Question

Nidhi purchased two sarees for ${\text{Rs}}\,2,150$ each. She sold one saree at a loss of $8\% $ and the other at a gain. If she had a gain of ${\text{Rs}} \,1,230$ on the whole transaction, find the selling price of the second saree.

Answer 1

Hint: Here, we are required to find the selling price of the second saree when we are given the cost price of both the sarees and the information about loss and gain. First of all, we will find the selling price of the first saree by using its cost price and the given loss percentage. Now, since, we are given the overall gain and the overall cost price of both the sarees, we will be able to find their combined selling price. Subtracting the selling price of the first saree from the total, we will get the required selling price of the second saree.

Formula Used:
1.${\text{Loss}} = {\text{CP}} - {\text{SP}}$
2.${\text{Profit}} = {\text{SP}} - {\text{CP}}$

Complete step-by-step answer:
The Cost Price (C.P.) of two sarees is ${\text{Rs}}\,2,150$ each.
Hence, the total Cost Price (C.P.) of two sarees $ = 2150 \times 2 = {\text{Rs}}\,4300$
Now, for the first saree, it is given that it is sold at a loss of $8\% $
Hence, this means that Nidhi faced a loss of $8\% $ on ${\text{Rs}}\,2,150$
$ \Rightarrow {\text{Loss}} = \dfrac{8}{{100}} \times 2150 = \dfrac{{17200}}{{100}} = 172$
Now, as we know, when the cost price is greater than the selling price, then, it’s a loss.
$ \Rightarrow {\text{Loss}} = {\text{CP}} - {\text{SP}}$
Substituting the above values, we get,
$ \Rightarrow 172 = 2150 - {\text{S}}{{\text{P}}_1}$
$ \Rightarrow {\text{S}}{{\text{P}}_1} = 2150 - 172 = 1978$
Therefore, the selling price (S.P.) of the first saree is ${\text{Rs}}\,1,978$
Now, according to the question, Nidhi had a gain of ${\text{Rs}}\,1,230$ on the whole transaction.
We know that,
${\text{Profit}} = {\text{SP}} - {\text{CP}}$
Hence, here, total selling price is $\left( {1,978 + {\text{S}}{{\text{P}}_2}} \right)$
Also, the total cost price$ = 2150 \times 2 = {\text{Rs}}\,4300$
Therefore,
$1230 = \left( {1978 + {\text{S}}{{\text{P}}_2}} \right) - 4300$
$ \Rightarrow 5530 = \left( {1978 + {\text{S}}{{\text{P}}_2}} \right)$
Subtracting 1978 from both sides,
$ \Rightarrow {\text{S}}{{\text{P}}_2} = 5530 - 1978 = {\text{Rs}}\,3552$
Therefore, the required selling price of the second saree is ${\text{Rs}}\,3552$.
Hence, this is the required answer.


Note: Cost Price is the original price of an article. It is the price at which an article is manufactured or bought. Whereas, Selling Price is the price at which an article is sold to a customer. Whenever our cost price is greater than our selling price, it means that we are selling a particular item at a lesser price than we had paid to buy it; hence, it’s a loss. Similarly, whenever our cost price is lesser than our selling price, it means that we are making extra money or profit. Thus these are the basic differences between cost price and selling price.