Question

students of class 10 collected Rs 9000.they wanted to divide it equally among a certain number of students residing in slum areas .when they started distributing the amount, 20more students from near by slum also joined. now each students got Rs 160 less.

(a) find the original number of students living in slum.

(b) which value is depicted by students of 10 class?

Answer 1

A 20 from slum and B 180

Answer 2

Answer:

Let x be the original number of students,

Since, The total amount collected = 9000 rupees,

Thus, the original amount each student gets = $\frac{9000}{x}$

After coming 20 new students,

The new amount that each student gets = $\frac{9000}{x+20}$

According to the question,

$\frac{9000}{x}=\frac{9000}{x+20}+160$

$\implies \frac{9000}{x}-\frac{9000}{x+20}=160$

$\implies 9000(\frac{1}{x}-\frac{1}{x+20})=160$

$\implies \frac{1}{x}-\frac{1}{x+20}=\frac{160}{9000}$

$\implies \frac{20}{x(x+20)}=\frac{4}{225}$

$\implies 4500=4x(x+20)$

$\implies 4x^2+80x-4500=0$

$\implies x^2+20x-1125=0$

By solving this equation,

We get,

x = 25 or -45( not possible )

Hence,  the original number of students living in slum = 25,

New number of students = 25 + 20 = 45