Question

The price of a table is Rs. 400 more than that of a chair. If 6 tables and 6 chairs together cost Rs. 4800, by what percent is the price of the chair less than that of the table?
A. $33\dfrac{1}{3}%$
B. $50%$
C. $66\dfrac{2}{3}%$
D. None of these

Answer 1

Hint: For the above question we will assume the cost of the chair to be a variable, say Rs. x and then the cost of table can be expressed as Rs. x+400. Then, we can make the equations according to the given conditions in the question. After that find the percentage of the price of chair less than that of the table given by,
$\dfrac{price\ of\ table-price\ of\ chair}{price\ of\ table}\times 100$

Complete step-by-step answer:

We have been given that the price of a table is Rs. 400 more than that of a chair.
Let us suppose the price of chairs to be $Rs.x$.
Then, the price of the table is equal to $Rs.\left( x+400 \right)$.
Also, we have been given that 6 tables and chairs together cost $Rs.4800$.
Now, we know that cost of 1 chair $=Rs.x$
So, we get the cost of 6 chairs $=Rs.6x$
Now, we know that cost of 1 table $=Rs.\left( x+400 \right)$
So, we get the cost of 6 tables $=Rs.6\left( x+400 \right)$
According to question, we can formulate the equation as below,
$\begin{align}
  & 6x+6\left( x+400 \right)=4800 \\
 & \Rightarrow 6x+6x+2400=4800 \\
 & \Rightarrow 12x=4800-2400 \\
 & \Rightarrow 12x=2400 \\
 & \Rightarrow x=\dfrac{2400}{12} \\
 & \Rightarrow x=200 \\
\end{align}$
Hence, we get the price of 1 chair $=Rs.200$ and price of 1 table $=Rs.\left( 200+400 \right)=Rs.600$.
The percentage of the price of chair less than that of the table is given by,
$\dfrac{price\ of\ table-price\ of\ chair}{price\ of\ table}\times 100$
$\begin{align}
  & =\dfrac{600-200}{600}\times 100 \\
 & =\dfrac{400}{600}\times 100 \\
 & =\dfrac{200}{3}\% \\
 & =66\dfrac{2}{3}\% \\
\end{align}$
Therefore, the correct option is (C).

Note: Remember that while finding the percentage be careful as we have to divide the difference of price of chair and table by the price of table as we have been asked with respect to table. Sometimes we get confused at this point and divide it by the price of the chair and we get the incorrect answer.