A number consisting of two digits is seven times the sum of its digits. When 27 is subtracted from the number, 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).

According to question -

(10x + y) = 7(x + y)

⇒ 3x = 6y

⇒ x = 2y.....(1)

and,

(10x + y) - 27 = (10y + x)

⇒ 9x - 9y = 27

⇒ x - y = 3.....(2)

Substituting equation (1) into (2), we get -

y = 3

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

x = 6

Thus, the required number is 63.