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**Hint:**Assume the total money that is distributed as ‘x’. Find the amount A and B get by finding \[{{\left( \dfrac{3}{16} \right)}^{th}}\] part of x and \[{{\left( \dfrac{1}{4} \right)}^{th}}\] of part of x respectively. Now, calculate the amount of money C gets by subtracting the sum of money of A and B from total money. Equate the amount of money C gets with 81 and find the value of x. Finally, substitute this value of x in the expression of money obtained by B to get the answer.

**Complete step by step answer:**

Here, we have been given that a certain amount of money is distributed among A, B and C. Let us assume the total amount of money distributed is ‘x’.

Now, it is given that A gets \[\dfrac{3}{16}\] and B gets \[\dfrac{1}{4}\] of the whole amount. Therefore, we have,

Money obtained by A = \[\dfrac{3}{16}\times x=\dfrac{3x}{16}\]

Money obtained by B = \[\dfrac{1}{4}\times x=\dfrac{x}{4}\]

Therefore, the amount of money obtained by C will be the difference of total money and sum of money obtained by A and B. So, we have,

\[\Rightarrow \] Money obtained by C = \[x-\left( \dfrac{3x}{16}+\dfrac{x}{4} \right)\]

\[\Rightarrow \] Money obtained by C = \[x-\left( \dfrac{3x+4x}{16} \right)\]

\[\Rightarrow \] Money obtained by C = \[x-\dfrac{7x}{16}\]

\[\Rightarrow \] Money obtained by C = \[\dfrac{16x-7x}{16}\]

\[\Rightarrow \] Money obtained by C = \[\dfrac{9x}{16}\]

It is given that money obtained by C is Rs.81. Therefore, equating it with the expression of money obtained by C, we get,

\[\begin{align}

& \Rightarrow \dfrac{9x}{16}=81 \\

& \Rightarrow x=\dfrac{16\times 81}{9} \\

\end{align}\]

\[\Rightarrow x=\] Rs.144

Therefore, the total amount of money that was distributed is Rs.144.

Now, we have to find the amount of money obtained by B. So, substituting the obtained value of x in the expression of money obtained by B, we get,

Money obtained by B = \[\dfrac{144}{4}\] = Rs.36

**So, the correct answer is “Option a”.**

**Note:**One may note that we do not have to assume the amount of money obtained by A and B as different variables. It may confuse us. We just have to assume one variable and carry out our calculation using that assumption. Note that the amount of money obtained by C was given to us. That is why we equated it with the obtained expression for money obtained by C. Remember that the value of x is not our solution, we have to substitute it in the expression \[\dfrac{x}{4}\]. Sometimes in a hurry students just write the value of ‘x’ as the answer. So, the question must be read carefully.

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