Question

120 kites were divided equally among a certain number of children in school. If 4 children were less each would have got 1 kite more. Find the number of children.
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Answer 1

If there are n students and each get x kites

Meaning

$\frac{120}{n}$ = x

If there are n-4 students , then each will get x+1 kites

$\frac{120}{n-4}$ = x +1

$\frac{120}{n-4}$ = $\frac{120}{n}$ +1

$\frac{120}{n-4}$ - $\frac{120}{n}$ = 1

$\frac{120{n-(n-4)]}{n(n-4)}$ = 1

$\frac{480}{n(n-4)}$ = 1

480 = $n^{2}$ -4n

$n^{2}$ -4n - 480 =0

Solving this equation we get,

n = 24 , - 20

Since the number of student can't be negative

Number of Student = 24