Question

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Rs. 480 is divided equally among 'x' children. If the number of children were 20 mre, then each
would have got Rs. 12 less. Find x'
What number should be subtracted from each of the numbers 23. 30, 57 and 78 so that he​

Answer 1

Correct 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 :

$\star \:\textsf{Present Number of Students be x.}\\\\{\bf\dag} \:\sf Initial\:Share_{(1\: Student)} = \dfrac{Money}{Student}= \dfrac{480}{x}\\\\{\bf\dag} \:\sf New\:Share_{(1\: Student)} = \dfrac{Money}{New \:Student}=\dfrac{480}{(x + 20)}$

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$\underline{\bigstar\:\textsf{According to the Question Now :}}$

$:\implies\tt (Initial\:Share-New\:Share)_{(1\:Student)}=Rs.12\\\\\\:\implies\tt\dfrac{480}{x} - \dfrac{480}{x + 20} = 12\\\\\\:\implies\tt480 \bigg(\dfrac{1}{x} - \dfrac{1}{x + 20} \bigg) = 12\\\\\\:\implies\tt \dfrac{x + 20 - x}{x(x + 20)} = \dfrac{12}{480}\\\\\\:\implies\tt \dfrac{20}{{x}^{2} + 20x} = \dfrac{1}{40}\\\\\\:\implies\tt20 \times 40 = {x}^{2} + 20x\\\\\\:\implies\tt {x}^{2} + 20x - 800 = 0\\\\\\:\implies\tt {x}^{2} + (40 - 20)x - 800 = 0\\\\\\:\implies\tt {x}^{2} + 40x - 20x - 800 = 0\\\\\\:\implies\tt x(x + 40) - 20(x + 40) = 0\\\\\\:\implies\tt(x - 20)(x + 40) = 0\\\\\\:\implies\tt \green{x = 20} \quad or \quad \red{x = - 40}$

⠀

$\therefore\:\underline{\textsf{Hence, Number of Children is \textbf{20.}}}$

Answer 2

Answer:

Answer is in the attachment