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 number ?

Answer 1

Given That:

• The sum of the two digits = 9

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

To find:

• The number.

Solution:

Let us take the digit in units place be x

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

Thus the two-digit number will be

→ 10(9 – x) + x

↳ Let us reverse the digit

After reversing the number becomes 10x + (9 – x)

As per the condition given,

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

Thus, the digit in units place = 6

Digit in tens place is,

⇉9 – x

⇉9 – 6

⇉3

Hence the required number is 36.

_______________

Hope it's helpful

@Auяoяà

Answer 2

Answer:

Step-by-step explanation:

Let the unit digit be y and tens digit be = x

Number formed = 10x + y

Reverse number = 10y + x

x + y = 9 (Given)…………………………eq1

10y + x = 10x + y + 27…………………….eq2

9y - 9x = 27

y - x = 3……………………………………..eq3

Solving eq1 and eq3 ,we get

x = 3 and y = 6

Original Number = 36 Reversed Number = 63

You can crosscheck the answer by putting up the values obtained either in eq1 or eq2 or eq 3

Also can take a look at the attachment below :)

AbhiraSingh