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

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

⇒10x−6x+y−6y=0

⇒4x−5y=0 ……(1)

Number obtained on reversing its digits=10y+x

∴10x+y−9=10y+x

⇒9x−9y=9 or x−y=1 ……..(2)

On multiplying (2) by 5, we get

5x−5y=5 ………(3)

On subtracting (1) from (3),we get

x=5

On substituting x=5 in (1), we get

4×5−5y=0

⇒20−5y=0

⇒y=4

∴The number =10x+y=10×5+4=50+4=54

Hence the required number is 54