**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**.