Question

on selling an item for rs 1000 ram suffers a loss of 5% what should be the selling price of item so that he earns 8% profit​

Answer 1

➤ Given :-

Selling price of an item :- ₹1000

Loss percentage :- 5%

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➤ To Find :-

The selling price if it's sold at 8% of profit...

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★ How to do :-

Here, we are given with the selling price of an item and the loss percentage obtained to that item. We are asked to find the new selling price of the same item if it's sold at a profit of 8%. Ww use two formulas in this problem. One is to find the cost price and the other is to find selling price. First, we'll find the cost price of the item by using the selling price and the loss percentage of first statement. Then, we should find the selling price by using the cost price and the new profit percentage. So, let's solve!!

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➤ Solution :-

Cost price of the item :-

${\sf \leadsto \underline{\boxed{\sf \dfrac{100}{(100 - Loss \bf\%)} \times SP}}}$

Substitute the given values.

${\sf \leadsto \dfrac{100}{(100 - 5)} \times 1000}$

Subtract the values in denominator and cancel the fraction.

${\sf \leadsto \cancel \dfrac{100}{95} \times 1000 = \dfrac{20}{19} \times 1000}$

Multiply the remaining numbers.

${\sf \leadsto \dfrac{20 \times 1000}{19} = \dfrac{20000}{19}}$

Write the fraction in lowest form by cancellation method.

${\sf \leadsto \cancel \dfrac{20000}{19} = 1052.63}$

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New selling price of the item :-

${\sf \leadsto \underline{\boxed{\sf \dfrac{(100 + Profit \bf\%)}{100} \times CP}}}$

Substitute the given values.

${\sf \leadsto \dfrac{(100 + 8)}{100} \times 1052.63}$

Add the numbers in numerator and cancel the fraction.

${\sf \leadsto \cancel \dfrac{108}{100} \times 1052.63 = \dfrac{27}{25} \times 1052.63}$

Multiply the remaining numbers.

${\sf \leadsto \dfrac{27 \times 1052.63}{25} = \dfrac{28421.01}{25}}$

Write the fraction in lowest form by cancellation method to get the answer.

${\sf \leadsto \dfrac{28421.01}{25} = \pink{\underline{\boxed{\sf Rs \: \: 1136.84 \approx}}}}$

$\Huge\therefore$ The new selling price of the item is 1136.84.

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$\dashrightarrow$ Some related formulas :-

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