Question

Rs. 480 is divided equally among ‘x’ children. If the number of children were 20 more then each would have got Rs. 12 less. Find ‘x’.

Answer 1

Share of each child = ₹`(480)/x`
Now, number of children
= x + 20
∵ Share of each child
= ₹`(480)/(x + 20)`
Now, According to the question
`(480)/x - (480)/(x + 20)` = 12
⇒ `(480 x + 9,600 - 480x)/(x(x + 20)` = 12
⇒ 9,600 = 12x (x + 20)
⇒ 800 = x² + 20x
⇒ x² + 20x - 800 = 0
⇒ x² + 40x - 20x - 800 = 0
⇒ x(x + 40) - 20 (x + 40) = 0
⇒ (x - 20) (x + 40) = 0
⇒ x = 20
or
⇒ x = -40  ...(not possible)
∴ x = 20

Answer 2

Share of each child = ₹`(480)/x`
According to the question

`(480)/(x + 20) = (480)/x - 12`

⇒ `(480)/(x + 20) = (480 - 12x)/x`

⇒ `(480)/(x + 20) = (12(40 - x))/x`

⇒ (x + 20)(40 - x) = 40x
⇒ 40x  x² + 800 - 20x = 40x
⇒ x² + 20x - 800 = 0
⇒ x² + 40x - 20x - 800 = 0
⇒ x(x + 40) -20(x + 40) = 0
⇒ (x + 40)(x - 20) = 0
⇒ x = -40, x = 20
-ve value of x is not possible
∴ No. of children = 20.