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Deepak Bora
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If three times the larger of two numbers is divided by the smaller, we get 4 as the quotient and 8 as the remainder. If five times the smaller is divided by the larger, we get 3 as the quotient and 5 as the remainder. find the numbers.

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This is the Important question based on Linear Equations in two Variables Chapter of R.S Aggarwal book for
ICSE & CBSE Board.
Question Number 8 Exercise 3E of RS Aggarwal Solution
Here the quotient and remainder of the n time of larger and n time of smaller of two numbers is given. you have
to find the numbers.

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  1. Let the larger number be x and the smaller number be y.

    Given that 3 times, the larger number is divided by smaller we get 4 as Quotient and 8 as remainder.

    = > 3x = y * 4 + 8

    = > 3x = 4y + 8

    = > 3x – 4y = 8   ——— (1)

    Given that if five times the smaller is divided by larger we get 3 as Quotient and 5 as remainder.

    = > 5y = 3x + 5

    = > 5y – 3x = 5   

    = > -3x + 5y = 5  ——— (2)

    On solving (1) & (2), we get

    = >  3x – 4y = 8

    = > -3x + 5y = 5

         ——————–

                  y = 13

    Substitute y = 13 in (1), we get

    = > 3x – 4y = 8

    = > 3x – 4(13) = 8

    = > 3x – 52 = 8

    = > 3x = 52 + 8

    = > 3x = 60

    = > x = 60/3

    = > x = 20.

    Therefore the numbers are 20, 13.

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