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Rajan@2021
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A two digit number is such that the product of the digit is 35, when 18 is added to the number, the digit interchange their places. Find the number.

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One of the most important and conceptual question from linear equations in two variables in which we have been asked to find the number a two digit number is such that the product of the digit is 35, when 18 is added to the number, the digit interchange their places.

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 3E, question no 16

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1 Answer

  1. Let the two digit no. be xy.
     Decimal expansion of xy=10×x+y

    digits are interchanged, i.e. yx.
     Decimal expansion of yx=10×y+x

    x×y=35{Given}
    x=35​/y(i)
    Given that when 18 is added to the number, the digits are interchanged, i.e. yx.
    (10x+y)+18=(10y+x)
    9x9y+18=0
    9(xy+2)=0
    xy+2=0
    35​/y y+2=0{from eqn(i)}
    35+2y=0
    2y35=0
    (y+5)(y7)=0
    y≠5
    y=7
    Substituting the value of y in eqn(i), we get
    x=35/7=5
    Hence the two digit no. is 57.

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