Question

a shopkeeper sells 2 air conditioners for ₹2,500 each, gaining 10% on one and losing 20% , on other find find his overall gain or loss percentage ​

Answer 1

Question :-

A shopkeeper sells two air conditioners for ₹2500 such that he gains 10% on one and loses 20% on the other. Find his overall gain or loss percentage.

Solution :-

Case 1 , First AC

Cost price for air conditioner =Rs 2500

Here, Profit is 10%

Therefore, Selling price = 10%×2500 + 2500

Selling price = 2750 rupees.

Case 2, AC 2

Cost price = 2500

Loss = 20%

Therefore, Selling price = 2500 - 20% × 2500

Selling price = 2000 rupees.

Total profit or loss : clearly, He has loss

Hence , Loss = total loss / total Cost price × 100

Tota Loss = 5000 - 4750 / 5000 × 100

→ 250/5000 × 100

→ 250 / 50

→ 5 %

Therefore,He got loss Total loss is 5% .

Be brainly♡~

Answer 2

➤ Given :-

Selling price of each air conditioner :- ₹2500

Profit percentage of first one :- 10%

Loss percentage of second one :- 20%

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➤ To Find :-

Overall gain or loss percentage of air conditioners

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➤ Formula required :-

${\large \tt \dashrightarrow \orange{\boxed{\tt \gray{\dfrac{Profit \: (or) \: Loss}{Total \: CP} \times 100}}}}$

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★ How to do :-

Here, we are given that two air conditioners are sold for ₹2500 each. On one there is a profit of 10% and on other there is a loss of 20%. We should find the total loss or profit percentage. So, first we should find the cost price of both the machines and we should find the loss or profit by subtracting the sum of cost price and selling price.

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➤ Solution :-

Cost price of first machine :-

${\tt \leadsto \dfrac{100}{(100 + 10)} \times 2500}$

${\tt \leadsto \dfrac{100}{110} \times 2500 = \dfrac{10 \times 2500}{11}}$

${\tt \leadsto \dfrac{25000}{11} = \boxed{\tt 2272.72}}$

Cost price of second machine :-

${\tt \leadsto \dfrac{100}{(100 - 20)} \times 2500}$

${\tt \leadsto \cancel \dfrac{100}{80} \times 2500 = \dfrac{5}{4} \times 2500}$

${\tt \leadsto \dfrac{5 \times 2500}{4} = \dfrac{12500}{4}}$

${\tt \leadsto \cancel \dfrac{12500}{4} = \boxed{\tt 3125}}$

Total cost price :-

${\tt \leadsto 2272.72 + 3125}$

${\tt \leadsto 5397.72}$

Total selling price :-

${\tt \leadsto 2500 + 2500}$

${\tt \leadsto 5000}$

Total loss :-

${\tt \leadsto 5397.72 - 5000}$

${\tt \leadsto 397. 72}$

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Now,

Loss percentage :-

${\tt \leadsto \dfrac{397.72}{5397.72} \times 100}$

${\tt \leadsto \dfrac{397.72 \times 100}{5397.72}}$

${\tt \leadsto \cancel \dfrac{39772}{5397.72} = \boxed{\tt 7.36 \bf\%}}$

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$\Huge\therefore$ The overall loss percentage obtained to the shopkeeper is 7.36%.