Question

** In a two digit number ,the the sum of the digits is 11. If the digits are reversed , the resulting number will be 27 more than the original number. Find the original number.

Answer 1

Suppose the unit digit of the number is X and the tens digit is Y. Then:(1) Y+X=11, (2) 10Y+X+27=10X+Y. Solving (1) and (2) by substitution method: Y=11-X (from 1)-(III), from (2): 27=9X-9Y-(IV),applying (III) in (IV), we get: 126=18X ;=> X=7;=> Y=11-7=4. Hence the original number is: 47.

Answer 2

Let us assume, x and y are the two digits of the two-digit number 

Therefore, the two-digit number = 10x + y and reversed number = 10y + x

Given:

x + y = 11 --------------1

Also given:

10y + x = 27 + 10x + y
9y - 9x = 27
y - x = 3 ----------------2

Adding equation 1 and equation 2 

2y = 14
y = 7

Therefore, x = 11 - y = 11 - 7 = 4

Therefore, the two-digit number = 10x + y = 10 * 4 + 7 = 47