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?
Please answer this I am giving you 15 points
Explanation​

Answer 1

Answer:

36

Step-by-step explanation:

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

Answer 2

Answer:

36

Step-by-step explanation:

let two digit number be 10x+y

then,

reverse of the two digit number will be 10y+x

now,

by question,

x+y=9

y=9-x....eq1

10y+x=(10x+y) + 27...eq2

or, 9y=9x+27

or, 9y-9x=27

or, y-x=3

putting value of y from eq 1

(9-x)-x=3

or, 9-3=2x

or, 6=2x

or, x=3 ...eq3

now to find y,

from eq 1 and eq 3

y=9-x

or, y=9-3

or, y=6

since, the two digit number is 10x+y,

putting value of x and y,

=10*3+6

=36