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
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)
⇒9x−9y+18=0
⇒9(x−y+2)=0
⇒x−y+2=0
⇒35/y −y+2=0{from eqn(i)}
⇒35−y²+2y=0
⇒y²−2y−35=0
⇒(y+5)(y−7)=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.