# The sum of the digits of a two number is 12. the f 54 is subtracted from the number, the digits get reversed. find the number

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by siddhimalviya0

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2015-12-23T14:36:40+05:30

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Let the digits of the number are x and y, so number will be (10x+y)
A/q,
x+y =12
and, (10x +y) -54 = (10y +x)
⇒9x -9y = 54
⇒x-y =6
⇒x =(6 +y), putting this value in first equation,
(6 +y) +y =12
⇒2y =6
⇒y =3
so, x= 6+3 =9
so, the number will be 93
2015-12-23T16:56:33+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Let the digits of the number be x and y
the number = 10x+y
Given x+y = 12   --------------------(1)
Also given 10x+y -54 = 10y+x
⇒10x + y - 10y - x = 54
⇒9x - 9y - 54 = 0
⇒9( x - y - 6 = 0)
⇒x - y -6 = 0/9
⇒ x - y = 6  --------------------(2)
x + y = 12
x -  y = 6

⇒2x - 0 = 18
⇒ x = 18/2
∴x = 9
Substituting x = 9 in (1)
⇒ x+y =12
⇒9+y = 12
⇒y = 12-9
∴ y = 3
Therefore the number is 10x + y
= 10(9) + 3
= 90 + 3
= 93
∴The number is 93