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A number consists of 3 digits whose sum is 10. The middle digit is equal to the difference of the other two and the number will be increased by 99 if its digits are reversed. What is the square of the number?

172225

xyz- is the number and we have: x+y+z=10 ---->(1) y=z-x ---->(2) 100x+10y+z+99=100z+10y+x ---->(3) xyz^2=?

(3) => 99z-99x=99 => z-x=1 => z=x+1 (2) => y=z-x=x+1-x=1 (1) => x+y+z=x+1+(x+1)=10 => x=4 => z=5 xyz=415 xyz^2=415^2=172225

514 is the number

5+1+4 = 10 5-1 =4 514 - 415 = 99

I'm thinking of a number.

What is the number?

The year 1978 is such that the sum of the first two digits and the latter two digits is equal to the middle two digits, i.e. 19 + 78 = 97. What is the next year (after 1978) for which this is true?

The sum of the digits of a three digit number is 12. If the hundreds digit is 3 times the tens digit and the tens digit is 1/2 the units digit, what is the tens digit of the number?