Question

Q20) Calculate the profit percent if shopkeeper sold a notebook at Rs30/- and actual price
of notebook is Rs20/-.
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Answer 1

$\underline{ \underline{ \Large \pmb{\sf { \purple{Answer:}} }} }$

• Profit % is 50 %.

$\underline{ \underline{ \Large \pmb{\sf { \purple{Given:}} }} }$

• Selling price of a notebook = Rs. 30

• Actual price (cost price) of a notebook = Rs. 20

$\underline{ \underline{ \Large \pmb{\sf { \purple{To \: calculate:}} }} }$

• Profit %.

$\underline{ \underline{ \Large \pmb{\sf { \purple{Required \: formulae:}} }} }$

✰ $\textbf {\textsf \purple{ Profit = S.P - C.P} }$

✰ $\sf \purple{ Profit \: \%= \Bigg \lgroup \dfrac{Profit}{C.P} \times 100 \Bigg \rgroup \: \% }$

$\underline{ \underline{ \Large \pmb{\sf { \purple{Calculation:}} }} }$

Here, firstly we'll find the total profit gained by the shopkeeper. As we know that, whenever the S.P is greater than the C.P , there is profit. In order to calculate profit, we subtract C.P from S.P. So,

✰ ${\underline {\boxed {\Large {\rm \purple { Profit = S.P - C.P } }}}}$

$\longmapsto \sf {Profit = Rs. \: ( 30 - 20 ) }$

• Performing substraction.

$\longmapsto \sf {Profit = Rs. \: 10 }$

Henceforth,

• He got the profit of Rs. 10.

Now, let's calculate the ptofit %. Whenever there is profit & C.P given, profit % is given by this formula :

✰ $\sf \purple{ Profit \: \%= \Bigg \lgroup \dfrac{Profit}{C.P} \times 100 \Bigg \rgroup \: \% }$

Substituting values:-

$\longmapsto \sf { Profit \: \%= \Bigg \lgroup \dfrac{10}{20} \times 100 \Bigg \rgroup \: \% }$

Cancel the denominator and numerator in R.H S by 10.

$\longmapsto \sf { Profit \: \%= \Bigg \lgroup \dfrac{1}{2} \times 100 \Bigg \rgroup \: \%}$

$\longmapsto \sf { Profit \: \%= \Bigg \lgroup \dfrac{100}{2} \Bigg \rgroup \: \%}$

$\longmapsto \boxed{ \sf\purple { Profit \: \%= 50 \: \%}}$

Therefore,

• Profit % is 50 %.

Answer 2

Given :-

• S.P = Rs 30
• C.P = Rs 20

To Find :-

• Gain or loss %

Solution :-

• Here, as we are given that S.P and C.P , so to find gain or loss %, we have to find whether here is gain or loss.
• In order to calculate gain or loss, we'll compare C.P and S.P. If S.P is greater than there is gain, if C.P is greater than there is loss.
• And then we'll find the gain or loss % by the given formula:

If there is gain :

• Gain% = Gain / C.P × 100

If there is loss :

• Loss% = Loss / C.P × 100

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S.P = Rs 30

C.P = Rs 20

•›» Since, S.P is greater than C.P. Thus, there is gain. We know that :

➞ Gain = Selling Price - Cost Price

➞ Gain = 30 - 20

➞ Gain = Rs 10

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Clearly, there is gain of Rs 10 Now, we have to find the rate of gain i.e gain% . So, we know that :

⟾ Gain% = Gain / C.P × 100

⟾ Gain% = 10 / 20 × 100

⟾ Gain% = 10 / 2 × 10

⟾ Gain% = 10 × 5

⟾ Gain% = 50%

Thus Gain% is 50%

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Extra Information:

$\small\boxed{ \begin{array}{cc}\large\sf\dag \: {\underline{More \: Formulae}} \\ \\ \bigstar \: \sf{Gain = S.P – C.P} \\ \\ \bigstar \:\sf{Loss = C.P – S.P} \\ \\ \bigstar \: \sf{Gain \: \% = \Bigg( \dfrac{Gain}{C.P} \times 100 \Bigg)\%} \\ \\ \bigstar \: \sf{loss \: \% = \Bigg( \dfrac{loss}{C.P} \times 100 \Bigg)\%} \\ \\ \bigstar \: \sf{S.P = \dfrac{100+Gain\%}{100} \times C.P} \\ \\ \bigstar \: \sf{ C.P =\dfrac{100}{100+Gain\%} \times S.P} \\ \\\bigstar \: \sf{ S.P = \dfrac{100-loss\%}{100} \times C.P} \\ \\ \bigstar \: \sf{ C.P =\dfrac{100}{100-loss\%} \times S.P}\end{array} }$

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