the restaurant bill of a party for a certain number of people is rupees 19200 if there were 10 more persons the bill each person had to pay

Question

the restaurant bill of a party for a certain number of people is rupees 19200 if there were 10 more persons the bill each person had to pay should have been reduced by rupees 160 find the no of people

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Autumn 4 weeks 2021-10-01T15:43:15+00:00 1 Answer 0 views 0

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    2021-10-01T15:45:02+00:00

    Answer:

    Number of people will be 30 .

    Step-by-step explanation:

    Let, number of people be x

    and

    amount paid by each person be y

    then,

     y = 19200 / x   ___ ①

    Now,

    it is given that when there would be 10 more persons then bill paid by each person will be reduced by Rs 160

    so,

     y – 160 = 19200 / (x + 10)

    using equation ①

    →  (19200/x) – 160 = 19200/(x+10)

    →  (19200/x) – (19200/(x+10)) = 160

    Taking LCM in LHS

    → (19200 x+192000-19200 x)/(x²+10 x) = 160

    → 192000 / (x² + 10 x) = 160

    cross multiplying

    160 x² + 1600 x = 192000

    dividing by 160 both sides

    x² + 10 x = 1200

    → x² + 10 x – 1200 = 0

    → x² + 40 x – 30 x – 1200 = 0

    → x ( x + 40 ) – 30 ( x + 40 ) = 0

    →  ( x – 30 ) ( x + 40 ) = 0

    →  x = 30   or   x = -40

    Since, number of people cannot be negative

    therefore we will neglect x = -40

    And thus,

    Number of people is 30 .

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