Question

sum of the digits of a two digit number is 9.when we interchange the digits its is found that the resulting new number is grater than the original number by 27 what is the two digit number​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

꧁SOLUTION ꧂

✧♥༻༺♥✧

☆GIVEN☆

• The sum of 2 digit number=9

☆Let

• the number be 10y+x
• the ones digit be X
• the tens digit be y

☆Sum of two digits number=9

• x+y=9---------(1)

☆Given that when we interchange the digits

it's found that the resulting new number

is is greater than the original number by 27

$⇒10y + x+27 = (10x + y) \\ \\ ⇒10x - x + y - 10y = 27 \\ \\ ⇒9x - 9y = 27 \\ dividing \: by \: 9 \: on \: both \: side \\ \\ ⇒x - y = 3........(2)$

Equation 1 and 2 putting together

$⇒x + y = 9 \\ \\ ⇒x - y = 3 \\ \\ ⇒2x = 12 \\ \\ ⇒x = 6 \\ putting \: the \: value \: of \: x \: in \: equation \: 1 \\ ⇒x + y = 9 \\ \\ ⇒6 + y = 9 \\ \\ ⇒y = 9 - 6 \\ \\⇒ y = 3$

✮Hence:-

• the number is
• 10y+X
• 10*3+6
• 30+6
• 36