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# A number Consists of two digits. When it is divided by the sum of its digits, the quotient is 6 with no remainder. When the number is diminished by 9, the digits are reversed. Find the number.

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This is the Important question based on Linear Equations in two Variables Chapter of R.S Aggarwal book for ICSE & CBSE Board.
Here a number of consists of two digits. when it is divided by the sum of its digits, the quotient is given, when the number is diminshed by the given number the digits are reversed.
You have to find the number.
This is the Question Number 15 Of Exercise 3E of RS Aggarwal Solution.

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1. Solution :-
Let the original number be 10x + y
Therefore, according to the question.
(10x +y)/(x + y) = 6
10x + y = 6x + 6y
10x – 6x – 6y + y = 0
4x – 5y = 0 ……………………(1)
And,
10x + y – 9 = 10y + x
10x – x + y – 10y = 9
9x – 9y = 9 …………………….(2)
Now, multiplying the equation (1) by 9 and (2) by 4, we get
36x – 45y = 0 …………………(3)
36x – 36y = 36 ……………….(4)
Now, subtracting (4) from (3), we get
36x – 45y = 0
36x – 36 y = 36
– + –
_______________
– 9y = – 36
_______________
– 9y = – 36
y = 36/9
y = 4
Substituting the value of y = 4 in (1), we get.
4x – 5y = 0
4x – (5*4) = 0
4x – 20 = 0
4x = 20
x = 20/4
x = 5
Number is (10*5) + 4
= 50 + 4
= 54
Hence, the original number is 54.

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