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)