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

Answer:

The number is 36.

Step-by-step explanation:

Let unit place digit be x.

Ten’s place digit = 9 – x

Original number = x + 10(9 – x)

Condition I: 10x + (9 – x) (Interchanging the digits)

Condition II: New number = original number + 27

⇒ 10x + (9 – x) = x + 10(9 – x) + 27

⇒ 10x + 9 – x = x + 90 – 10x + 27 (solving the brackets)

⇒ 9x + 9 = -9x + 117 (Transposing 9x to LHS and 9 to RHS)

⇒ 9x + 9x = 117 – 9

⇒ 18x = 108

⇒ x = 108 ÷ 18 (Transposing 18 to RHS)

⇒ x = 6

Unit place digit = 6

Ten’s place digit = 9 – 6 = 3

Thus, the required number = 6 + 3 × 10 = 6 + 30 = 36.

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Answer 2

Answer:

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Given

The sum of the two digits = 9

On interchanging the digits, the resulting new number is greater than the original number by 27.

Let us assume the digit of units place = x

Then the digit of tens place will be = (9 – x)

Thus the two-digit number is 10(9 – x) + x

Let us reverse the digit

the number becomes 10x + (9 – x)

As per the given condition

10x + (9 – x) = 10(9 – x) + x + 27

⇒ 9x + 9 = 90 – 10x + x + 27

⇒ 9x + 9 = 117 – 9x

On rearranging the terms we get,

⇒ 18x = 108

⇒ x = 6

So the digit in units place = 6

Digit in tens place is

⇒ 9 – x

⇒ 9 – 6

⇒ 3

Hence the number is 36