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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. 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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