Question

a number consists of two digits .when it is divided by the sum of its digits , the quotient is 6 with no reminder. when the number is diminished by 9,, the digits are reversed .find the number

Answer 1

The answer to this question is given in this image with explanation.

Answer 2

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.
Answer.