Question

Price of chair greater than the price of a table by $Rs.400$. If the price of $6$ chairs and $6$ table is $Rs.4800$, then by how much percent the price of a table is less than the price of a chair?
A. $\dfrac{200}{3}\%$.
B. $25\%$.
C. $37\dfrac{12}{2}\%$.
D. $\dfrac{2}{3}\%$.

Answer 1

Hint: In this problem we have found how much percent the price of a table is less than the price of a chair. In this problem first we have to calculate the prices of the chair and table. In question we have given the price of the chair is greater than the price of the table. Also given $6$ chairs and $6$ table is $Rs.4800$ and also given Price of chair greater than the price of a table by $Rs.400$. Then we will use the two equations we will find the prices of the chair and table. then we will find how much percent the price of a table is less than the price of a chair. Then we will get the final result.

Formula use:
1. Percentage of decrease in $X$ by $Y$ is given by $\dfrac{X-Y}{X}\times 100$.

Complete Step by Step Solution:
Given that,
Price of the chair is greater than the price of the table by$Rs.400$, then we will assume
Price of Chair $=X$.
Price of Table $=Y$.
Then the mathematical representation of the given statement is
$X=Y+400........\left( \text{i} \right)$
In the problem we also have the price of $6$chairs and $6$ table is $Rs.4800$. Now the mathematical representation of this stamen is given by
$6X+6Y=4800$
Now we will substitute $X=Y+400$ in the above equation, then
$6\left( Y+400 \right)+6Y=4800$.
Now we will simplify the above equation, then
$\begin{align}
  & 6Y+2400+6Y=4800 \\
 & 12Y=4800-2400 \\
 & 12Y=2400 \\
\end{align}$
Now the price of the table is given by
$\begin{align}
  & Y=\dfrac{2400}{12} \\
 & \Rightarrow Y=200 \\
\end{align}$
Now we will find the chair price by using the table price. Substituting the table price in the equation $\left( \text{i} \right)$, then
$\begin{align}
  & X=Y+400 \\
 & \Rightarrow X=200+400 \\
 & \Rightarrow X=600 \\
\end{align}$
Hence the price of the chair and table are
Price of Chair $=600$.
Price of Table $=200$.
Now we will find the how much percent the price of a table is less than the price of a chair by using the formula $\dfrac{X-Y}{X}\times 100$
Now we will substitute the chair price and table price in the above expression, then
$\Rightarrow d\%=\dfrac{600-200}{600}\times 100$
Now we will simplify the above equation, then
$\Rightarrow d\%=\dfrac{200}{3}\%$

Then we will get the final result, which is option A.

Note:
In this problem they have mentioned the statement “Price of chair greater than the price of a table by $Rs.400$”. There are many chances to mention this statement. They can also mention the statement like “the difference between the price of a chair and the price of a table is $Rs.400$”.