The sum of the digits of a two digit number is 9. When 9 is added to the number, the digits of the number will reverse.

What is the original number?

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Solution

The correct option is D
45

Since sum of the digits is 9, if one digit is x then the other digit will be 9 – x.

Let the digit in the ten’s place be x and units place be (9 – x).

The number is 10x + (9 – x). After reversing the digits , the number will be 10(9 – x) + x.

10x + (9 – x) + 9 = 10(9-x) + x (given)

9x + 18 = 90 -9x

9x + 9x = 90 – 18

18 x = 72

x = 72 ÷ 18 = 4

$∴$ The number is 45.

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The sum of the digits of a two digit number is 9. When 9 is added to the number, the digits of the number will reverse. What is the original number?

The sum of the digits of a two digit number is 9. When 9 is added to the number, the digits of the number will reverse.

What is the original number?