Question

9,000 were divided equally among a certain no of persons . had there been 20 more person each would have got rupees 160 . find the original no of persons​

Answer 1

let the number of persons be " x "

and , let each person get
`(9000)/(x)\\`rupees.

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let's first see why each person got
`(9000)/(x)\\` rupees ,

let us suppose each person gets an amount of " r " rupees.

then ,

`x * r = amount \: we \: have \: with \: us \\ \dashrightarrow{xr = 9000} \\ \dashrightarrow{ r = (9000)/(x)}`

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According to Question ,

hαd thєrє вєєn 20 mσrє pєrѕσnѕ, єαch pєrѕσn wσuld'vє gσt rupєєѕ 160 lєѕѕ.

hєncє, wє αrє nσw ín α ѕtαtє tσ frαmє αn єquαtíσn whích íѕ αѕ fσllσwѕ -

`\fbox{(x + 20)(r - 160) = 9000}`

lєt'ѕ nσw plug ín thє vαluє σf r αѕ
`(9000)/(x)\\`

`(x + 20)( (9000)/(x) - 160) = 900 0\\ \\ \cancel{9000} + (180000)/(x) - 160x - 3200 =\cancel{ 9000} \\ \\ taking\:LCM, \\ \\ - 160x {}^(2) - 3200x + 180000 = 0`

on dividing the complete equation by (- 160)

`x { }^(2) + 20x - 1125 = 0`

now , use the method of splitting the middle term so that we get the value of x.

`x {}^(2) + 45x - 25x - 1125 = 0 \\ \\ x(x + 45) - 25(x + 45) \\ \\ (x + 45)(x - 25) = 0 \\ \\ \fbox{x = - 45 \: \: or \: \: 25}`

since number of persons can't be negative. therefore ,

number of persons = x = 25

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hope helpful :D