The sum of the digit of a two digit number is 7. the number is 2 more than twice the number formed by inter changing the digit of the number. find the number
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Let the number be 10x+y where x is tens digit and y is units digit.
x+y=7
y=7-x --------->(1)
The number formed when the digits are interchanged is 10y+x
10x+y=2(10y+x)+2
=> 10x+y=20y+2x+2
=> 8x-19y=2
Substituting value of y in the above equation
8x-19(7-x)=2
=> 8x+19x-133=2
=> 27x=135
=>x=135/27=5
y=7-x
=7-5=2
The number is 10x+y=10(5)+2=52
x+y=7
y=7-x --------->(1)
The number formed when the digits are interchanged is 10y+x
10x+y=2(10y+x)+2
=> 10x+y=20y+2x+2
=> 8x-19y=2
Substituting value of y in the above equation
8x-19(7-x)=2
=> 8x+19x-133=2
=> 27x=135
=>x=135/27=5
y=7-x
=7-5=2
The number is 10x+y=10(5)+2=52
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