a number consist of two digits.when it is divided by sum of its digits the quotient is 6 with no remainder. when the number diminished by 9 the digits are reserved. find the number ?
Answers
Answer:
54
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.