# The sum of the digits of a 2-digit number is 9. If 27 is added to the number the number is reversed. Find the number

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by dbanta2002

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by dbanta2002

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The Brainliest Answer!

Then actual number = 10x+y

Sum of digits = x+y = 9 ----------------(1)

27 added to the number = 10x+y+27

Then the number is reversed

⇒ 10x+y+27 = 10y+x

⇒ 10x+y+27-10y-x =0

⇒ 9x - 9y +27 = 0

⇒ 9(x - y +3) = 0

⇒ x - y +3 = 0/9

⇒ x - y +3 =0

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

Solving (1) and (2)

x + y = 9

x - y = -3

⇒ 2x = 6

⇒ x =6/2

∴ x = 3

Substituting x =3 in eq (1)

⇒ x + y = 9

⇒ 3 + y =9

⇒ y = 9 -3

∴ y = 6

The number = 10x+y

= 10(3) + 6

= 30+6

= 36