plz give the easiest solution i am preparing 4 bank clerk xam i have sol bt nt able 2 understand plz give detail description of how eqn is formed
300 apples r distributed equally among a certain no of stdudents had there been 10 more students each would have recd 1 apple less find number of students
The original average is the number of apples (300) divided by the number of students (let's call this "n").
Thus we begin with A1 = (300/n).
We add 10 students, which decreases the average by 1. But we still have the same number of apples.
Then the new average is A2 = (300/n+10)
We now can say A1 - A2 = 1
Substituting, we have:
(300/n) - (300/n+10) = 1
Combining the two fractions on the left, we end up with
(300n + 3000 - 300n)/n(n + 10) = 1
This reduces to
3000/n(n + 10) = 1
Simplifying, we get a quadratic equation:
n2 + 10n - 3000 = 0
(n - 50)(n + 60) = 0
Solving, we find that n = 50 or n = -60.
The negative answer is meaningless because we can't have negative students, so we select n = 50.
The original number of students was 50. Adding 10 made the number 60 and reduced the average number of apples from 6 to 5.
x = number of students
Since 300 apples are distributed among x students we will use the expression 300/x.
If there were 10 more students we would have x + 10, so we will use 300/(x + 10). Also, since they would have recevied one less apple if there were 10 more students, we will call that 300/(x + 10) + 1.
Setting the two expression equl to each other, we have:
300/x = 300/(x + 10) + 1
If we multiply both sides by x(x + 10), we will have:
300(x + 10) = 300x + x(x + 10)
After distributing, we have
300x + 3000 = 300x + x2 + 10x
By subtracting everything on the right side, we have:
300x + 3000 - x2 - 300x - 10x = 0
Simplified, we have
-x2 -10x + 3000 = 0
After multiplying by -1, we have
x2 + 10x - 3000 = 0
When we factor, we have:
(x - 50)(x + 60) = 0
Set each factor equal to zero and solve
x - 50 = 0 x + 60 = 0
x = 50 x = -60
Since you cannot have a negative number of students, the answer is 50 students.