If the cost price of 12 pens is equal to the selling price of 8 pens, the gain percent is?

\[\text { Let the cost price of one pen be Rs . C, and the selling price be Rs } . S\]

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• Answer : (c)SP of 10 pens = CP of 12 pens = Rs. 100 (suppose)∴ SP of 1 pen =Rs.10010=Rs.10and CP of 1 pen =Rs.10012=Rs.253Gain = SP - CP = Rs. 10−253=Rs.53 (adsbygoogle = window.adsbygoogle || []).push({}); Gain % =Total gain×100CP=5×100×33×25=20%
• If the selling price of 10pens is equal to the cost price of 14pens, find the gain percent.
• Is the selling price of 10 pens is the same as the cost price of 12 pens then gain percent is?
• How do you find selling price when given cost and percentage?
• Is the cost price of 12 pens is equal to the selling price of 15 pencils then the loss percentage?

\[\text { Therefore,} 10S = 14C\]

\[C = \frac{10}{14}S\]

\[\text { However, the cost price is less than the selling price } . \]

\[S . P . = \left( \frac{100 + \text {profit %}}{100} \right)C . P\]

\[S = \left( \frac{100 +\text {  profit % }}{100} \right)C\]

\[\frac{S}{C} = \left( \frac{100 + \text { profit % }}{100} \right)\]

\[\frac{14}{10} = \left( \frac{100 +\text {  profit % }}{100} \right)\]

\[\frac{1400}{10} = 100 + \text { profit %} \]

\[140 - 100 = \text { profit % } \]

\[\text { Profit % }= 40\]

\[ =\text {  40 % } \]

\[\text { Therefore, the required profit percent is 40 % }. \]

Solution

Answer : (c)SP of 10 pens = CP of 12 pens = Rs. 100 (suppose)∴ SP of 1 pen =Rs.10010=Rs.10and CP of 1 pen =Rs.10012=Rs.253Gain = SP - CP = Rs. 10−253=Rs.53 (adsbygoogle = window.adsbygoogle || []).push({}); Gain % =Total gain×100CP=5×100×33×25=20%

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Last updated on Sep 26, 2022

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

Answer

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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.

Is the selling price of 10 pens is the same as the cost price of 12 pens then gain percent is?

Gain % =Total gain×100CP=5×100×33×25=20%

How do you find selling price when given cost and percentage?

Cost price = Selling price + loss ( when selling price and loss is given ) Cost price =100×Selling Price100+Profit%( when selling price and profit % is given ) Cost price =100×Selling Price100−loss%( when selling price and loss % is given )

Is the cost price of 12 pens is equal to the selling price of 15 pencils then the loss percentage?

Hence, the loss percent is 20%.

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