a number consists of two digits whose sum is 8. if 18 is added to the number its digits are reversed . find the number .
Answers
Answer:
Let the number be original number be XY
According to the question:
X+Y = 8
XY + 18 = YX
2 digit numbers who have the sum of digits = 8
17, 26, 35, 44, 53, 62, 71
here, we can see when digits are reversed:
17 will be 71
26 will be 62
35 will be 53
( 44 won't change )
Thus, the above are the only possible options.
Since we are adding 18 to the original number XY to get YX,
XY < YX
Therefore, the possible number will be 17, 26 or 35.
( they can't be 71 or 62 or 53 as if we add 18 to them the result will not lie in the above spectrum mentioned )
( it can't be 44 as well as both the digits are the same whatsoever )
Possible answers:
17 + 18 = 35 ( wrong )
26 + 18 = 44 ( wrong )
35 + 18 = 53 ( right )
35 digits reversed = 53
Therefore, the original number is 35.
P.S. I hope you understood atleast something as it was difficult for me to explain through typing. You need to use your logical reasoning, that is it.
Hope you understood ;)
OR
Let one digit of the number be x , then its ten digits digits will be (8−x) .
So , given number =10(8−x)+x
=80−10x+x
=80−9x
Now if digits are reversed , then Number obtained
=10x+(8−x)
=10x+8−x
=9x+8
According to question
(80−9x)+18=9x+8
98−9x=9x+8
90=18x
x=5
⇒ given number =80−9x
=80−9×5
=80−45
=35
∴ the number is 35
btw, got this from toppr, this will help you.