Question

If the C.P of 9 watches at a gift shop is the same as the S.P of 6 watches, find the gain percent.

Answer 1

Hint: To solve the above question, we will write the cost price of one watch in terms of its selling price. After doing this, we will find the gain which is obtained by subtracting cost price from selling price. And then we will find the gain percent according to the formula shown:
Gain % \[=\dfrac{\text{Selling Price }-\text{Cost Price}}{\text{Cost Price}}\times 100\]

Complete step-by-step answer:
Before we solve the question, we must know about some terms given in the question like C.P, S.P, and gain. CP is the short form of cost price which is the price at which we have purchased an article/good. SP is the short form of the selling price which is the price at which we have sold an article / a good to someone. Gain on any item is obtained by subtracting the cost price of that item from its selling price.
Now, it is given in the question that the cost price of 9 watches at a gift shop is equal to the selling price of 6 watches. Let us assume that the cost price of 1 watch is x and the selling price of the same watch is y. According to the question, we have the following equation:
\[9\times x=6\times y\]
\[9x=6y\]
\[x=\dfrac{6}{9}y\]
\[x=\dfrac{2}{3}y\]
Now, we have to find the gain percent on a single watch. The gain percent is given by the formula:
Gain % \[=\dfrac{\text{Selling Price }-\text{Cost Price}}{\text{Cost Price}}\times 100\]
Gain % \[=\dfrac{y-x}{x}\times 100\]
Now, we will substitute the value of \[x=\dfrac{2y}{3}\] in the above equation. After doing this, we will get:
Gain % \[=\dfrac{y-\dfrac{2}{3}y}{\dfrac{2}{3}y}\times 100\]
Gain % = \[=\dfrac{\dfrac{1}{3}y}{\dfrac{2}{3}y}\times 100\]
Gain % = \[\dfrac{y\times 1\times 3}{y\times 2\times 3}\times 100\]
Gain % = \[\dfrac{1}{2}\times 100\]
Gain % = 50 %
Thus, the gain % on a single watch is 50 %.

Note: We can also solve the above question in the way shown: The ratio of selling price of one watch to the cost price of one watch is \[\dfrac{3}{6}\] i.e.
\[\dfrac{\text{Selling Price}}{\text{Cost Price}}=\dfrac{9}{6}=\dfrac{3}{2}....\left( i \right)\]
Now, the gain % \[=\dfrac{\text{Selling Price }-\text{Cost Price}}{\text{Cost Price}}\times 100\]
Gain % \[=\left( \dfrac{\text{Selling Price }}{\text{Cost Price}}-\dfrac{\text{Cost Price}}{\text{Cost Price}} \right)\times 100\]
Gain % \[=\left( \dfrac{3}{2}-1 \right)\times 100\]
Gain % \[=\dfrac{1}{2}\times 100\]
Gain % = 50 %
Thus we get the same answer from this method.