Question

A man bought a certain number of chairs for ₹ \[10,000.\] He kept one for his own use and sold the rest at the rate ₹ \[50\] more than he gave for one chair. Besides getting his own chair for nothing, he made a profit of ₹\[450.\]How many chairs did he buy?

Answer 1

Hint:In the given question, man bought chairs worth ₹ \[10,000,\] out of those chairs he kept one for himself. And he sold the rest of the chairs at the rate ₹ \[50\] more in cost price. So, the selling price is more than the cost price. He made a profit of ₹\[450.\] extra after selling the chairs.

Complete step-by-step solution
We have been given the cost price of certain number of chairs i.e., ₹ \[10,000.\]
Now, let us assume he bought x number of chairs.
So, cost price of 1 chair $ = $ $\dfrac{{10000}}{x}$
Then it is mentioned in the question that he sells each chair with an extra amount of ₹ \[50\] more in cost price.
So, selling price of 1 chair $ = $ $\dfrac{{10000}}{x} + 50$
Now, according to the question, let the man buy\[x\] chair and sell \[\left( {x - 1} \right)\] chairs.
Selling price of \[\left( {x - 1} \right)\] chairs $ = $ $(x - 1)[\dfrac{{10000}}{x} + 50]$
We know that, Selling price \[-\] Cost price \[ = \] Profit
\[\therefore \]$(x - 1)[\dfrac{{10000}}{x} + 50]$$ - $$10000 = 450$
On solving the above equation, we get
\[\begin{array}{*{20}{l}}
\Rightarrow {{X^2}-{\text{ }}10x{\text{ }}-{\text{ }}200{\text{ }} = {\text{ }}0} \\
\Rightarrow {\left( {x + 10} \right){\text{ }}\left( {x - 20} \right){\text{ }} = {\text{ }}0} \\
\Rightarrow {X{\text{ }} = {\text{ }} - 10,{\text{ }}20}
\end{array}\]
We will neglect \[ - 10\] here, so, x \[ = {\text{ }}20\]
Thus, the man bought $20$ chairs.

Note:Students should notice that here we have neglected value \[ - 10\] because chairs can’t be of negative value. Hence, we chose $20$ here.