Digits are Complicated

Let the digit at ten's place be x and one's place be y.

Then according to the question:-

x+y = 14.............(i)

and it is said that switching the ones' digit to the tens' digit, the new number is 36 less than the original's.

So, (10x+y)-36= 10y+x

or 10x+y-36= 10y+x

or 9x-9y=36

or x-y = 4.................(ii)

By adding (i) and (ii)... we get

(x+y)+(x-y) = 14+4

or 2x=18

or x= 9 and y=(14-x) = 5 ....

By:- @Sayan Karmakar

Try to sum up the numbers between 1-9 to get 14.

The possible 2 digits to sum up to 14 are

9 & 5

8 & 6

7 & 7

Now check the sum after altering the digits and find the difference

95 - 59 = 36 (This is what you need)

86 - 68 = 18

77 - 77 = 0

Easy........

Write the original number as 10a+b where a is the tens' digit and b is the ones' digit. The sum of the digits is 14, ie a+b=14. ''If I switch the ones' digit to the tens' digit, the new number is 36 less than the original's'' this allows us to write: 10b+a+36=10a+b, this can be simplified to a-b=4. Solving a+b=14 and a-b=4 simultaneously gives a=9 and b=5, hence original number is 95.

Let x = the 10's digit

Let y = the units

:

10x + y = the original two digit number

:

The sum of the digits of a two-digit number is 14.

x + y = 14

:

"If the digits are reversed, the number is 18 less than the original number."

Rev no. = orig no. - 36

10y + x = 10x + y - 36

10y - y = 10x - x - 36

9y = 9x - 36

simplify, divide by 9

y = x - 4

:

In the sum equation replace y with (x-4)

x + (x-4) = 14

2x = 14 + 4

2x = 18

x = 9

obviously y = 5

:

95 is the original number

:

:

Check solution in the statement:

"If the digits are reversed, the number is 36 less than the original number."

59 = 95- 36