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`.

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Solution

Let the number of children $= x$

Therefore

$\frac{480}{x} - \frac{480}{x+20} = 12$

$480x+9600-480x= 12 (x^2+20x)$

$\to 12 x^{2} + 240 x - 9600 = 0$
$\to x^{2} + 20 x - 800 = 0$
$\to x^{2} + (40 - 20) x - 800 = 0$
$\to x^{2} + 40 x - 20 x - 800 = 0$
$\to x (x + 40) - 20 (x + 40) = 0$
$\to (x + 40) (x - 20) = 0$
$\to x + 40 = 0$
$\to x = - 40 (n o t p o s s i b l e)$
$\to x - 20 = 0$
$∴ x = 20$

Hence the number of children is 20.

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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`.

Let the number of children Therefore →12x2+240x−9600=0 →x2+20x−800=0 →x2+(40−20)x−800=0 →x2+40x−20x−800=0 →x(x+40)−20(x+40)=0 →(x+40)(x−20)=0 →x+40=0 →x=−40(notpossible) →x−20=0 ∴x=20 Hence the number of children is 20.