Question

. Manohar purchased two carpets for Rs.2000 each. He sold carpets, gaining 6 % on one
and losing 4 % on the other which he sold to the manager of a night shelter. Find his gain
or loss percent in the whole transaction

Answer 1

➤ Given :-

Cost price of two carpets :- ₹2000

Gain percent of first carpet :- 6%

Loss percent of second percent :- 4%

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➤ To Find :-

The profit or loss percentage of whole transaction...

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★ How to do :-

Here, we are given with the cost price of two carpets. Both the carpets are sold by which at first a gain of 6% is obtained and on the second carpet we are obtained with a loss of 4%. We are asked to find the profit or loss percentage obtained for both the carpets together. So, first we should find the selling price of both carpets separately. Then, we should add both cost price together and both selling price separately. Then, we can find the loss rupees and the loss percentage. So, let's solve!!

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➤ Solution :-

Selling price of first carpet :-

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

Substitute the given values.

${\tt \leadsto \dfrac{(100 + 6)}{100} \times 2000}$

Firstly add the numbers on numerators and cancel the fraction.

${\tt \leadsto \cancel \dfrac{106}{100} \times 2000 = \dfrac{53}{50} \times 2000}$

Multiply the remaining numbers.

${\tt \leadsto \dfrac{53 \times 2000}{50} = \dfrac{106000}{50}}$

Write the obtained fraction in lowest form by cancellation method.

${\tt \leadsto \cancel \dfrac{106000}{50} = 2120}$

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Selling price of second carpet :-

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

Substitute the given values.

${\tt \leadsto \dfrac{(100 - 4)}{100} \times 2000}$

Firstly subtract the numbers on numerators and cancel the fraction.

${\tt \leadsto \cancel \dfrac{96}{100} \times 2000 = \dfrac{23}{25} \times 2000}$

Multiply the remaining numbers.

${\tt \leadsto \dfrac{23 \times 2000}{25} = \dfrac{46000}{25}}$

Write the obtained fraction in lowest form by cancellation method.

${\tt \leadsto \cancel \dfrac{46000}{25} = 1840}$

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Now, let's find the total cost price and total selling price.

Total cost price :-

${\tt \leadsto 2000 + 2000}$

Add the values to get the total cost price.

${\tt \leadsto Rs.4000}$

Total selling price :-

${\tt \leadsto 2120 + 1840}$

Add the values to get the total selling price.

${\tt \leadsto Rs.3960}$

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Now, let's find the loss rupees by subtracting the cost price and selling price.

Loss rupees :-

${\sf \leadsto \underline{\boxed{\sf Cost \: price - Selling \: price}}}$

Substitute the given values.

${\tt \leadsto 4000 - 3960}$

Subtract the values to get teh loss rupees.

${\tt \leadsto Rs.40}$

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Now, let's find the loss percentage.

Loss percentage :-

${\sf \leadsto \underline{\boxed{\sf \dfrac{Loss}{CP} \times 100}}}$

Substitute the given values.

${\tt \leadsto \dfrac{40}{4000} \times 100}$

Write the fraction in lowest form by cancellation method.

${\tt \leadsto \cancel \dfrac{40}{4000} \times 100 = \dfrac{4}{400} \times 100}$

Multiply the remaining numbers.

${\tt \leadsto \dfrac{4 \times 100}{400} = \dfrac{400}{400}}$

Write the fraction in lowest form by cancellation method.

${\tt \leadsto \cancel \dfrac{400}{400} = 1 \bf\%}$

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${\red{\underline{\boxed{\bf So, \: the \: loss \: percentage \: of \: both \: carpets \: is \: 1 \bf\%.}}}}$

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$\dashrightarrow$ Some related formulas :-

$\begin{gathered} \small \boxed{\begin{array} {cc} \large \dag \: \sf More \: Formulas \\ \\ \sf \bigstar \: Profit = SP - CP \\ \\ \sf \bigstar \: Profit \: percent = \dfrac{Profit}{Cost \: price} \times 100 \\ \\ \sf \bigstar \: Cost \: price = \dfrac{100}{(100 + profit\%)} \times SP \\ \\ \sf \bigstar \: Cost \: price = \dfrac{100}{(100 - loss\%)} \times 100 \end{array}} \end{gathered}$