Question

I'll Mark As Brainliest.



Ranjan, on her birthday, distributed 540 oranges equally among the students. if there would have been 30 students more, it would have received 3 oranges less. find the number of students.

please hurry

Answer 1

Let the number of students be x

and the number of oranges distributed per one student be y.

By first condition

xy=540..................(1)
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By second condition,

(x+30)(y-3)=540

But from (1), 540 = xy

thus

(x+30)(y-3)=xy

Multiply on the L.H.S

x(y-3)+30(y-3)=xy

xy-3x+30y-90= xy

Subtracting xy from both sides,

-3x+30y-90=0

Dividing each term by 3

-x+10y-30=0. (Anything divides 0 becomes zero)

-x-30= -10y. ( Moving 10y to R.H.S. Yeah it's sign 
changes)


-1(x+30)= -1(10y). ( Making -1 as common on both sides)

x+30= 10y. ( Say Multiplying by -1 on both sides)
------------------
x=10y-30. (Moving 30 to R.H.S and got value of 
x)

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Let's substitute value of x in equation (1) ( Hope you didn't forgot equation (1) that was above)

Equation (1) was

xy = 540

(10y-30)(y)=540

Now, I have to change keyboard.

Multiplying the terms





Dividing each term by 10




Moving the constant to right





Oh! It's a quadratic equation, there are various ways to solve it

Let us go for the beginners method i.e "FACTORISATION"

SPLITING -3y as a sum or difference




In first two terms, getting common as y and in next two getting common as 9




Again common as (y+6)




Now

y-9 = 0. or. y+6 = 0

y = 9. or. y = -6

These are the roots of the quadratic equation

Let's confirm which one is useful to us

y means the number of oranges distributed per one. So it is not going to be negative

So 





is the required solution

OH BUT WE WANT THE NUMBER OF STUDENTS

From (1)

xy=540

x(9)=540

x=540/9

x=60

ANS:- THE NUMBER OF STUDENTS IS 60

Hope I've helped you. Best wishes from me for your SSC exams