Let digit in the tens place be X and digit in the ones place be Y.
A 2-digit number is equals to four times the sum of its digits: To get the number, we multiply the first digit in the tens place by 10 and add it to Y. This will be equal to four times the sum of X and Y.
10X + Y = 4(X + Y)
10X + Y = 4X + 4Y
6X = 3Y
2X = Y
Y – 2X = 0 —– (1)
If the digits of the number are reversed, the new number formed is 27 more than the original number: To get the new number, we multiply Y by 10 since it is now in the tens place and add it to Y. This will equal the original number (10X + Y) plus an additional 27.
10Y + X = (10X + Y) + 27
9Y – 9X = 27
Y – X = 3 —– (2)
(2) – (1)
(Y – X) – (Y – 2X) = 3 – 0
X = 3
Sub x = 3 into (2):
Y – 3 = 3
Y = 6
∴ The number is 36.