + 240) (R-200)=0

=> .°. R = -240 & 200

[Neglect minus term, because the number of children can't negative.]

=>Therefore, the original number of children is 200.

$\huge\bold{\red{\boxed{\green{\mathcal{Be \: Brainly }}}}}$