Question

Rs 250 were equally divided among a certain number of children . If there were 25 more children, each would have eived 50 paise less . Find the no of children . PLEASE HELP !!!!

Answer 1

Answer:

100

Step-by-step explanation:

Total Amount = Rs 250

Let say number of children = X

then each children received = 250/X  Rs

If 25 More children then number of children

= X + 25

then Each children would receive = 250/(X+25)

each children would have received 50 Paise less

50 Paisa = 50/100 Rs = 1/2 RS

250/(X+25)  = 250/X  - 1/2

Multiplying both sides by 2X(X+25)

2X × 250 = 2(X+25)×250  - X(X+25)

500X = 500X + 12500 - X² - 25X

X² + 25X - 12500 = 0

X² + 125X - 100X -12500 = 0

X (X+125) -100(X+125) = 0

(X-100)(X+125) = 0

X = 100   ( X = -125 not possible as students cant be negative)

100 No of children

Answer 2

Supposition:-

• let the no. of children be x
• amount that 1 child will get = $\sf\dfrac{250}{X}Rs.$

• if 25 childrens are increased, then the amount that one child will get :- $\sf\dfrac{250}{x+25}Rs.$

• 50 paise = $\sf\dfrac{1}{2}Rs$

Solution:-

:$\implies$$\sf\bigg(\dfrac{250}{X}\bigg)-\bigg(\dfrac{1}{2}\bigg) =\sf\bigg(\dfrac{250}{x+25} \bigg)$

:$\implies$$\sf\bigg(\dfrac{250}{X}\bigg)- \sf\bigg(\dfrac{250}{x+25} \bigg)=\dfrac{1}{2}$

:$\implies$$\sf \dfrac{250(x+25)-250x}{x (x+25)} = \dfrac{1}{2}$

:$\implies$$\sf \dfrac{250x+625-250x}{x²+25x)} = \dfrac{1}{2}$

:$\implies$$\sf 12500 = x²+25x$

:$\implies$$\sf x²+25x-12500$

:$\implies$$\sf x²+(125-100)x-12500$

:$\implies$$\sf x²+125x-100x-12500$

:$\implies$$\sf x (x+125)-100(x+125)$

:$\implies$$\sf (x-100)(x+125)$

:$\implies$$\sf x = 100, -125$

since, the amount of children can never be -ve, hence, 100 Childrens is the right answer