Question

the sum of digit of a two digit number is 7 the number obtained by inter change the digit exceed the original number by 27 find the number
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Answer 1

Let the tens and units digit be x and y respectively.

In the given question,

x + y = 7   ------ [Equation 1]

Tens | Ones

   x   |    y

Original Number → 10x + y

On Reversing,

Tens | Ones

   y   |    x

Interchanged number → 10y + x

Here,

10y + x = 27 + (10x + y)

⇒ 10y + x = 27 + 10x + y

⇒ 10y - y = 27 + 10x - x

⇒ 9y = 27 + 9x

⇒ 9y - 9x = 27

⇒ 9(y - x) = 27

⇒ y - x = 27 ÷ 9

⇒ y - x = 3

⇒ -x + y = 3   ----- [Equation 2]

Adding Equation 1 and 2,

                 x + y = 7

        {+}    -x + y = 3

                      2y = 10

⇒ y = 10 ÷ 2

∴ y = 5

Substitute value of y in Equation 1;

x + y = 7

⟶ x + 5 = 7

⟶ x = 7 - 5

∴ x = 2

The original number is of the form 10x + y

10x + y

= 10(2) + 5

= 20 + 5

= 25

∴ The Required number is 25