# The sum of digits of a 2 digit number is 5. On adding 27 to the number, its digits are reversed. Find the original number.

2
by Bummy

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by Bummy

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Joining the 2 numbers=1 joined 4=14

and 14+27=41

14 revered is 41

so 14 is the answer

and 14+27=41

14 revered is 41

so 14 is the answer

then the no = 10x + y

given that sum of digits = 2

⇒ x+ y = 5 --------------(1)

On adding 27 we get the reverse of the no

⇒ 10x+y+27 = 10y +x

⇒10x -x +y - 10y +27 = 0

⇒9x - 9y = - 27 --------------(2)

Solving (1) and (2)

9x - 9y = -27

x + y = 5

9x - 9y = -27

9[x + y = 5]

9x - 9y = -27

9x + 9y = 45

⇒ 18x = 18

⇒ x = 18/18

∴ x = 1 in eq (1)

⇒ x+y = 2

⇒ 1 +y = 2

⇒ y = 2-1

∴ y = 1

∴ the no = 10x+y = 10(1) + 1 = 10+1 = 11