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

1
by manishveer31

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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

1
by manishveer31

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(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