Question

Q28
Rs. 250 were divided equally among a certain number of children. If
there were 25 more children, each would have received 50 paisa less.
[3]
Find the number of children.​

Answer 1

Answer:

there are 100 children

Step-by-step explanation:

Let the number of children be x.

It is given that Rs 250 is divided amongst x students.

So, money received by each child = Rs 250/x

Since, the number of students cannot be negative,

so, x = 100.

Hence, the number of students is 100.

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