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Mathematics

The sum of the digits of a two digit number is 5. If the digits are reversed, the number is reduced by 27. Find the number.

Linear Equations

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Answer

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

Number = 10 × y + x = 10y + x

Given,

Sum of the digits of a two digit number is 5.

∴ x + y = 5

⇒ x = 5 - y ……..(1)

If the digits are reversed, then number = 10x + y.

Given,

If the digits are reversed, the number is reduced by 27.

∴ 10x + y = 10y + x - 27

⇒ 10x - x = 10y - y - 27

⇒ 9x = 9y - 27

⇒ 9x = 9(y - 3)

⇒ x = y - 3 ……..(2)

From (1) and (2), we get :

⇒ y - 3 = 5 - y

⇒ y + y = 5 + 3

⇒ 2y = 8

⇒ y = 82\dfrac{8}{2} = 4.

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

⇒ x = 4 - 3 = 1.

Number = 10y + x = 10(4) + 1 = 40 + 1 = 41.

Hence, the number = 41.

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