sum of the digit of a 2 digit number is 12 when the digit are intechanged new number obtained is 54.more than the original number. find the original number
Answers
Step-by-step explanation:
Given:-
Sum of the digit of a 2 digit number is 12 when the digit are intechanged new number obtained is 54.more than the original number.
To find:-
Find the original number ?
Solution:-
Let the digit at tens place be X
Let the digit at ones place be Y
The place value of X = 10×X = 10X
The place value of Y = 1×Y = Y
Then the number = 10X+Y
If the digits are interchanged then the number = 10Y +X.
Given that
Sum of the digits = 12
X+Y = 12 --------(1)
the digit are intechanged new number obtained is 54 more than the original number.
=> 10Y+X = 10X+Y +54
=> 10Y+X-10X-Y = 54
=> (10Y-Y)+(X-10X) = 54
=> 9Y -9X = 54
=> 9(Y-X) = 54
=> Y-X = 54/9
=> Y-X = 6
=> -X +Y = 6--------------(2)
On adding (1)&(2) then
X + Y = 12
-X + Y = 6
(+)
__________
0+2Y = 18
__________
=> 2Y = 18
=> Y = 18/2
=> Y = 9
On Substituting the value of Y in (1) then
X+9 = 12
=> X = 12-9
=> X = 3
The number = 39
Answer:-
The original number for the given problem is 39
Check:-
Sum of the digits = 3+9 = 12
Number obtained by reversing the digits = 93
93 = 39+54
New number = Original number+54
Verified the given relations