Question

Pens are bought at 12 for a rupee and sold at 9 for a rupee. Find the gain or loss percent.

Answer 1

Hint: Here, we need to find the gain or loss percent on the sale of the pens. First, we will calculate the selling price and cost price on each pen. Then, we will calculate the gain on the sale of the pens. Finally, using the cost price and gain, we will find the gain percent on the sale of the pens.

Formula Used:
 We will use the following formulas to solve the question:
The gain on the sale of an object is given by \[{\rm{Gain}} = S.P. - C.P.\], where \[S.P.\] is the selling price of the object and \[C.P.\] is the cost price of the object.
The gain percent is given by \[{\rm{Gain Percent}} = \dfrac{{{\rm{Gain}}}}{{C.P.}} \times 100\].

Complete step-by-step answer:
The cost price of an object is the price at which the object is bought.
It is given that 12 pens are bought for a rupee.
Therefore, we get
Cost price of 12 pens \[ = {\rm{Rs}}{\rm{. }}1\]
Dividing both sides by 12, we get
Cost price of 1 pen \[ = {\rm{Rs}}{\rm{. }}\dfrac{1}{{12}}\]
Thus, the cost price of each pen is \[{\rm{Rs}}{\rm{. }}\dfrac{1}{{12}}\].
The selling price of an object is the price at which the object is being sold at.
It is given that 9 pens are sold for a rupee.
Therefore, we get
Selling price of 9 pens \[ = {\rm{Rs}}{\rm{. }}1\]
Dividing both sides by 9, we get
Selling price of 1 pen \[ = {\rm{Rs}}{\rm{. }}\dfrac{1}{9}\]
Thus, the selling price of each pen is \[{\rm{Rs}}{\rm{. }}\dfrac{1}{9}\].
Now, we know that the gain or loss of an object is the difference between the selling price and the cost price of the object.
We can find the gain using the formula \[{\rm{Gain}} = S.P. - C.P.\], where \[S.P.\] is the selling price of the object and \[C.P.\] is the cost price of the object.
Substituting \[S.P. = {\rm{Rs}}{\rm{. }}\dfrac{1}{9}\] and \[C.P. = {\rm{Rs}}{\rm{. }}\dfrac{1}{{12}}\] in the formula, we get
\[{\rm{Gain}} = {\rm{Rs}}{\rm{. }}\left( {\dfrac{1}{9} - \dfrac{1}{{12}}} \right)\]
Taking the L.C.M., we get
\[ \Rightarrow {\rm{Gain}} = {\rm{Rs}}{\rm{. }}\left( {\dfrac{{12 - 9}}{{108}}} \right)\]
Subtracting the terms, we get
\[\begin{array}{l} \Rightarrow {\rm{Gain}} = {\rm{Rs}}{\rm{. }}\dfrac{3}{{108}}\\ \Rightarrow {\rm{Gain}} = {\rm{Rs}}{\rm{. }}\dfrac{1}{{36}}\end{array}\]
\[\therefore \] The gain on each pen is \[{\rm{Rs}}{\rm{. }}\dfrac{1}{{36}}\].
Finally, we will find the gain percent on the sale of the pens.
Substituting \[{\rm{Gain}} = {\rm{Rs}}{\rm{. }}\dfrac{1}{{36}}\] and \[C.P. = {\rm{Rs}}{\rm{. }}\dfrac{1}{{12}}\] in the formula \[{\rm{Gain Percent}} = \dfrac{{{\rm{Gain}}}}{{C.P.}} \times 100\], we get
Gain Percent \[ = \dfrac{{\dfrac{1}{{36}}}}{{\dfrac{1}{{12}}}} \times 100\]
Rewriting the expression, we get
\[ \Rightarrow \]Gain Percent \[ = \dfrac{{12}}{{36}} \times 100\]
Simplifying the expression, we get
\[ \Rightarrow \]Gain Percent \[ = \dfrac{1}{3} \times 100 = \dfrac{{100}}{3}\% \]
Rewriting the percentage in decimal form, we get
\[ \Rightarrow \]Gain Percent \[ = 33.33\% \]
Therefore, the gain percent on the sale of the pens is \[33.33\% \].

Note: We can make a mistake in calculating the gain as zero, since the cost price and selling price is equal to Re. 1. This is incorrect because the selling price is 9 pens for a rupee, compared to the cost price 12 pens for a rupee.