Top

# Profit & Loss

1.

A watch dealer incurs an expense of$$Rs. 150$$ for producing every watch. He also incurs an additional expenditure of $$Rs. 30,000,$$ which is independent of the number of watches produced. If he is able to sell watch during the season, he sells it for $$Rs. 250.$$ If he fails to do so, he has to sell each watch for $$Rs. 100.$$ If he produces $$1500$$ watches, what is the number of watches that he must sell during the season in order to breakeven, given that he is able to sell all the watches produced?

Total cost to produced $$1500$$ watches $$= (1500 \times 150 + 30000) = Rs. 2,55,000$$

Let he sells $$x$$ watches during the season, therefore

Number of watches sold after the season $$= (1500 - x)$$

$$\Rightarrow 250 \times x + (1500 - x) \times 100 = 150x + 150000$$

Now, break - even is achieved if production cost is equal to the selling price.

$$150x + 150000 = 2,55,000$$

$$x = 700$$

Enter details here

2.

A shopkeeper sells one transistor for $$Rs. 840$$ at a gain of $$20$$ % and another for $$Rs. 960$$ at a loss of $$4$$ %. His total gain or loss percent is:

Cost Price of $$1st$$ transistor $$= Rs. (\frac{100}{120} \times 840) = Rs. 700.$$

Cost Price of $$2nd$$ transistor $$= Rs. (\frac{100}{96} \times 960) = Rs. 1000$$

So, total Cost Price $$= Rs. (700 + 1000) = Rs. 1700.$$

Total Selling Price $$= Rs. (840 +960) = Rs. 1800.$$

$$\therefore$$ Gain % $$= (\frac{100}{1700} \times 100)$$ % $$= 5\frac{15}{17}$$ %

Enter details here

3.

The Cost Price of item B is $$Rs. 200/-$$ more than the cost price of item $$A$$. Item $$A$$was sold at a profit of $$20$$ % and item $$B$$ was sold at a loss of $$30$$ %. If the respective ratio of Selling Prices of items $$A$$ and $$B$$ is $$6 : 7,$$ what is the cost price of item $$B$$ ?

Let the Cost Price of item $$A$$ be $$x$$

Cost Price of item $$B$$ is $$x + 200.$$

$$\frac{(\frac{120}{100} \times x)}{(x + 200) \times \frac{70}{100}} = \frac{6}{7}$$

$$\frac{120x}{(x + 200) \times 70} = \frac{6}{7}$$

$$\frac{20x}{10(x + 200)} = 1$$

$$x = Rs 200.$$

Cost Price of item $$B$$ is $$200 + 200 = Rs 400.$$

Enter details here

4.

Susanta buys an old scooter for $$Rs. 4700$$ and spends $$Rs. 800$$ on its repairs. If he sells the scooter for $$Rs. 5800$$, his gain percent is:

Cost Price (C.P.) $$= Rs. (4700 + 800) = Rs. 5500.$$

Selling Price (S.P.) $$= Rs. 5800.$$

Gain = (S.P.) - (C.P.) $$= Rs. (5800 - 5500) = Rs. 300.$$

Gain % $$= (\frac{300}{5500} \times 100)$$$$= 5\frac{5}{11}$$%

Enter details here

5.

A person $$X$$ sold an Item to $$Y$$ at $$40$$% loss, then $$Y$$ sold it to third person $$Z$$ at $$40$$% profit and finally $$Z$$ sold it back to $$X$$ at $$40$$% profit. In this whole process what is the percentage loss or profit of X?

Let the Cost Price $$= Rs. 100.$$ for $$X.$$

$$Y's$$ Cost Price $$= Rs. 60.$$

$$Z's$$ Cost Price $$= Rs. 84.$$

Finally, $$X's$$ Cost Price $$RS. 117.6.$$

$$\therefore X's$$ loss $$117.6 - 60 = Rs. 57.6$$

$$\therefore X's$$ loss percentage $$= 57.6$$%

Enter details here

6.

The percentage profit earned by selling an article for $$Rs. 1920$$ is equal to the percentage loss incurred by selling the same article for $$Rs. 1280.$$ At what price shoule the article be sold to make $$25$$ % profit?

Let Cost Price be $$Rs. x.$$

Then, $$\frac{1920 - x}{x} \times 100 = \frac{x - 1280}{x} \times 100$$

$$\Rightarrow 1920 - x = x - 1280$$

$$\Rightarrow 2x = 3200$$

$$\Rightarrow x = 1600$$

$$\therefore$$ Required Selling Price $$= 125$$ % of $$Rs. 1600 = Rs. (\frac{125}{100} \times 1600) = 2000.$$

Enter details here

7.

On selling $$17 balls$$ at $$Rs. 720,$$ there is a loss equal to the cost price of $$5 balls.$$ The cost price of a ball is:

(Cost price of $$17 balls$$) - (Selling Price of $$17 balls$$$$=$$ (Cost Price of $$5balls$$)

$$\Rightarrow$$ Cost Price of $$12 balls$$ = Selling Price of $$17 balls$$ = $$Rs. 720.$$

$$\Rightarrow$$ Cost Price of $$1 balls$$  = $$Rs. (\frac{720}{12}) = Rs. 60.$$

Enter details here

8.

The percentage profit earned by selling an article for $$Rs. 2120$$ is equal to the percentage loss incurred by selling the same article for $$Rs. 1520.$$ At what price should the article be sold to make $$25$$% profit?

The Cost Price be

$$2120 + 1500 = 3640$$

$$\frac{3640}{2} = 1820.$$

Selling Price $$= \frac{1820 \times 125}{100} = \frac{1820 \times 5}{4}$$

$$= Rs 2275$$

Enter details here

9.

A trader mixes $$26 kg$$ of rice at $$Rs. 20$$ per kg with $$30 kg$$ of rice of other variety at $$Rs. 36$$ per kg and sells the mixture at $$Rs. 30$$ per kg. His profit percent is:

Cost Price of $$56 kg$$ rice $$= Rs. (26 \times 20 + 30 \times 36) = Rs. (520 + 1080) = Rs. 1600.$$

Selling Price of $$56kg$$ rice $$= Rs. (56 \times 30) = Rs. 1680.$$

$$\therefore$$ Gain $$= (\frac{80}{1600} \times 100)$$ % $$= 5$$ %.

Enter details here

10.

A man buys a cycle for $$Rs. 1400$$ and sells it at a loss of $$15$$ %. What is the selling price of the cycle?

Selling Price $$= 82$$ % of $$Rs. 1400 = Rs. (\frac{85}{100} \times 1400) = Rs. 1190$$