the sum of the digits of a two digit number is 10. if 36 is subtracted from the number the digits interchange their places. find the number.
Answers
Step-by-step explanation:
Given :-
The sum of the digits of a two digit number is 10. if 36 is subtracted from the number the digits interchange their places.
To find :-
Find the number ?
Solution :-
Let the digit at tens place of a two digit number be X
The place value of X = 10×X = 10X
Let the digit at ones place of the two digit number be Y
The place value of Y = 1×Y = Y
Then the Original two digit number = 10X+Y
If the digits interchanged their places then the new number = 10Y+X
Given that
The sum of the digits of a two digit number = 10
=>X+Y = 10 ---------(1)
And
If 36 is subtracted from the number the digits interchange their places.
=> (10X+Y)-36 = 10Y+X
=> (10X+Y)-(10Y+X) = 36
=> 10X+Y-10Y-X = 36
=> 9X-9Y = 36
=> 9(X-Y) = 36
=> X-Y = 36/9
=> X-Y = 4 -------------(2)
On adding (1)&(2) then
X+Y = 10
X-Y = 4
(+)
_______
2X+0 = 14
________
=> 2X = 14
=> X = 14/2
=> X = 7
On Substituting the value of X in (1) then
=> 7+Y = 10
=> Y = 10-7
=> Y = 3
Therefore, the digits are 7 and 3
The number = 73
Answer:-
The required number for the given problem is 73
Check:-
The original number = 73
The sum of the digits = 7+3 = 10
If 36 is subtracted from 73 then
=> 73-36
=> 37
=> Digits are interchanged
Verified the given relations in the given problem.