Question

A shopkeeper sold an article for Rs. 9408 at a profit of 12%. Had the article been sold at Rs. 252 more, what percent would the shopkeeper have gained ?​

Answer 1

➤ Given :-

Selling price of article :- ₹9408

Profit percentage :- 12%

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➤ To Find :-

Profit percentage if it's sold at still ₹252 more.

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➤ Formula required :-

${\tt \large \dashrightarrow \orange{\boxed{\tt \gray{\dfrac{Profit}{Cost \: price} \times 100}}}}$

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★ How to do :-

Here, we are given with the selling price and the profit percentage of an article. The other statement says that what percentage will the shopkeeper gain if he sold the article at ₹252 more than earlier. To find that, we should use the formula given above. But first we should find the cost price which is necessary for finding the profit percentage. So, first we will find the cost price of that same article and then we can subtract the selling price and the cost price to find the profit. Then, we can use the given formula. So, let's solve!!

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➤ Solution :-

Cost price of the article :-

${\tt \leadsto \dfrac{100}{(100 + 12)} \times 9408}$

${\tt \leadsto \dfrac{100}{\cancel{112}} \times \cancel{9408} = \dfrac{100}{1} \times 84}$

${\tt \leadsto \dfrac{100 \times 84}{1} = \dfrac{8400}{1}}$

${\tt \leadsto \cancel \dfrac{8400}{1} = Rs \: \: 8400}$

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Now,

Selling price if sold at more :-

${\tt \leadsto 9408 + 252}$

${\tt \leadsto Rs \: \: 9660}$

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Profit rupees :-

${\tt \leadsto 9660 - 8400}$

${\tt \leadsto Rs \: \: 1260}$

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Profit percentage :-

${\tt \leadsto \dfrac{1260}{8400} \times 100}$

${\tt \leadsto \dfrac{1260}{\cancel{8400}} \times \cancel{100} = \dfrac{1260}{84}}$

${\tt \leadsto \cancel \dfrac{1260}{84} = \boxed{\tt 15 \bf\%}}$

$\Huge\therefore$ The profit percentage of the second statement is 15%.

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$\dashrightarrow$ Some related formulas :-

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