Question

if a place of 2 digits of a number is changed to each other, then the new number increases 18 from the original old number, what was the original old number?​

Answer 1

Given:

On replacing the digits of a 2 digit no. the the new number increases by 18.

To Find:

The original old number.

Solution:

- Let the digit at tens place be x and at ones place be y.

- Then, according to the question, the old no is:

10x + y

- New number = 10y + x

- According to the question:

10y + x = (10x + y) + 18

⇒ 9y = 9x + 18

⇒ y = x + 2

- If x = 1 then y = 3 and the old no is 13.

- If x = 2 then y = 4 and the old no is 24.

- If x = 3 then y =5 and the old no is 35.

- If x = 4 then y = 6 and the old no is 46.

- If x = 5 then y = 7 and the old no is 57.

- If x = 6 then y =8 and the old no is 68.

- If x = 7 then y = 9 and the old no is 79.

- All the above numbers satisfy the given conditions.