Question

The sum of the two digit number is 7if the digits are reversed the new number decreased by two equals twice the original number

Answer 1

       

Let the two digit number be 10x + y.

x + y = 7     →     (1)

If digits are interchanged, we will get 10y + x.

Given that,

10y + x - 2 = 2(10x + y)

⇒ 10y + x - 2 = 20x + 2y

⇒ 10y - 2y - 2 = 20x - x

⇒ 8y - 2 = 19x

⇒ 8y - 19x = 2     →     (2)

(1) × 19

⇒ 19(x + y) = 19 × 7

⇒ 19x + 19y = 133     →     (3)

(2) + (3)

⇒ 8y - 19x + 19x + 19y = 2 + 133

⇒ 27y = 135

⇒ y = 135 / 27

⇒ y = 5

From (1),

x + y = 7

⇒ x + 5 = 7

⇒ x = 7 - 5

⇒ x = 2

So the two digit number is,

10x + y = 10 × 2 + 5 = 20 + 5 = 25.

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