# A two digit number is four times the sum of its digits. If 27 is added to the number the digits are reversed, find the number.

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by manavi

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by manavi

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Let the digits be x,y

so according to question

10x+y= 4(x+y)

⇒10x+y=4x+4y

⇒6x-3y=0

⇒2x-y=0 ......... (i)

again,

10x+y+27=10y+x

⇒9x-9y +27= 0

⇒x-y+3=0 .......................(ii)

substracting (ii) from (i)

⇒2x-y-x+y-3=0

⇒x = 3

in (ii)

⇒3-y+3=0

⇒y=6

so the number is 36

so according to question

10x+y= 4(x+y)

⇒10x+y=4x+4y

⇒6x-3y=0

⇒2x-y=0 ......... (i)

again,

10x+y+27=10y+x

⇒9x-9y +27= 0

⇒x-y+3=0 .......................(ii)

substracting (ii) from (i)

⇒2x-y-x+y-3=0

⇒x = 3

in (ii)

⇒3-y+3=0

⇒y=6

so the number is 36

now , acc. to question

a 2 digit number that is (10x+y) is 4 times the sum of the digits that is 4(x+y) ..

now, if 27 is added to the number thats is 27+10x+y then the digits are reversed that is 10y+x...

therefore,

10x+y=4(x+y)

10x+y=4x+4y

10x-4x=4y-y

6x=3y

2x=y

2x-y=0 ---------------------- (1)

now ,

27+10x+y=10y+x

27+10x-x+y-10y=0

9x-9y= -27

9(x-y)= -27

x-y= -3 ------------------ (2)

now , we have 2 simuntaneous equations,

2x-y=0

x-y=3

2x-y=0

2(x-y)=2(-3)

2x-y=0

2x-2y= -6

- + +

_______

y=6

now , putting the value of y=6 in equation (2) ,

x-y= -3

x-6= -3

x= -3 + 6

x=3

therefore the number = 10x+y = 10(3) + (6)

=30+6

= 36