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

Total amount = Rs. 480

Let the number of children be x.

The amount each children got = `480/x`

when the number of children were 20,

Amount of each children = `480/(x + 20)`

From the given information, we have:

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

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

`9600/(x(x + 20)) = 12`

`800/(x(x + 20)) = 1`

x² + 20x – 800 = 0

x² + 40x – 20x – 800 = 0

x(x + 40) – 20(x + 40) = 0

(x – 20)(x + 40) = 0

x = 20, – 40

Since, number of children cannot be negative.

So, x = 20

Number of children = 20.