Question

the sum of digit of two digit number is 7 if the digits are reversed the new number decreased by 2 equal to is twice the original number find the number

Answer 1

Please see the attachment

Answer 2

Step-by-step explanation:

AnswEr :

Let us Consider that x & y be two digits numbers.

And, Original Number be = 10x + y.

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⠀⠀⠀⠀⠀As Per Given Question -

Sum of two digits numbers is = 7.

$:\implies\sf x + y = 7$ -eq. (1)

Now, Reversing the Digits.

$:\implies\sf 10y + x$

$:\implies$ 2( Original Number) = Reversed Number - 2.

[Reversed Number is Decreased by 2 (Given) ]

$:\implies\sf 2(10x + y) = 10y + x - 2 \\ \\ \\ \implies\sf 20x + 2y = 10y + x - 2 \\ \\ \\ \implies\sf 19x + 2 = 8y \\ \\ \\ \implies\sf 8y - 2 = 19x \\ \\ \\ \implies\sf -2 = 19x = 8y$ -eq. (2)

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From eq(1) & (2).

$:\implies\sf x + y = 7$

$:\implies\sf 19x - 8y = -2$

⠀⠀⠀⠀Multiplying eq(1) with 19 & eq(2) with 1

$:\implies\sf 19x + 19y = 133$

$:\implies\sf 19x - 8y = -2$

$:\implies\sf 27y = 135$

$:\implies\sf y = \cancel\dfrac{135}{27}$

$:\implies\sf\red{y \: = \: 5}$

We get value of y = 5

$:\implies\sf x + y = 7$⠀⠀⠀⠀⠀⠀[From eq(1)]⠀⠀

$:\implies\sf x + 5 = 7$

$:\implies\sf\red{x \: = \: 2}$

Hence, Value of x & y is 2 & 5

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⠀⠀⠀⠀Now, Original Number -

$:\implies\sf 10x + y$

$:\implies\sf 10(2) + y$

$:\implies\sf 20 + 5$

$:\implies\sf\pink{25}$

Thus, the orignal Number is 25.