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Rajan@2021
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A number consist of two digits. When it is divided by the sum of its digit, the quotient is 6 with no reminder. When the number is diminished by 9, the digits are reversed. Find the number.

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This is the basic and exam oriented question from linear equations in two variables in which we have to find the number if a number consist of two digits. When it is divided by the sum of its digit, the quotient is 6 with no reminder. When the number is diminished by 9, the digits are reversed.

Kindly solve the above problem

RS Aggarwal, Class 10, chapter 3E, question no 15

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1 Answer

  1. We know that Dividend=Divisor×Quotient+Remainder
    Let the tens and the units digits of the required number be x and y,Respectively.
    Required number=10x+y
    10x+y=(x+y)×6+0
    10x6x+y6y=0
    4x5y=0       ……(1)
    Number obtained on reversing its digits=10y+x
    10x+y9=10y+x
    9x9y=9 or xy=1       ……..(2)
    On multiplying (2) by 5, we get
    5x5y=5       ………(3)
    On subtracting (1) from (3),we get
    x=5
    On substituting x=5 in (1), we get
    4×55y=0
    205y=0
    y=4
    The number =10x+y=10×5+4=50+4=54
    Hence the required number is 54

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