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Mathematics

The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Then the original number is :

  1. 90

  2. 18

  3. 81

  4. 54

Linear Equations

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Answer

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

Number = 10x + y,

Given,

Sum of the digits of a two-digit = 9

⇒ x + y = 9     ….(1)

Given,

Nine times the number is twice the number obtained by reversing the order of the digits,

⇒ 9(10x + y) = 2(10y + x)

⇒ 90x + 9y = 20y + 2x

⇒ 90x - 2x = 20y - 9y

⇒ 88x = 11y

⇒ y = 8811x\dfrac{88}{11}x

⇒ y = 8x     ….(2)

Substituting value of y from equation (2) in equation (1), we get :

⇒ x + 8x = 9

⇒ 9x = 9

⇒ x = 99\dfrac{9}{9} = 1.

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

⇒ y = 8x

⇒ y = 8(1) = 8.

Number = 10x + y = 10(1) + 8 = 18.

Hence, option 2 is the correct option.

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