Question

pls solve this question

Answer 1

Answer:

Step-by-step explanation:

Let the total number of students= x

Total number of oranges= 300

1st case:

Number of oranges received by each student= 300/x

2nd case:

In this case number of boys increased (x+10)

Number of oranges 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

Answer 2

Let the number of students = x

number of oranges each one get = y

So x × y = 300

=> xy = 300

if there were 10 more students, each would have got 1 less orange.

(x+10) × (y-1) = 300

=> xy + 10y - x - 10 = 300

=> 300 + 10y - x -10 = 300

=> 10y - x = 300 - 300 + 10

=> 10y - x = 10

=> x = 10y - 10
___________________

We have xy = 300

=> (10y - 10)y = 300

=> 10y^2 - 10y = 300

=> y^2 - y = 30

=> y^2 - y -30 = 0

=> y^2 - 6y + 5y - 30 = 0

=> y(y-6) +5(y-6) = 0

=> (y-6)(y+5) = 0

=> y = -5, 6

y can't be negative. So y = 6

x = 10y - 10 = 10×6 - 10 = 50

Number of students = 50