A certain number of two digits is four times the sum of the digits. If

1.	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» 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)) Correct option is C) 12

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»

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))

Correct option is C) 12