Question

A certain number of two digits is four times the sum of the digits. If 9 is added to the number the digits in the number are reversed, then the number is ………………… 

A) 13 

B) 23 

C) 12 

D) 14

Answer 1

Correct option is (C) 12

Let the two-digit number be ab whose unit digit is b and ten's digit is a.

\(\therefore\) Required number is ab = 10a + b   _________(1)

Reversed number is ba = 10b + a     _________(2)

Sum of digits = a + b

According to given conditions, we have

10a + b = 4 (a+b)

and 10a + b + 9 = 10b + a

\(\Rightarrow\) 6a - 3b = 0

and 9a - 9b + 9 = 0

\(\Rightarrow\) 2a - b = 0          _________(3)

and a - b + 1 = 0   _________(4)

Subtract equation (4) from (3), we get

(2a - b) - (a - b + 1) = 0 - 0

\(\Rightarrow\) a - 1 = 0

\(\Rightarrow\) a = 1

\(\therefore\) b = 2a = 2    (From (3))

\(\therefore\) Required number is ab = 12.   (From (1))

Answer 2

Correct option is C) 12