The sum of the digits of two-digit number is 10, while when the digits are reversed, the number decrease by 54. Find the changed number.

A. 28

B. 19

C. 37

D. 46

E. 82

Answer: Option A

Solution(By Examveda Team)

Let number be (10x + y)
According to question,
(10x + y) - (10y + x) = 54
10x - 10y + y - x = 54
Or, 9x - 9y = 54
Or, x - y = 6 -------(i)
Sum of digits,
(x + y) = 10 ------- (ii)
(i) - (ii)
So, x - y - x - y = 6 - 10
Or, -2y = -4
Or, y = 2 and, x = 8
Then, the required number is
= (10y + x)
= 10 × 2 + 8
= 28