Rs. 480 is Divided Equally Among ‘X’ Children. If the Numbers of Children Were 20 More Then Each Would Have Got Rs. 12 Less. Find ‘X’. - Mathematics

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

Solution

The number of children = x.

The share of each child = Rs 480/x

If number of children are x + 20, then share of each child = Rs 480/(x + 20)

According to the given information,

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

=> 480(1/x - 1/(x + 20)) = 12

=> 480(20/(x(x + 20))) = 12

=> (480 xx 20)/12 = x(x + 20)

=> x^2 + 20x - 800 = 0

=> x^2 - 20x + 40x - 800 = 0

=> (x - 20)(x + 40) = 0

=> x = 20 or x = -40

But, the number of children cannot be negative.

Therefore, x = 20

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