The sum of two digit number and the number formed by interchanging its digit is 110. If 17 is subtracted from the first number, the new number is 2 times the sum of the digits in the first number. Find the first number.
Answers
Step-by-step explanation:
Given:-
The sum of two digit number and the number formed by interchanging its digit is 110. If 17 is subtracted from the first number, the new number is 2 times the sum of the digits in the first number.
To find:-
Find the first number ?
Solution:-
Let the digit at 10's place be X
The place value of X = 10X
Let the digit at 1's place be Y
The place value of Y = Y
The number = 10X+Y
The first number = 10X+Y
The number obtained by reversing digits = 10Y+X
Given that
The sum of two digit number and the number formed by interchanging its digit is 110
=> (10X+Y)+(10Y+X) = 110
=> 10X+X +Y+10Y = 110
=> 11X+11Y = 110
=> 11(X+Y) = 110
=> X+Y = 110/11
X+Y = 10 ---------------(1)
If 17 is subtracted from the first number, the new number is 2 times the sum of the digits in the first number
(10X+Y)-17 = 2(X+Y)
=> 10X+Y-17-2X-2Y = 0
=> 8X -Y -17 = 0
=> 8X-Y = 17-----------(2)
On adding (1)&(2)
X+Y = 10
8X-Y = 17
(+)
________
9X +0 = 27
________
=> 9X = 27
=> X = 27/9
=>X = 3
from (1)
3+Y = 10
=> Y = 10-3
Y = 7
The first number = 37
The new number = 73
Answer:-
The first number for the given problem is 37
Check:-
The first number = 37
The new number = 73
Sum of the numbers = 37+73 = 110
If 17 is subtracted from the first number, the new number is 2 times the sum of the digits in the first number
=>37-17 = 2(3+7)
=>20=2(10)
=>20=20
Verified the given relations.