Question

Sum of the digits of a two-digit number is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. What is the two-digit number?

Answer 1

Let tense digit be 'x' and ones digit be 'y'.

We know that the digits of a two digit is 9.

• x + y = 9 --------- (1)

As it 'x' is tense digit, and 'y' is ones digit, we will write it as,

• 10x + y = original number

When we interchange the digits, the resulting new number is greater than the original number by 27,

• 10y + x = 27 + (10x + y)

Taking (10x + y), to the another side,

⟹ (10y + x) - (10x - y) = 27

⟹ (10y - y) - (10x - x) = 27

⟹ 9y - 9x = 27

Cancelled through 9, we get,

• x - y = 27 --------- (2)

Adding both (1) & (2) :

x + y = 9

y - x = 3

______

2y = 12

______

• While adding both (x) & (-x) will get cancelled.

⟹ 2y = 12

⟹ y = 12 / 2

⟹ y = 6

Substituting ' y ' in ' Eq 1 ' :

⟹ x + y = 9

⟹ x + 6 = 9

⟹ x = 9 - 6

⟹ x = 3

• ∴ The original number is 36.

Answer 2

Answer:

The number whose sum of the digits is 9, and when we interchange the digits the new number is 27 greater than the earlier number, is 36.

Step-by-step explanation:

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