Sum of the digits of a two digits 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?
Answers
Answer:
number. is 36
Step-by-step explanation:
let the unit digit number be y and tens digit number be x
given x + y = 9-------------1
original number with place value is
=> 20x + y
number after interchaning digits is
=> 20y + x
as per the given condition,
=> 10y + x = 27 + 10x + y
=> 10x - x + y - 10 y = -27
=> 9x - 9y = - 27
=> x - y = -3 [ divide both sides by 9 ]-----++2
on solving 1 and 2
x - y = - 3
x + y = 9
---------------
2x = 6
therefore x = 3 and y = 6
therefore the original number is
=> 10x + y => 10*3 + 6 => 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