Question 569048: the sum of two digits of a natural number is 7. when the digits are reversed, the number is increased by 27.
Answer by Maths68(1474)   (Show Source):
You can put this solution on YOUR website! the sum of two digits of a natural number is 7. when the digits are reversed, the number is increased by 27.
Let x and y are two digits of a number
When y is unit and x is ten
10x+y=n......(1)
when the digits are reversed, the number is increased by 27
Now y is ten and x is unit
x+10y=n+27.............(2)
the sum of two digits of a natural number is 7
x+y=7........(3)
Subtract (2) from (1)
10x+y=n
-x-10y=-n-27
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9x-9y=-27
9(x-y)=-27
9(x-y)/9=-27/9
x-y=-3...............(4)
Add (3) and (4)
x+y=7
x-y=-3
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2x=4
2x/2=4/2
x=2
Plug in the value of x in (1)
x+y=7
2+y=7
y=7-2
y=5
Number is 25
Check
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sum of digits = 2+5 = 7
When digits are reversed it is increased by 27
52=25+27
52=52
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