a two digit number is equal to seven times the sum of its digits. the number obtained by interchanging the digits is 9 less than the original number. find the number
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a two digit no. is expressed as 10x+y
(example 45=40+5=4(10)+5)
10x+y=7(x+y)=7x+7y
3x=6y
x=2y
number obtained by interchanging is expressed as 10y+x
(example: 45 interchanged to 54=5(10)+4)
10y+x+9=10x+y
9x-9y=9
x-y=1
as x=2y
2y-y=1
y=1
therefore x=2
the number is 21
(example 45=40+5=4(10)+5)
10x+y=7(x+y)=7x+7y
3x=6y
x=2y
number obtained by interchanging is expressed as 10y+x
(example: 45 interchanged to 54=5(10)+4)
10y+x+9=10x+y
9x-9y=9
x-y=1
as x=2y
2y-y=1
y=1
therefore x=2
the number is 21
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