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Mathematics

Sum of digits of a two digit number is 8. If the number obtained by reversing the digits is 18 more than the original number, then the original number is

  1. 35

  2. 53

  3. 26

  4. 62

Linear Equations

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Answer

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

Given, sum of digits = 8.

x + y = 8 …….(i)

Number = 10 × x + y = 10x + y

On reversing digits number = 10 × y + x = 10y + x.

Given, number obtained by reversing the digits is 18 more than the original number.

⇒ 10y + x = 10x + y + 18

⇒ 10y - y + x - 10x = 18

⇒ 9y - 9x = 18

⇒ y - x = 2 ………(ii)

Adding (i) and (ii) we get,

⇒ x + y + (y - x) = 8 + 2

⇒ 2y = 10

⇒ y = 5.

Substituting value of y in (i) we get,

⇒ x + 5 = 8

⇒ x = 3.

Number = 10x + y = 10(3) + 5 = 35.

Hence, Option 1 is the correct option.

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