Math, asked by imanilinnocent, 3 months ago

sum of the digit of a two digit number is 9 when we interchange the digits it is found that the resulting number is greater than the original number by 27 what is the two digit number ?​

Answers

Answered by gpranathi09
0

Answer:

The new number is greater than the old number by 27, i.e. Adding the two equations, we get 2y = 12 or y = 6. Thus, x = 3. Therefore, the original number is 36.

Answered by nilesh102
2

Given data : Sum of the digit of a two digit number is 9 when we interchange the digits it is found that the resulting number is greater than the original number by 27.

To find : What is the two digit number ?

Solution : Sum of the two digit number is 9.

Let, unit/one's place digit be x

Hence, unit/one's place digit is 9 - x

  • Units/one's place digit, x = x ----{1}
  • Ten's place digit, y = 9 - x ----{2}

So, here,

Number is represented by 10y + x

Hence,

➜ Original number = 10y + x

➜ Original number = 10 * (9 - x) + x ----{3}

➜ Original number = 90 - 10x + x

➜ Original number = 90 - 9x

Now, after interchanging the digits;

➜ New number = 10x + y

➜ New number = 10x + (9 - x) ----{4}

➜ New number = 10x + 9 - x

➜ New number = 9x + 9

The resulting number is greater than the original number by 27.

➜ New number = Original number + 27

➜ New number - Original number = 27

➜ (9x + 9) - (90 - 9x) = 27

➜ 9x + 9 - 90 + 9x = 27

➜ 9x + 9x + 9 - 90= 27

➜ 18x - 81 = 27

➜ 18x = 27 + 81

➜ 18x = 108

➜ x = 108/18

➜ x = 6

{Hence, unit/one's place digit is 6}

Put value of x in eq. {3}

➜ Original number = 10 * (9 - x) + x

➜ Original number = 10 * (9 - 6 ) + 6

➜ Original number = 10 * 3 + 6

➜ Original number = 30 + 6

➜ Original number = 36

Answer : Hence, the two digit number is 36.

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