# The sum of the digits of a two digit number is 11.If the digits are reversed the number increases by 27.Find the number

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by khushi143

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by khushi143

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Let the tenth place be x and the units place be y

the no.=10x+y

x+y=11 -(1)

if the digits are reversed unit=x and tenth place =y

the no.=10y+x

(10x+y) +27=10y+x

10y+x - 10x-y=27

9y-9x=27

9(y-x)=27

y-x=3(27divided by 3)

-x +y=3 -(2)

x + y = 11

-x+y = 3

---------------

0+2y=14

2y=14

y=7

y=7 in equation (1)

x+y=11

x+7=11

x=11-7

x=4

hence the no.=10x+y

=10(4)+7

=40 + 7

=47

the no.=10x+y

x+y=11 -(1)

if the digits are reversed unit=x and tenth place =y

the no.=10y+x

(10x+y) +27=10y+x

10y+x - 10x-y=27

9y-9x=27

9(y-x)=27

y-x=3(27divided by 3)

-x +y=3 -(2)

x + y = 11

-x+y = 3

---------------

0+2y=14

2y=14

y=7

y=7 in equation (1)

x+y=11

x+7=11

x=11-7

x=4

hence the no.=10x+y

=10(4)+7

=40 + 7

=47