a no. consists of two digit whose sum is 8.if 18 is added to the no.its digits are reversed.Find the
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A no. consists of two digits whose sum is 8.
If 18 is added to the no., its digits are reversed.
Find the no.
x + y = 8
10x + y + 18 = 10y + x
9x 
A no. consists of two digits whose sum is 8.
If 18 is added to the no., its digits are reversed.
Find the no.
x + y = 8
10x + y + 18 = 10y + x
9x  9y = 18
9(x  y) = 18
x  y = 2
x + y = 8
x  y = 2
2x = 6
x = 3
y = 5
The number is 35
The number is
10x + y, not xy
Lots of excellent answers here, with methodical solutions. One of those deserves best answer.
I just wanted to add, for competitions, sometimes it's faster to guess and check. The digits must add to 8. Not too many combinations of that (when order does not matter): 17 & 71, 26 & 62, 35 & 53, 44 & 44. I stared with 44, which is the reverse of itself. The difference is 0, not 18. My next guess was 35 & 53, which happen to have a difference of 18. Then looking back at the problem, they're looking for the smaller number, so 35.
A no. consists of two digit whose sum is 8.
If 18 is added to the no. its digits are reversed.
The no. is 35.
"ab" represents the digits of the number.
a+b = 8
b = 8a
value of the number = 10a+b = 10a + (8a) = 9a + 8
add 18 to the number
9a+8 + 18 = 10b + a
9a + 26 = 10(8a) + a
9a + 26 = 809a
a = 3
b = 8a = 5
35
Let unit digit =x
and tens digit = y
As sum of two digit whose sum is 8
Hence x+y=8...........(i)
Then number =10y+x
When 18 is added to the number digits are reversed i.e number becomes 10x+y
Hence 10y+x+18 =10x+y
i.e. 9y9x = 18..........(ii)
From (i) x=8  y.....(iii)
Hence from (ii) and (iii) we get
9y9(8y) =18
i.e. 9y72+9y=  18
i.e. 18y=54 hence y=54/18=3
and x= 8y=83=5
Hence the number = 35
Number = ab has value 10a+b
a+b = 8
b = 8a
18+10a+b = 10b+a
18+10a+8a = 8010a+a
26+9a = 809a
18a = 54
a = 3
b = 5
Answer 35
x+y = 8
10x+y + 18 = 10y+x
9(yx) = 2*9
yx = 2
2y = 10
y = 5
x = 3
35+18 = 53
Let the two digits be xy
The number's value is 10x+y
x+y=8 (1)
If the digits are reversed, yhe number becomes yx with value 10y+x
10x+y+18 = 10y+x
9x9y =18 (2)
form (1) y=8x
9x9y =18
9x 9(8x) = 18
9x72+9x =18
18x =18+72
18x = 54
x= 3
y=8x =83=5
xy = 35
Check:
35+18= 53
let our number be x
x = 10a + b where a, b are integers between 0 and 9 (i.e. the digits, x = ab)
a + b = 8
10a + b + 18 = 10b + a
9a + 18 = 9b
a + 2 = b
a + b = 8
so 2a = 6
a = 3
b = 5
x = 35
35
35+18= 53


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