Mathematics

The sum of digits of a two digit number is 11. If the digit at ten's place is increased by 5 and the digit at unit's place is decreased by 5, the digits of the number are found to be reversed. Find the original number.

10 Likes

Let digit at ten's place be x and digit at unit's place be y.

Given,

The sum of digits of a two digit number is 11.

∴ x + y = 11

⇒ x = 11 - y ……….(1)

Given,

If the digit at ten's place is increased by 5 and the digit at unit's place is decreased by 5, the digits of the number are found to be reversed.

∴ 10(x + 5) + (y - 5) = 10y + x

⇒ 10x + 50 + y - 5 = 10y + x

⇒ 10x + y - 10y - x + 45 = 0

⇒ 9x - 9y + 45 = 0

⇒ 9y = 9x + 45

⇒ y = x + 5

⇒ x = y - 5 ………..(2)

From equation (1) and (2), we get :

⇒ 11 - y = y - 5

⇒ y + y = 11 + 5

⇒ 2y = 16

⇒ y = $\dfrac{16}{2}$ = 8.

Substituting value of y in equation (2), we get :

⇒ x = 8 - 5 = 3.

Number = 10x + y = 10(3) + 8 = 30 + 8 = 38.

Hence, number = 38.

Answered By

6 Likes