[Math] the mathematical explanation for this trick

puzzle

I found the following method to find one's age. It is working exactly for my case. I like to understand and solve this puzzle. If this is wrong forum, my sincere apologies. Please guide me solve this.

  1. Take last digit of your mobile number
  2. Multiply it by 2
  3. Add 5 with the above answer
  4. Multiply the answer with 50
  5. Add 1764 with the answer
  6. Subtract the your birth year from the result in part 5 (example 1985, 1973, etc.)

Now you will get 3 digit number. The first one is last digit of your mobile number, last two digits are your age.

Best Answer

  1. Let $n$ be the last digit of your mobile number.
  2. $2n$
  3. $2n+5$
  4. $50(2n+5)=100n+250$
  5. $100n+250+1764=100n+2014$ (fixed by Daniel R)
  6. Let $y$ be your year of birth. Then we have $100n+(2014-y)$.

Since $2014-y$ is your age (assumed to be $<100$), the hundreds digit is $n$ and the last two digits are your age.

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