Question

The cost price of 11 pens is equal to the selling price of 10 pens. Find the loss or the gain percent.

Answer 1

Hint: At first we will assume the cost price of a pen to be x, using this we’ll find the selling price of 1 pen as given that the cost price of 11 pens is equal to the selling price of 10 pens, and then will find the profit or the loss on 11 pens.
Now we get all the required values to find the gain or loss percent, so we’ll find the gain or loss percent as asked.

Complete step-by-step answer:
Given data: The cost price of 11 pens is equal to the selling price of 10 pens
Let the cost price of a 1 pen be x
Therefore the total cost price of the 11 pens $ = 11x$
It is given that the cost price of 11 pens is equal to the selling price of 10 pens
The total cost price of the 11 pens $ = 10$ (selling price of 1 pen)
 $ \Rightarrow 11x = 10$ (selling price of 1 pen)
\[ \Rightarrow \]The selling price of 1 pen $ = \dfrac{{11}}{{10}}x$
\[ \Rightarrow \]The total selling price of 11 pens is 11 times the selling price of one pen.
 \[ = 11 \times \dfrac{{11}}{{10}}x\]
 $ = \dfrac{{121}}{{10}}x$
 $ = 12.1x$
Now it is clear that there is a profit as $12.1x > 11x$
i.e. $S.P. > C.P.$
Now, we know that $profit = S.P. - C.P.$
Therefore, profit on 11 pens
 $ = \dfrac{{121}}{{10}}x - 11x$
Taking 11x common from both the terms we get,
 $ = 11x\left( {\dfrac{{11}}{{10}} - 1} \right)$
Simplifying the bracket terms by taking LCM we get,
 $ = 11x\left( {\dfrac{{11 - 10}}{{10}}} \right)$
On simplification we get,
 $ = \dfrac{{11}}{{10}}x$
We know that the gain percent formula is given by $\dfrac{{profit}}{{C.P.}} \times 100$
Therefore the gain percent on 11 pens $ = \dfrac{{\dfrac{{11}}{{10}}x}}{{11x}} \times 100$
Dividing numerator and denominator by 11x, we get,
 $ = \dfrac{{100}}{{10}}$
On simplification we get,
 $ = 10\% $
The required gain percent is $10\% $

Note: Most of the students while writing the formula for gain percent, they take the selling price in the denominator which is not correct. It should be the cost price that is the main reference, so while writing formulas like this we should remember all the terms to apply them correctly.