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.

Question

Philoid · Accepted Answer

Let the two - digit number be xy (i.e. 10x + y).

After reversing the digits of the number xy, the new number becomes yx (i.e. 10y + x).

We know that -

Dividend = Quotient × Divisor + Remainder

According to question -

(10x + y) = 6(x + y)

⇒ 4x = 5y

⇒ x = (5/4)y.....(1)

and,

(10x + y) - 9 = (10y + x)

⇒ 9x - 9y = 9

⇒ x - y = 1.....(2)

Substituting the value of x in equation (2), we get -

y = 4

Substitute the value of y in equation (1), we get -

x = 5

Thus, the number is 54.