Question

The sum of the digits of a two digit number is 11. If the units and tens digit are interchanged then the new number is 9 more than the original number. Find the original number.

Answer 1

let the x be at unit place and y be at tens place
according to question
x+y=11......eq1
original digit =10y+x
when digits interchanged
new num = 10x+y
10x+y=10y+x+9....... eq2
solving x and y from equation 1 and 2 we get...
original number =56

Answer 2

Hi friend,
Let the number be xy
x is tens, y is ones place.
Given that

x + y = 11.
It means it has 4 pairs.
(65,56),(47,74),(38,83),(29,92)

as digits are interchanged,
New number is yx
y is tens, x is ones place.
Given :
yx = 9 + xy
Therefore yx - xy = 9

Hence there is only one pair accepting the above condition which is (65,56)
yx = 65
xy = 56 = Original number.

Hope you find my answer useful and hope you mark my answer as brainliest !
:)

Regards,
Harith
Ambitious