Question

300 apples r distributed equally among a certain no. of students. Had there been 10 more students , each would have received 1 apple less. find d total no. of students.

Answer 1

Let the total number of students= x

Total number of Apples= 300

1st case:
Number of apples received by each student= 300/x

2nd case:

In this case number of boys increased (x+10)
Number of Apples received by each boy= 300/(x+10)

A.T.Q

(300/x) -1 = 300/(x+10)

300/x -300/(x+10) =1

Lcm = x(x+10)

300(x+10) - 300x/( x(x+10)) = 1

300x+3000-300x = x(x+10)
3000= x²+10x

x²+10x-3000=0
[ Factorization by middle term splitting]

x²+60x-50x-3000=0
x(x+60)- 50(x+60)=0
(x+60)(x-50)=0

x+60=0,. x=-60
x-50=0
x= 50

Therefore,X= -60 cannot be taken as Number of students are always positive.

Hence, the total number of students in the class= 50

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Hope this will help ....

Answer 2

Thanks for the question!

Let the original no. of students be "x"

We have, Total number of Apples= 300

So, Number of apples received by each student= 300/x

(300/x) -1 = 300/(x+10)

300/x -300/(x+10) =1

300(x+10) - 300x/( x(x+10)) = 1

300x+3000-300x = x(x+10)

3000= x²+10x

x²+10x-3000=0

x²+60x-50x-3000=0

x(x+60)- 50(x+60)=0

(x+60)(x-50)=0

x+60=0, x = -60

x-50=0,  x= 50

Number of students has to be positive. So, the total number of students in the class= 50

Hope this helps!!!