Question

The cost price of 13 chairs is the same as the selling price of 18 chairs. Find the gain and loss percent.

Answer 1

Hint: Assume the cost price and selling price of each chair to be unknown quantities. Now, establish the relationship between those two quantities from the given condition in the question. If the selling price is higher than the cost price of each chair, then there is a net profit, otherwise there is a loss. Now, calculate the profit or loss on each chair and find their percentage.

Complete step by step solution:
Let us assume the cost price of each chair be Rs. x and the selling price of each chair be Rs. y.
Now, it is given that the cost price of 13 chairs is the same as the selling price of 18 chairs.
Thus, by the problem, it can be formulated that,
$\begin{align}
  & 13x\text{ = 18}y \\
 & \therefore \ y\text{ = }\dfrac{13x}{18} \\
\end{align}$
Thus, in terms of the cost price, the selling price is Rs. $\dfrac{13x}{18}$. Since, the selling price of a chair is less than the cost price, it can be said that the person incurred a loss.
Now, total loss suffered = Cost Price – Selling Price
$\begin{align}
  & =\text{ Rs}\text{. }\left( x\text{ }-\text{ }\dfrac{13x}{18} \right) \\
 & =\text{ Rs}\text{. }\dfrac{5x}{18} \\
\end{align}$
$\therefore $ Percentage of loss suffered
$\begin{align}
  & =\text{ }\dfrac{\text{ Loss suffered}}{\text{Cost}\ \text{price}}\text{ }\times \text{ }100 \\
 & =\text{ }\dfrac{\dfrac{5x}{18}}{x}\text{ }\times \text{ }100 \\
 & =\text{ }27.77\% \\
\end{align}$
Now, since loss is negative profit, it can be said that the percentage of loss is equivalent to the negative percentage of profit.
Thus, percentage of profit = -27.77 %
 Hence, the loss percent is 27.77% and the profit percent is -27.77%.

Note: From this problem, it is clear that in order to gain money in a business, one has to buy more in comparison to what he or she sells at the same price. As here more number of chairs are sold at the same price than what has been bought, loss is suffered.