Profit and Loss - Easy and Fast ways to Calculate

Profit and Loss

What is Profit or Loss? In this post we will understand the meaning of all terms related with profit and loss. Later we will learn how to calculate profit and loss percentage, methods to find selling price and cost price of anything. We will learn how Discount works when we purchase something.

TERMINOLOGY

 1.  COST PRICE: Cost price of an article is price at which an article has been purchased. It is abbreviated as C.P.

 2.  SELLING PRICE: Selling price of an article is price at which an article has been sold. It is abbreviated as S.P.

 3.  PROFIT or GAIN: If the selling price of an article is more than the cost price, there is a gain or profit.

 4.  LOSS: If the cost price of an article is greater than the selling price, there is a loss.

 

 5.  MARKED PRICE: It is the price printed on the item. It is also known as list price or printed price. It is the general price of any item without any discount. It is abbreviated as M.P.

 6.  DISCOUNT: Rebate given on marked price is known as discount. It is the difference between the marked price and selling price of any item.

 METHODS 

To find Profit-Loss percentage

 1.  Profit or gain% = (Gain/C.P) x 100
 2.  Loss% = (Loss/C.P) x 100 

Example: A man bought an old type writer for Rs 1200 and spent Rs 200 on its repair. He sold it for Rs 1680. His profit percentage is?
Solution: Cost price = 1200 + 200 = Rs 1400

Selling Price = Rs 1680

   ⇒ Gain = 1680 - 1400 = Rs 280

   ⇒ Profit % = 280/1400 x 100 = 20%

To find Selling Price when (Profit or Loss)% is given

 1.  S.P. = [(100 + Gain%)/100] x C.P
 2.  S.P. = [(100 - Loss%)/100] x C.P 

Example: A man bought a Laptop for Rs 20000. He sold it at a loss of 20%. Find his selling price?
Solution: Cost price = 20000 and Loss % = 20%

   ⇒ S.P = [(100 - 20)/100] x 20000 = Rs 16000

If C.P of m articles is equal to S.P of n articles

Profit or loss percentage = [(m - n)/n] x 100
If m ≻ n then profit, if m ≺ n then loss.

Example: If the S.P of 12 articles is equal to the cost price of 18 articles, then determine profit or loss percentage?
Solution: Here m = 18 and n = 12
   ⇒ Gain% =[(18 - 12)/12] x 100 =50%

When two articles are sold at same S.P

 1.  If getting Gain of x% on one and loss of x% on second, then overall % loss = x2/100
 2.  If Gain is x% on first and loss is y% on second, then net gain% or loss% = 

Here x will be positive and y will be negative.

Example: Aman sold two T.V sets for Rs 5000 each gaining 20% on one and loosing 20% on the other. Find total gain or loss percent.
Solution: Overall loss % = 202/100 = 4% 

Dishonest Dealer using false Weight

A merchant uses faulty measure and sells his goods at gain/loss of x%. The overall gain or loss% (y) is given by:

NOTE: 1. If merchant sells his goods at cost price then x = 0.

2. If sells at profit then x will be positive and if sells at loss then x will be negative.

Example: A grocer sells wheat at a profit of 10% and uses a weight which is 20% less. Find his total percentage gain.
Solution: 20% less weight means for every 1000 gm he used 800 gm weight.
   ⇒ (100 + y)/(100 + 10) = (1000/800)
   ⇒ Y = 37.5% 

Successive Discount

If two successive discounts on any article are x% and y% respectively, then a single discount equivalent to the successive discounts will be: (x + y - xy/100)%

Example: Find the equivalent discount of two successive discounts of 10% and 20%.
Solution: Overall discount = 10 + 20 - 10 x 20/100 = 28% 

Rules of Fractions

• If there is a gain of x%, the calculating figures would be 100 and (100 + x).

• If there is a loss of y%, the calculating figures would be 100 and (100 – y).

 1.  If our required value is greater than the supplied value, we should multiply the supplied value with a fraction which is more than one. Our multiplying fractions will be [(100 + x)/100] or [100/(100 - y)].

 2.  If our required value is less than the supplied value, we should multiply the supplied value with a fraction which is less than one. Our multiplying fractions should be [100/(100 + x)] or [(100 - y)/100]. 

Example: A man bought a cycle for Rs 250. For how much should he sell it so as to gain 10%.
Solution: He wanted to sell at a gain, so selling price must be greater than cost price. So we need to multiply C.P with more-than-one value fraction.
   ⇒ 250 x 110/100 = Rs 275

When commodity is sold with changed price

A man sold a commodity at a profit/loss of x%, if he increased or decreased the price by 'R' rupees, then he will gain/loss y%.
In such cases:

Example: A man sold a book at a profit of 12%. Had he sold it for Rs 18 more, 18% would have been gained. Find the Cost Price.
Solution:  Method 1  Let C.P = Rs x and Profit = 12%
   ⇒ Selling Price = 112x/100

New Gain = 18%
   ⇒ New Selling Price = 118x/100

Difference in both Selling Price = Rs 18
   ⇒ 112x/100 - 118x/100 = 18
   ⇒ x = 18 x 100/6 = Rs 300

 Method 2  Formula Based: Difference in Percentage profit = 18 - 12 = 6%
Cost Price = 18 x 100/6 = Rs 300

These methods of profit loss calculation are not only useful for examination purpose but this chapter is useful in real life too. We can easily calculate equivalent discount using above formulas during shopping. These methods help us in calculating cost price of any article before purchasing it. Overall, no one can charge extra penny from us. Good Luck 👍