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

# 3 Answers

The original average is the number of apples (300) divided by the number of students (let's call this "n").

Thus we begin with A_{1} = (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 A_{2 }= (300/n+10)

We now can say A_{1} - A_{2} = 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:

n^{2} + 10n - 3000 = 0

Factoring,

(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 + x^{2} + 10x

By subtracting everything on the right side, we have:

300x + 3000 - x^{2} - 300x - 10x = 0

Simplified, we have

-x^{2} -10x + 3000 = 0

After multiplying by -1, we have

x^{2} + 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.

## Comments

sir i tried 2 solve ans bt still nt getting still thank u so much

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