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# Juhi sells a washing machine for $Rs.13500$. She loses $20%$ in the bargain . What was the price at which she bought it?

Last updated date: 20th Mar 2023
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Hint: Here we have to find the Cost price. Since there is a loss use Loss $=C.P-S.P$. Also, the Loss percentage is given to be $20%$. Use Loss percentage $=\dfrac{Loss}{C.P}\times 100%$. Find Loss and substitute Loss in Loss $=C.P-S.P$. You will get the answer.

In retail systems, the cost price represents the specific value that represents the unit price purchased. The money paid by the shopkeeper to the manufacturer or wholesaler to buy the goods is called the cost price ($C.P$).
Cost price is also known as $C.P$ cost price is the original price of an item. The cost is the total outlay required to produce a product or carry out a service. Cost price is used in establishing profitability in the following ways:
Selling price (excluding tax) fewer costs results in profit in money terms.
Profit/selling price (excluding tax) when expressed as a percentage produced (gross profit) or GP%.
Expense / net sales yield a percentage that when used as the target margin will produce a gross profit.
The term ‘selling price’($S.P$) is defined as the price at which a good or service is sold by the seller to the buyer. It is generally expressed as currency units. In other words, it is market value or agreed on exchange value that enables a buyer to purchase goods or services. It is also known as a list price, quoted price, market price, or sale price.

The price of the product or service is set by a contract of sale in which the price is agreed upon by the parties involved in the contract. The selling price of a good or service depends upon the following three factors:

• The price which a buyer is willing to pay.

• The price which a seller is willing to receive.

• The price which is competitive in the market.
Now for Profit $=S.P-C.P$
And for Loss $=C.P-S.P$
Here in question, we can see that Juhi has a Loss of $20%$.
So here in question $S.P=Rs.13500$.
So Loss percentage $=20%$.
We know that Loss $=C.P-S.P=C.P-13500$
So $C.P=13500+Loss$………….. (1)
So we know the Loss percentage $=\dfrac{Loss}{C.P}\times 100%$.
$20%=\dfrac{Loss}{C.P}\times 100%$
$\dfrac{20}{100}=\dfrac{Loss}{Loss+13500}$ ………… (from(1))

$\dfrac{1}{5}=\dfrac{Loss}{Loss+13500}$
Now cross multiplying,
$Loss+13500=5Loss$
Simplifying we get,
$13500=4Loss$
$Loss=\dfrac{13500}{4}=3375$
$Loss=Rs.3375$
Substituting $Loss=Rs.3375$in (1).
$C.P=13500+3375$
$C.P=Rs.16875$
So the price at which she bought the washing machine is $Rs.16875$.

Note: Carefully read the question. You should be familiar with Cost price and Selling price. You should know the formula of Profit and Loss which is Profit$=S.P-C.P$and Loss$=C.P-S.P$. Do not miss any term while cross multiplying.