the sum of the digits of 2 digit number is 11.the number got by interchanging the digit is 27 more than the original number
Answers
Answer:
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Step-by-step explanation:
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Step-by-step explanation:
Given :-
The sum of the digits of 2 digit number is 11.the number got by interchanging the digit is 27 more than the original number.
To find :-
Find the number ?
Solution :-
Let the digit at 10's place be X
Then the place value of X = 10X
Let the digit at 1's place be Y
Then the place value of Y = Y
Given that
The sum of the digits = 11
=> X+Y = 11 ----------(1)
=> X = 11-Y -----------(2)
The original number = 10X+Y
The number obtained by reversing the digits = 10Y+X
According to the given problem
The number got by interchanging the digit is 27 more than the original number.
=> 10Y+X = 10X+Y+27
=> 10Y+X-10X-Y = 27
=> 9Y-9X = 27
=> 9(Y-X) = 27
=> Y-X = 27/9
=> Y-X = 3
=> Y-(11-Y) = 3
=> Y-11+Y = 3
=> 2Y -11 = 3
=> 2Y = 3+11
=> 2Y = 14
=> Y = 14/2
=> Y = 7
The digits at 1's place = 7
From (2)
=> X = 11-7
=> X = 4
The digit at 10's place = 4
The number = 47
Answer :-
The original number for the given problem is 47
Check:-
The number = 47
Sum of the digits = 4+7 = 11
The sum of the digits of 2 digit number is 11
The number obtained by reversing the digits = 74
=> 47+27
=> 74
The number got by interchanging the digit is 27 more than the original number.
Verified the given relations.