Question

A certain amount of money is distributed among A, B and C. A gets \[\dfrac{3}{16}\] and B gets \[\dfrac{1}{4}\] of the whole amount. If C gets Rs.81; then what does B get?
(a) Rs.36
(b) Rs.56
(c) Rs.46
(d) Rs.63

Answer 1

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.