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Mathematics

The sum of the digits of a two digit number is 12. If the number is decreased by 18, its digits get reversed. The number is

  1. 48

  2. 84

  3. 57

  4. 75

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 = 12.

x + y = 12 …….(i)

Number = 10 × x + y = 10x + y

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

⇒ 10x + y - 18 = 10y + x

⇒ 10x - x + y - 10y - 18 = 0

⇒ 9x - 9y = 18

⇒ 9(x - y) = 18

⇒ x - y = 2 …….(ii)

Adding (i) and (ii) we get,

⇒ x + y + (x - y) = 12 + 2

⇒ 2x = 14

⇒ x = 7.

Substituting value of x in (i) we get,

⇒ 7 + y = 12

⇒ y = 5.

Number = 10 × x + y = 10 × 7 + 5 = 75.

Hence, Option 4 is the correct option.

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