The sum of the digits of a two digit number is 8. If the digits are reversed, the number is decreased by 54. Find the number. 

Correct option is (C) 71

Let the number be ab or (10a+b)

\(\therefore\) Sum of digits = a+b

Given that sum of digits of two-digit number is 8.

\(\therefore\) a+b = 8         __________(1)

Reversed number is ba or (10b+a)

Given that when digits are reversed, the number is decreased by 54.

i.e., (10a+b) - (10b+a) = 54

\(\Rightarrow\) 9a - 9b = 54

\(\Rightarrow\) a - b \(=\frac{54}9\) = 6   __________(2)

By adding equations (1) & (2), we obtain

2a = 8+6 = 14

\(\Rightarrow a=\frac{14}2=7\)

Then from (1), we obtain

b = 8 - a = 8 - 7 = 1

Hence, the number is ab = 71.

Correct option is C) 71