Question

If the selling price of 10pens is equal to the cost price of 14pens, find the gain percent.

Answer 1

Hint: We will assume the cost price (CP) of 1 pen to be let say ‘x’. So, we can say that selling price $ \text{SP of 10 pens=14x} $ . Then using the unitary method, we will find the selling price of 1 pen by taking that SP of 10 pens is equal to 14x then SP of 1 pen is equal to how much. Thus, we will get SP of 1 pen. Then we will find the gain amount using the formula $ gain=SP-CP $ . Then we will find gain% using the formula $ gain\%=\dfrac{gain}{CP}\times 100 $ . Thus, we will get an answer.

Complete step-by-step answer:
Here, we are given that the cost price (CP) of 14pens is equal to the selling price (SP) of 10pens. So, we can write it as
 $ \text{CP of 14 pens=SP of 10 pens} $
Now, if we assume that CP of 1 pen is let say ‘x’. Then CP of 14 pens will be equal to 14x.
So, we can write it as
 $ \text{SP of 10 pens=14x} $
So, from this we will find SP of 1 pen using a unitary method. We will get as
 $ \begin{align}
  & \text{SP of 10 pens=14x} \\
 & \text{SP of 1 pens=?} \\
\end{align} $
On solving we get as
 $ \text{SP of 1 pen=}\dfrac{14x}{10}=1.4x $
Now, we have to find gain percent i.e. profit percent. So, gain will be found by using the formula
 $ gain=SP-CP $
On substituting values of 1 pen we will get as,
 $ gain=1.4x-x=0.4x $
Now, to find gain% we will use the formula given as $ gain\%=\dfrac{gain}{CP}\times 100 $ .
On substituting the values, we get as
 $ gain\%=\dfrac{0.4x}{x}\times 100=40\% $
Thus, gain percent is 40%.

Note: Another method to solve is by assuming cost price to be any number let say 10. So, the cost price of 1 pen is Rs. 10 therefore, for 14 pens CP will be Rs. 140. So, selling price for 1 pen will be
 $ \begin{align}
  & \text{SP of 10 pens=140} \\
 & \text{SP of 1 pen=?} \\
\end{align} $ . On solving we will get Rs. 14. So, the gain amount will be $ gain=14-10=4 $ . Thus, gain percentage will be $ gain\%=\dfrac{4}{10}\times 100=40\% $ . Thus, we will get the same answer.