Sum of the digits of a two digit number is 11.The given number is less than the number obtained by interchanging the digits by 9.Find the number.
please tell!!!!!!!
Answers
Let the digits of a number: x and y
x+y=11
y=11-x
Given number =10x+y
=10x+(11-x)
=9x+11
Number formed by interchanging digits=10y+x
=10 (11-x)+x
=110-10x+x
=110-9x
Given that,
(110-9x)-9=9x+11
110-9x-9x-11=9
Or
(110-9x)-(9x+11)=9
110-9x-9x-11=9
110-11-9x-9x=9
99-18x=9
-18x=9-99
x=-90/-18
=5
y=11-x
=11-5
=6
Therefore, the number is 56
if you interchange the number it is 65
65-56=9
Hope it helps................
Answer:
Let the digits of a number: x and y
x+y=11
y=11-x
Given number =10x+y
=10x+(11-x)
=9x+11
Number formed by interchanging digits=10y+x
=10 (11-x)+x
=110-10x+x
=110-9x
Given that,
(110-9x)-9=9x+11
110-9x-9x-11=9
Or
(110-9x)-(9x+11)=9
110-9x-9x-11=9
110-11-9x-9x=9
99-18x=9
-18x=9-99
x=-90/-18
=5
y=11-x
=11-5
=6
Therefore, the number is 56
if you interchange the number it is 65
65-56=9
Step-by-step explanation: