Q. 205.0( 5 Votes )

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.

Answer :

Let unit’s digit = y

and the ten’s digit = x


So, the original number = 10x + y


The sum of the number = 10x + y


The sum of the digit = x + y


According to the question,



10x + y = 6(x + y)


10x + y = 6x + 6y


10x + y – 6x – 6y


4x – 5y = 0 …(i)


The reverse of the number = x + 10y


and 10x + y – 9 = x + 10y


10x + y – 9 = x + 10y


10x – x + y – 10y = 9


9x – 9y = 9


x – y = 1


x = y + 1 …(ii)


On substituting the value of x = y + 1 in Eq. (i), we get


4x – 5y = 0


4(y + 1) – 5y = 0


4y + 4 – 5y = 0


4 – y = 0


y = 4


On substituting the value of y = 4 in Eq. (ii), we get


x = y + 1


x = 4 + 1


x = 5


So, the Original number = 10x + y


= 10×5 + 4


= 50 + 4


= 54


Hence, the two digit number is 54.


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