Question

A shopkeeper makes a profit of 15% by selling a book for Rs.230. Find his cost price and his actual profit. [Rs.200,Rs.30]​

Answer 1

Given:

✰ A shopkeeper makes a profit of 15% by selling a book for Rs. 230.

To find:

✠ His cost price and his actual profit.

Solution:

• The price for which a commodity or an article is purchased is called the cost price.

We know that:

When selling price and profit is given, then

➛ Cost price = (SP × 100)/(100 + Profit%)

➛ Cost price = (230 × 100)/(100 + 15)

➛ Cost price = 23000/115

➛ Cost price = 200

∴ Cost price of a book = Rs 200

• If the selling price is more than the cost price then there is a profit.

We also know that:

➛ Profit = Selling price - Cost price

➛ Profit = 230 - 200

➛ Profit = 30

∴ Profit on selling a book = Rs 30

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Answer 2

Given :

• Selling Price (S.P) = Rs 230
• Profit % = 15%

To Find :

• Cost Price of Book
• Actual Profit

Formula :

$\blue \bigstar \: {\underline{\boxed {\mathcal{\pmb{ \red{\quad C.P \: = \: \dfrac{100}{ \: 100 \: + \: Gain\%} \: \times \: S.P}\quad}}}}}$

Solution :

$\qquad \quad {:} \longrightarrow \sf{\sf{C.P \: = \: \dfrac{100}{ \: 100 \: + \: Gain\%} \: \times \: S.P }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{C.P \: = \: \dfrac{100}{ \: 100 \: + \: 15} \: \times \: 230 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{C.P \: = \: \dfrac{100}{ \: 115} \: \times \: 230 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{C.P \: = \: \dfrac{100}{ \: \cancel{115}} \: \times \: \cancel{230}} }$

$\qquad \quad {:} \longrightarrow \sf{\sf{C.P \: = \: 100 \: \times \: 2 }}$

$\qquad \quad {:} \longrightarrow \sf \boxed{\bf{C.P \: = \: Rs \: 200}}$

Thus Cost Price of Book is Rs 200

Now,

✰ Actual Profit :

⟹ Profit = Selling Price - Cost Price

⟹ Profit = 230 - 200

⟹ Profit = Rs 30

Thus Actual Profit is Rs 30

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

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