Find the digits A, B and C, if

$\begin{matrix} & 7 & 3 & \text{A} \ - & \text{B} & \text{C} & 9 \ \hline & 3 & 4 & 8 \ \hline \end{matrix}$

$\begin{matrix} & 7 & 3 & \text{A} \ - & \text{B} & \text{C} & 9 \ \hline & 3 & 4 & 8 \ \hline \end{matrix}$

Firstly, we will find the value of A.

Clearly, A - 9 is a number whose ones digit is 8.

⇒ A - 9 = 8 , A - 9 = 18 , A - 9 = 28; and so on.

⇒ A = 8 + 9 , A = 18 + 9 , A = 28 + 9; and so on.

⇒ A = 17 , A = 27 , A = 37; and so on.

Since, A is a digit. ∴ A = 7.

Secondly, we will find the value of C.

$\begin{matrix} & 7 & \overset{2}{\cancel{3}} & \overset{17}{\cancel{7}} \ - & \text{B} & \text{C} & 9 \ \hline & 3 & 4 & 8 \ \hline \end{matrix}$

Clearly, 2 - C is a number whose ones digit is 4.

As it is not possible to subtract any number from 2 that gives 4. Hence, borrowing one number from preceding digit gives 12 - C.

$\begin{matrix} & \overset{6}{\cancel{7}} & \overset{12}{\cancel{3}} & \overset{17}{\cancel{7}} \ - & \text{B} & \text{C} & 9 \ \hline & 3 & 4 & 8 \ \hline \end{matrix}$

⇒ 12 - C = 4 , 12 - C = 14 , 12 - C = 24; and so on.

⇒ C = 12 - 4 , C = 12 - 14 , C = 12 - 24; and so on.

⇒ C = 8 , C = -2 , C = -12; and so on.

Since, C is a digit. ∴ C = 8.

Lastly, we will find the value of B.

Clearly, 6 - B is a number whose ones digit is 3.

⇒ 6 - B = 3 , 6 - B = 13 , 6 - B = 23; and so on.

⇒ B = 6 - 3 , B = 6 - 13 , B = 6 - 23; and so on.

⇒ B = 3 , B = -7 , B = -17; and so on.

Since, B is a digit. ∴ B = 3.

$\begin{matrix} & 7 & 3 & \text{7} \ - & \text{3} & \text{8} & 9 \ \hline & 3 & 4 & 8 \ \hline \end{matrix}$

Hence, A = 7, B = 3 and C = 8.