**Category : **7th Class

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.

**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.**

(a) 13%

(b) 16%

(c) 15%

(d) 18%

(e) None of these

**Answer:** (b)

**Explanation**

Let the S.P. of 1 orange = Rs 1

S. P of 42 oranges \[=Rs~1\times 42=42\]

Losses = S. P. to 8 oranges\[=Rs1\times 8=Rs8\]

C P. of 42 oranges \[~=\text{ }S.P.+loss=Rs42+Rs8=Rs50\]

**The price of pure mustard oil is Rs 100 per liter. A shopkeeper adulterates it with some other types of oil at Rs 50 per litre. He sells the mixture at the rate of Rs 96 per litre so that to gain 20 % on whole transaction. The ratio in which he mixed the two oil is:**

(a) 1:2

(b) 2:3

(c) 3:2

(d) 1:4

(e) None of these

**Answer:** (c)

**A man purchases one shirt and one T-shirt for Rs 6000. He sells the shirt at a profit of 20 % and T-shirt at a loss of 10 %, as a result he gains 2 % on whole transaction. The cost price of T-shirt is: **

(a) Rs 3600

(b) Rs 2400

(c) Rs 1200

(d) Rs 3400

(e) None of these

**Answer:** (a)

** The Price of two article is Rs 5500. If the price of the first article is increased by 11 % and other is increased by 20 % then the new price becomes Rs. 6330. What is the price of second article?**

(a) Rs 3000

(b) Rs 2500

(c) Rs 1500

(d) Rs 2400

(e) None of these

**Answer:** (b)

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