#### 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'.

#### Solution

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"=12)=12`

`(480"x"+480xx20-480"x")/("x"("x"+20))=12`

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

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

x^{2} + 20x - 800 = 0

x^{2} + 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

Is there an error in this question or solution?

Solution 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'. Concept: Quadratic Equations.