3. The sum of the digits of a 2-digit number is 10. If 36 is added to the number, the digits are reversed. Find the original number. with explanation
Answers
Step-by-step explanation:
Given:-
The sum of the digits of a 2-digit number is 10. If 36 is added to the number, the digits are reversed.
To find:-
Find the original number?
Solution:-
Let the digit at 10's place be X
Let the digit at 1's place be Y
The place value of X = 10×X = 10X
The place value of Y = 1×Y = Y
The number = 10X +Y
Condition-1:-
The sum of two the two digits = 10
X+Y = 10 --------------(1)
Condition-2:-
If 36 is added to the number, the digits are reversed.
10X+Y +36 = 10Y+X
=>10X+Y+36-10Y-X = 0
=>(10X-X)+(Y-10Y)=-36
=>9X -9Y = -36
=>9(X-Y)=-36
=>X-Y = -36/9
X-Y = -4----------------(2)
On solving (1)&(2) then
On adding (1)&(2)
X +Y = 10
X-Y = -4
(+)
-------------
2X +0 = 6
--------------
=>2X = 6
=>X = 6/2
=>X = 3
The value of X = 3
On Substituting the value of X in (1) then
3+Y = 10
=>Y = 10-3
Y = 7
The value of Y = 7
The required number = 37
Answer:-
The original number = 37
Check:-
The original number = 37
Their sum =3+7 = 10 , verified
If 36 is added to the number
=>37+36
=>73
=>Reversed number
Verified the given relations