Question

Rs 1200 were distributed equally among certain number of students. Had there been 8 more students, each would have recieved Rs5 less. find the number of students

Answer 1

This should be the answer

Answer 2

Answer:

40

Step-by-step explanation:

Let total no. of students be x

Since amount 1200 is divided equally among x students

So, each student got amount = $\frac{1200}{x}$

If number of students are increased by 8

Then total number of students are x+8

So, Now each student got amount = $\frac{1200}{x+8}$

We are also given that  each would have received Rs 5 less. when number of students were increased by 8

⇒$\frac{1200}{x}-\frac{1200}{x+8}=5$

⇒$\frac{9600+1200x-1200x}{(x)(x+8)}=5$

⇒$\frac{9600}{5}=(x)(x+8)$

⇒$1920=(x)(x+8)$

⇒$x^{2}+8x-1920=0$

⇒$x^{2}+48x-40x-1920=0$

⇒$(x-40)(x+48)$

So, x=40, x= -48

Since number of students cannot be negative

So, total number of students are 40