The sum of the digits of a two -digit number is 14. When the digits are reversed the difference between the original number and the new number is 36. find the original number

Question

How to find original number please

Answer 1

The sum of the digits of a two -digit number is 14. When the digits are reversed the difference between the original number and the new number is 36. find the original number

Let the number be N and the two digits comprising the number be a and b.

Then we can write the number N as ab.

We can also write the value of N as N = 10*a + b

Let the new number be M such that M = ba (the digits are reversed)

Now the can write the value of M as M = 10*b + a

We also have M - N = 36   (the difference between the original number and the new number is 36)

OR,                N - M = 36   (the difference between the original number and the new number is 36)

Using, M - N = 36

10b + a - (10a + b) = 36

9b - 9a = 36

b - a = 4

But, a + b = 14   (sum of digits is 14)

Adding these two equations,

2b = 18

b = 9, therefore, a = 5

Answer: N = 59

​N = 95 is also a possibility, (We would have got this if we had used N - M = 36)