Question

number, the digits are reversed. Find the number.
5. 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
A two-digit number is such that the product of its digits is 35. If 18 is added to the number,​

Answer 1

Answer:

Step-by-step explanation:

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.