Question

answer the attachment.....​

Answer 1

Question;

₹ 9000 were divided equally among a certain number of persons. had there been 20 more persons ,each would have got ₹ 160 less. find the original number of persons.

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Let x be the no of persons.

₹ 9000 divided equally between x persons, then each one get

$= \frac{9000}{x}$

if there were 20 more persons,

the amount of money get

$= \frac{9000}{x + 20}$

Given that ;

$\frac{9000}{x + 20} = \frac{9000}{x} - 160$

$\frac{9000}{x} - \frac{9000}{x + 20} = 160$

$\frac{9000(x + 20) - 9000x}{x(x + 20)} = 160$

$\frac{9000x + 180000 - 9000x}{x {}^{2} + 20x } = 160$

$\frac{180000}{160} = x {}^{2} + 20x$

$1125 = x { }^{2} + 20x$

$x {}^{2} + 20x - 1125 = 0$

$x {}^{2} + 45x - 25x - 1125 = 0$

$x(x + 45) - 25(x + 45) = 0$

$(x + 45)(x - 25) = 0$

then , x = - 45 or 25

since no of persons Cannot be negative then

x = 25

Therefore , the money ₹9000 has been divided among 25 persons .

Answer 2

$\huge{\blue{\underline{\purple{\mathbb{AnSwER}}}}} \\ original \: number \: of \: persons \: = a \\ 9000 \: were \: equally \: divided \: among \: certain \: people \: = \frac{9000}{a} \\ \frac{9000}{a} - 160 = \frac{9000}{(a + 20)} \\ \frac{9000 - 160n}{a} = \frac{9000}{a + 20} \\ 9000a = 9000a - {160a }^{2} + 180000 - 3200a \\ {a}^{2} + 10a = 1125 + 100 \\ {(a + 10)}^{2} = 1225 \\ a + 10 = 35 \\ a= 25 \\ 25 \: persons \: originally$