Let n be the unknown number. We can write it as
n = 10a + b
with a and b integers between 1 and 9 (either with positive or negative sign).
Reversing the digits gives another number
m = 10b + a
The first number is increased by 54 when the digits are reversed, which means
m = n + 54 → 10b + a = 10a + b + 54 → 9b - 9a = 54 → b - a = 6
The digit in the tens place of n is 3 times the digit in the ones place, so
a = 3b
Substitute this into the previous equation and solve for b :
b - a = b - 3b = -2b = 6 → b = -3
Solve for a :
a = 3b = 3(-3) = -9
Then the original number is n = 10a + b = 10(-9) + (-3) = -93
