Introduction
In our day to day life we exchange the things with the money with others. During such transaction either we get profit or loss. In this chapter we will frequently use the term profit, loss, profit percent and loss percent.
Terms Related to Profit and Loss
Cost Price
It is the price of an article at which the shopkeeper purchases the goods from manufacturer or wholesaler. In short it can be written as C.P.
Selling Price
It is price of the article at which it is sold by the shopkeeper to the customer. In short it can be written as S.P.
Profit and Profit Percent
If the S.P. of an article is greater than the C.P. then profit will occur and it is the difference between S.P. and C.P.
i.e. Profit = S.P. \[-\]C.P. and profit percent is written as:
Loss and Loss Percent
If the selling price of an article is less than the cost price then the difference between the cost price and the selling price is called loss.
i.e. Loss = C.P. - S.P. The loss percent is the loss that would be made on a cost price of Rs. 100.
i.e.
Relation between Profit and Loss
- To find the profit and loss when C.P., Profit % or Loss % are given :
(a) \[Profit=\frac{Profit%\times C.P.}{100}\]
(b) \[Loss=\frac{Loss%\times C.P.}{100}\]
- To find S.P. when C.P. & profit % or loss % are given:
(a) \[S.P.=C.P\times \left( \frac{100+\Pr ofit%}{100} \right)\]
(b) \[S.P.=C.P\times \left( \frac{100-Loss%}{100} \right)\]
- To find C.P when S.P & profit % are given:
(a) \[C.P.=\frac{S.P\times 100}{100-\Pr ofit%}\]
- To find C.P when S.P and loss % are given:
(b) \[C.P.=\frac{S.P\times 100}{100-Loss%}\]
A mobile phone is sold for Rs 3,120 at the loss of 4 %. What will be the gain or loss percent, if it is sold for Rs 3,640?
(a) 10%
(b) 11%
(c) 12%
(d) 13%
(e) None of these
Answer: (c)
Explanation
Here, S.P = Rs 3120, loss % = 4 %
\[\therefore C.P.=\frac{S.P\times 100}{100-Loss%}=Rs.\frac{100\times 3120}{100-4}\] \[=Rs\frac{100\times 3120}{96}=Rs.3250\]
Now, new S.P = Rs 3,640
\[\therefore \] Gain = S.P - C.P = Rs 3,640 - Rs 3,250 = Rs 390
Hence, gain \[%=\frac{Gain}{C.P.}\times 100=\frac{390}{3250}\times 100=12%\]
By selling 42 oranges, a person losses a sum equal to the selling price of 8 oranges. Find the loss percent.
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