Important Notes : Profit and Loss

PROFIT AND LOSS

CONCEPT OF C.P. AND S.P.

Cost Price: It is the price at which any article or unit or item is bought. It is known as CP.

Selling Price: It is the price at which any article or unit or item is sold. It is known as SP.

Profit: If Selling Price is greater than Cost Price then seller makes profit.

Profit = SP – CP

Loss: If Cost Price is greater than Selling Price then seller incurs loss.

Loss = CP – SP 

C.P. is always 100% in case of profit % 20 and % 20 loss.

In the case of profit & loss, the relation is generated between C.P. & S.P. 

Profit % =

Loss % =

SP =

CP =

Ex: % gain fetches a profit of Rs.300 on selling an article, so find the CP of the article?

Sol:

75/4 % = 300

1% =

100% = 16 x 100 

= Rs. 1600

Ex: By selling an article for Rs. 450 a man losses 25% .At what price will he sell it in order to gains 50%?

Sol:

75% = 450

1% =

150% =

= Rs. 900

Ex: The profit earn by sold an article for Rs 1920 is equal to the loss after selling the same article for Rs.1280 . Then what price it should to be sold to earn 25 percentage profit?

Sol: Profit = Loss 

C.P. = = Rs1600

S.P. = 1600 of 125%

= Rs.2000

Ex: Selling price of 20 articles is equal to the cost price of 25 articles. Find the profit or loss percentage?

Sol: S.P. of 20 articles = C.P. of 25 articles 

C.P. : S.P. = 20 : 25

= 4 : 5

Profit % =

= 25%

Ex: Ragini purchases oranges at Rs. 10 per dozen and sells them at Rs. 12 for every 10 oranges. What is the profit percentage?

Sol: CP = , SP =

Profit (%) = × 100

= 44%

Ex : The total price of the watches is Rs. 840. One watch is sold on the profit of 16% that of other on 12% loss. There is no profit%20and%20no loss on the whole transaction find the cost prices of both the watches.

Ex: A seller mark the price 50% above the cost price and give 10% discount on an item. While selling he cheats customer by giving 20% less in weight .Find his overall profit percent (approximate)?

Sol

CP = 100 , MRP = 150 Then SP = 135 

For cheating he sale 20% less in weight , new CP = 80 

Profit %

Ex: Rahul sells an IPhone to Kush at a loss of 20% who sells it to Saurabh at a profit of 25%. After finding some defect Saurabh return it back to Kush but could only recover Rs. 4.50 for every Rs. 5 he had paid. Find the amount of Saurabhs' loss if Rahul has paid Rs. 87500 for the IPhone?

Sol

Ex: A shopkeeper bought 84 identical shirts priced at Rs. 240 each. He spent a total of Rs. 3200 on transportation and packaging. He put the label of marked price of Rs. 420 on each shirt. He offered a discount of 15% on each shirt at the marked price. What is the total profit of the shopkeeper in the whole transaction?

Sol

Ex: Nutan bought 30 dozens of oranges for her juice stall in school fair. She paid Rs. 8 per dozen of oranges. She also had to pay Rs. 500 as the stall fee to the school authorities. She calculated that each glass of juice would need 3 oranges. How much should she charge per glass of juice so as to make 20% profit?

Sol

Ex. A man purchased 150 pens at the rate of Rs. 12 per pen. He sold 50 pens at a gain of 10%. The percentage gain at which he must sell the remaining pens so as to gain 15% of the whole outlay is :

Sol

Ex . A fruit seller buys some oranges at the rate of 4 for Rs. 10 and an equal number more at 5 for Rs. 10. He sells the whole lot at 9 for Rs. 20. What is his loss or gain percent?

Sol

Ex. A man bought a number of oranges at 3 for a rupees and an equal number at 2 for a rupees. At what price per dozen, should he sell them to make a profit of 20% ?

Sol

Ex.A horse and a cow were sold for Rs. 540, making a profit of 25% on the horse and 20% profit on the cow. If profit on horse is 20% and on cow is 25%, total selling price is Rs. 538. Find the cost price of the horse.

Sol

Ex. An item was bought at Rs. X and sold at Rs.Y, thereby earning a profit of 15%. Had the value of X been 15% less and the value of Y been Rs.52 less, a profit of 20% would have been earned, What was the value of X ?

Sol