The document Basic Concept- Profit, Loss, and Discount Quant Notes | EduRev is a part of the CAT Course Quantitative Aptitude (Quant).

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**Introduction**

- The profit and Loss formula is used in mathematics to determine the price of a commodity in the market and understand how profitable a business is.
- Every product has a cost price and a selling price.
- Based on the values of these prices, we can calculate the profit gained or the loss incurred for a particular product.

**Profit, Loss, and Discount**

**1. Cost Price (CP)**

The amount paid for a product or commodity to purchase it is called a cost price. Also, denoted as CP.**This cost price is further classified into two different categories:**

**Fixed Cost:**The fixed cost is constant, it doesn’t vary under any circumstances**Variable Cost:**It could vary depending as per the number of units

**2. Selling price (SP)**

- The amount for which the product is sold is called Selling Price. It is usually denoted as SP. Also, sometimes called a sale price.

**3. Profit and Loss**

**Profit: **When an article is sold for more than the cost of the article, then we say there is a Profit or Gain.

- Profit or Gain = S.P - C.P

**Loss: **When an article is sold for less than the cost of the article, then we say there is a Loss.

- Loss = C.P - S.P

**The formula for the profit and loss percentage is:**

**Profit percentage**= (Profit / Cost Price) x 100**Loss percentage**= (Loss / Cost price) x 100

**4.** **Marked Price Formula (MP)**

This is basically labeled by shopkeepers to offer a discount to the customers in such a way that,

**Discount = Marked Price – Selling Price****Discount Percentage**= (Discount/Marked price) x 100

**Profit and Loss Common Formulas**

You have learned until now how to calculate profit as well as loss and also the percentage of them. Here is a list of the most commonly used formulas for all related questions:

**Profit and Loss Tricks**

Now let us look at some additional tricks or formulas that can be used to solve maths problems based on gain and loss:

- SP = {(100 + P%)/100} x CP
- SP = {(100 – L%)/100} x CP
- CP = {100/(100 + P%)} x SP
- CP = {100/(100 – L%)} x SP
- SP = MP - Discount
- For false weight, profit percentage will be P% = (True weight – false weight/ false weight) x 100.
- When there are two successful profits say m% and n%, then the
**net percentage profit**equals to (m+n+mn)/100 - When the profit is m% and loss is n%, then the net % profit or loss will be: (m-n-mn)/100
- If a product is sold at m% profit and then again sold at n% profit then the
**actual cost price of the product**will be: CP = [100 x 100 x P/(100+m)(100+n)].

In case of loss, CP = [100 x 100 x P/(100-m)(100-n)] - If P% and L% are equal then, P = L and %loss = P2/100

**Some Solved Problems**

**To understand the concept let's first open a shop say a local retail stationery shop.**

**Example 1: ****Now suppose a student shows up and wants to buy 5 gel pens worth ₹ 5 each. So, what is the profit earned by the shopkeeper in net terms and its profit percentage?**

This ₹ 5 is the

selling price,the price at which the commodity is sold to its buyer. And let ₹ 4 is the price at which the shopkeeper has bought these pens from his supplier and this price is known asCost Price.

Thus, this difference between the price at which the shopkeeper buys his pen and at which it is sold is known as profit/ loss earned. Now ifSelling Price > Cost Pricethen he will earnprofitand ifSelling Price < Cost Price, then he will earn loss.

Therefore,Profit = Selling Price – Cost Price=₹ 5 –₹4 =₹1 per pen

Now,i.e.

And consequently,Loss = Cost Price – Selling Pricei.e.

**Example 2: ****Suppose another customer comes to the shop and bought 2 registers worth ₹ 50 each and a pencil box from him. And this time the shopkeeper has earned 40% profit on the registers. He earned a profit of ₹10 on pencil box and the profit% on pencil box is 20%. Then what is the cost price and profit on register and selling price and cost price of pencil box?**

In this case, we are given

S.P. =₹ 50for each register andprofit% =40%. LetC.P.be x.

⇒ Profit % = {(50 – x)/x} * 100

⇒ 40 = {(50 – x)/x} * 100

⇒ 4x = 500 – 10x

⇒ 14x = 500

⇒ x = 35.71

⇒ Profit = 50 – 35.71 = 14.83

What if the profit of 40% is on selling price instead?

⇒ Profit = profit% * S.P = 0.4* 50 = ₹20

C.P. = S.P. – Profit = ₹50 – ₹20 = ₹30Let's now move on to calculate S.P. and C.P. of pencil box. Let C.P. of pencil box be y

∵ Profit % = (profit/ Cost price) *100

⇒ 20 = (10/y) *100

⇒ 2y = 100

⇒ y = ₹ 50

Therefore, S.P. = ₹50 + ₹10 = ₹60

Try yourself:**Alfred 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:**

View Solution

**Example 3: ****Since not many customers showed up on the first day of the shop. Therefore, to popularize the shop the shopkeeper puts up discount of 20% on all the products. The first customer shows up and bought a packet of pencils and 3 erasers and still making up the profit of 30% on both the items. Then what is the actual cost price of both the items when the pencil is marked as ₹30 and the eraser ₹ 5 each?**

What does the underlined marked mean?Here marked means Marked Price is the price that is offered to customer before discount basically, discount is just difference between marked price and Selling price i.e.

Discount = M.P. – S.P.

In this case, Discount = 0.2 * Price of packet of pencil = 0.2 *30 = ₹ 6

Therefore, S.P = 30 – 6 = ₹ 24

∵ Profit is 30% on C.P., assume C.P. be x

⇒ 0.3 = (24 – x)/x

⇒ 0.3x = 24 – x

⇒ 1.3x = 24

⇒ x = 18.46

Similarly,

Discount = 0.2 * Price of 3 erasers = 0.2* 3*5 = ₹ 3

Hence, S.P. = (3*5) - 3 = ₹ 12

∵ Profit is 30% on C.P., assume C.P. be y

⇒ 0.3 = (12 – y)/y

⇒ 1.3y = 12

⇒ y (C.P. of 3 eraser) = 9.23The above method of solving questions was a direct straightforward way of finding the solution. There's also an alternative way of doing so. Let's now learn that alternative method but this time instead of earning profit the seller was earning the loss.

**Example 4: ****Consider this situation, that the stationery sold a parker pen at a loss of 20% for ₹ 100 and a pack of colored sketch pens at the loss of 15% on S.P. What are the cost price and selling price of both the articles?**

First, let's find out the

C.P.andS.P.parker pen,

∵ Loss is 20% on C.P.

Let C.P. be x and S.P. be 100

⇒ S.P. = 0.8 of C.P.

⇒ 100 = 0.8x

⇒ 100/0.8 = x

⇒ 125 = x

For sketch pens,

∵ Loss is 15% on S.P.

Let S.P. be y and C.P. be 100

⇒ Loss = 0.15y

⇒ C.P. = 1.15 y

⇒ 100 = 1.15y

⇒ 100/1.15 = y

⇒ y = ₹ 87

Try yourself:**The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:**

View Solution

**The problems explained above are rather simple and easy ones. Now let's do some problems that are bit complex and have come up in the previous year's CAT exam.**

**Example 5: ****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 a 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 is ab****le to sell only 1,200 out of 1,500 watches he has made in the season, then he has made a profit of:(a) ₹ 90000(b) ₹ 75000(c) ₹ 45000(d) ₹ 60000**

This question is not basic and direct as the problems given above. This one came in CAT 2016 paper and you should expect to get this level of questions in the exam and not the ones explained above earlier. Now let's see how to solve this problem

Here, first find out cost he has incurred to produce the watches.

∵ He made 1500 watches costing ₹ 150 each and an additional ₹ 30000expense on them.

⇒ Total Cost = (1500*150) + 30000 = ₹ 255000

∵ He's able to sell 1200 watches in the season = ₹250 each

So, the revenue earned by him during the season = ₹250 * 1200 = ₹ 300000

Also, the leftover 300 pieces of clocks would have been sold by the watchmaker in off-season = 100 each.

Revenue earned through these 300 watches = 300*100 = ₹ 30000

Total Revenue = ₹ 300000 + ₹30000 = ₹330000

Profit = Revenue - Cost = 330000 - 255000 = ₹ 75000

Try yourself:**A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 20%?**

View Solution

**Example 6: ****Instead of a meter scale, a cloth merchant uses a 120cm scale while buying, but uses an 80cm scale while selling the same cloth. If he offers a discount of 20% on cash payment, what is his overall profit percentage?**

This question above is a special one with the

faulty dealer. Here, the dealer is earning profit by using a false scale.

To solve this problem, first assume that the price of the cloth is ₹ 1/cm

∵ He's using a 120 cm scale.

⇒ C.P. = (100/120) * ₹1 = ₹ 0.8333/cm

∵ This merchant again uses faulty scale to sell the cloth to his customers. He uses a scale that measures 80cm as 100cmi.e.he sells 80cm for ₹100

Now he also gives a discount of 20% on the cloth.

⇒ His mark up price is ₹100/80cm

∵ S.P. = M.P. - M.P. * Discount% = M.P. (1 - Discount%) = (100/80)*(80/100) = ₹1/cm

Therefore, his profit % = (1 – 0.8333)/0.8333 *100 = 20%

Try yourself:**When a plot is sold for Rs. 18,700, the owner loses 15%. At what price must that plot be sold in order to gain 15%?**

View Solution

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