Question

Perform $12 \div 9$ using Nikhilam sutra method on base 10. Also, find the quotient $\left( Q \right)$ and remainder $\left( R \right)$.
(A)$Q = 1$ and $R = 3$
(B) $Q = 1$ and $R = 2$
(C) $Q = 1$ and $R = 0$
(D) $Q = 1$ and $R = 1$

Answer 1

Hint: To find the quotient and remainder we will follow the Nikhilam sutra method. According to this method we will find the difference between the divisor and the given base. Then we will write the number in a column form having two columns $Q$ and $R$ such that number in the remainder column will be equal to the number of zeros in the given base. Then we will take down the value of $Q$, which will be the first digit of quotient. After that we will multiply the first digit of the quotient with the difference found between the divisor and base which will give the final quotient. Now, we will add the quotient with the number written in column $R$ to find the remainder.


Complete step by step solution
Given:
The dividend is $12$.
The divisor is $9$.
The base is $10$.

Since, we will find the difference between the divisor 9 and the base 10, which can be expressed as:
$\begin{array}{c}
{\rm{Difference}} = 10 - 9\\
 = 1
\end{array}$

Now, we will split the dividend into two parts $Q$ and $R$ such that the number of digits written on the remainder side will be equal to the number of zeros in the given base. In this case, it is 1.
Hence, we will express the dividend as:

1	2
$Q$	$R$

Now, we will take down the number at the place of $Q$ such that this will be the first digit of $Q$ .

1	2
1	$R$

As the difference is 1 in this case, we will multiply 1 with the first digit of $Q$ which can be expressed as:
$Q = 1 \times 1 = 1$

Now, to find the remainder we will add the quotient found above with the number written in the column $R$ .
$\begin{array}{l}
R = 1 + 2\\
R = 3
\end{array}$

 Hence the quotient $\left( Q \right)$ is 1 and remainder $\left( R \right)$ is 3. Therefore, option A is the correct answer.


Note: The Nikhilam sutra method is a part of Vedic mathematics. It is the shortcut method to do the division. This method is performed on the basis of nearest base. In our question the base is 10, but it can vary from question to question.