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a no. consists of two digit whose sum is 8.if 18 is added to the no.its digits are reversed.Find the

Author :

Submitted : 2018-06-14 08:01:41    Popularity:     

Tags: sum  8.  consists  digit  reversed  

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 -

Answers:

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 = 8-a

value of the number = 10a+b = 10a + (8-a) = 9a + 8

add 18 to the number
9a+8 + 18 = 10b + a
9a + 26 = 10(8-a) + a
9a + 26 = 80-9a
a = 3
b = 8-a = 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. 9y-9x =- 18..........(ii)
From (i) x=8 - y.....(iii)
Hence from (ii) and (iii) we get
9y-9(8-y) =-18
i.e. 9y-72+9y= - 18
i.e. 18y=54 hence y=54/18=3
and x= 8-y=8-3=5
Hence the number = 35

Number = ab has value 10a+b
a+b = 8
b = 8-a
18+10a+b = 10b+a
18+10a+8-a = 80-10a+a
26+9a = 80-9a
18a = 54
a = 3
b = 5
Answer 35

x+y = 8
10x+y + 18 = 10y+x
9(y-x) = 2*9
y-x = 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
9x-9y =-18 ----(2)

form (1) y=8-x
9x-9y =-18
9x -9(8-x) = -18
9x-72+9x =-18
18x =-18+72
18x = 54
x= 3
y=8-x =8-3=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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