*Wednesday, July 18th, 2018*

Profit and Loss is the one concept that we have been studying since class 6^{th }or 7^{th}. It is present in our day-to-day simple transactions from buying vegetables to purchasing expensive jewelry. Everything we purchase today includes profit and loss. Our whole economy from big MNC's to small retail outlets has been running with the same single intention to make profit. Whatever is being traded in the market has same motive to earn profit. Every seller aims to earn some profit over the product he is willing to sell and from the buyers' perspective he is earning profit in terms of utility he gets while consuming the product. This one basic concept has been there for centuries. And loss is like the other side of coin. With profit comes loss. Ups and downs are part and parcel of business. Sometimes firm make loss and at other times profit but, earning loss. Since, before starting any new venture or assessing the performance of the running one, it's necessary to understand and analyze the profitability of it. And this is the reason why this topic is so significant and is included in CAT exam. Â Therefore, in this blog you will learn about the very basic concept of profit and loss and its application into complex CAT problems.

To understand the concept let's first open a shop say a local retail stationary shop. Now suppose a student shows up and wants to buy 5 gel pens worthÂ â‚¹ 5 each. So, what is the profit earned by the shopkeeper in net terms and its profit percentage?

Now this â‚¹ 5 is the **selling price, **the price at which the commodity is sold to its buyer. And let â‚¹ 4 is the price at which the shopkeeper has bought these pens from his supplier and this price is known as **Cost Price**. Thus, this difference between the price at which shopkeeper buys his pen and at which it is sold is known as profit/ loss earned. Now if **Selling Price > Cost Price **then he will earn **profit **and if **Selling Price < Cost Price**, then he will earn loss i.e.

Therefore, **Profit = Selling Price â€“ Cost Price**

**= ****â‚¹ 5 – ****â‚¹4 = ****â‚¹1 per pen**

And consequently, **Loss = Cost Price â€“ Selling Price.**

Now **profit % = (profit/ Cost price) *100** or **profit % = {(selling price – cost price)/ Cost price} *100**

**= 1/5 * 100 = 20%**

Similarly, **Loss % = (loss/ Cost price) *100 **or **Loss % = {(Cost price – selling price)/ Cost price} *100**

Now suppose another customer comes to the shop and bought 2 registers worth â‚¹ 50 each and a pencil box from him. And this time the shopkeeper has earned 40% profit on the registers. He earned profit of â‚¹10 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. = ****â‚¹ 50/ each** and **profit% **as **40%**. Let **C.P.** be x. Now,

**Profit % = (50 â€“ x / x) * 100**

**40 = (50 â€“ x / x) * 100**

**4x= 500 â€“ 10x**

**14x = 500**

**x = 35.71**

**Profit = 50 â€“ 35.71**

**= 14.83**

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

Then, **Profit = profit% * S.P**

**= 0.4* 50**

**= ****â‚¹20**

**C.P. = S.P. â€“ Profit**

**= ****â‚¹50 – ****â‚¹20**

**= ****â‚¹30**

Let's now move on to calculate S.P. and C.P. of pencil box. Let C.P. of pencil box be y

Since, **profit % = (profit/ Cost price) *100**

**20 = (10/y) *100**

**2y = 100**

**y = â‚¹ 50**

Therefore, **S.P. = â‚¹50 + â‚¹10**

**Â Â = â‚¹60**

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Now since not many customers showed up on the first day of 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 pencil 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 â‚¹30 and eraser â‚¹ 5/ each.

Now 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. â€“ S.P.**

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

**= 0.2 *30**

**= â‚¹ 6**

Therefore, **S.P = 30 â€“ 6**

**= â‚¹ 24**

And profit is 30% on C.P., assume C.P. be x. Then,

**0.3 = (24 â€“ x/x) **

**0.3x = 24 â€“ x**

**1.3x = 24**

**X = 18.46**

Similarly, **Discount = 0.2 * Price of packet of pencil**

**= 0.2* 3*5**

**= â‚¹ 3**

**Hence, S.P. = 12**

And, **0.3 = 12 â€“ y/y**

**1.3y = 12**

**Y (C.P. of 3 eraser) = 9.23**

The 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. Consider this situation, that the stationer sold a parker pen at a loss of 20% for â‚¹ 100 and a pack of colored sketch pens at loss of 15% on S.P. Â What is the cost price and selling price of both the articles?

First let's find out the **C.P. **and **S.P. **parker pen,

Since loss is 20% on C.P. Then,

**S.P. = 0.8 of C.P.**

**100 = 0.8x**

**100/0.8 = C.P.**

**125 = C.P.**

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 = â‚¹87**

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 previous year CAT exam

**Problem 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 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 able to sell only 1,200 out of 1,500 watches he has made in the season, then he has made a profit of

â‡’â‚¹ 90000

â‡’â‚¹ 75000

â‡’â‚¹ 45000

â‡’â‚¹ 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.

Since, he made **1500 watches **costing **â‚¹ 150 each **and an additional **â‚¹ 30000Â **expense on them.

Thus, **total Cost = (1500*150) + 30000**

**Â = â‚¹ 255000**

Now we will calculate the revenue he earned from selling them. As, he's able to sell 1200 watches in the season @ â‚¹250 each

So, the revenue earned by him during the season = **â‚¹250 * 1200**

= **â‚¹ 300000**

Also, the left over 300 pieces of clocks would have been sold by the watchmaker in off season @ **100 each.**

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

**Â **= **â‚¹ 30000**

**Total Revenue = â‚¹ 300000 + â‚¹30000 = â‚¹330000**

**Profit = Revenue â€“ Cost**

**Â Â Â Â Â Â Â Â Â Â =â‚¹ 330000 â€“ 255000**

**Â Â Â Â Â Â Â Â Â Â = â‚¹ 75000**

**Problem 2:**

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 false scale.

To solve this problem, first assume that price of cloth is **â‚¹ 1/cm**

Now he's using 120 cm scale. Therefore his **C.P. **= **(100/120)*â‚¹1** =**0.8333/cm**

Now this merchant again uses faulty scale to sell the cloth to his customers.

He uses a scale that measures 80cm as 100cm i.e. he sells 80cm for â‚¹100

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

Thus, his mark up price is **â‚¹100/80cm**

So, after deducting [email protected]%.

**S.P. = â‚¹1/cm**

Therefore, his profit % = **(1 â€“ 0.8333)/0.8333 *100**

= **20%**

As you can see the above problem was a bit tricky, you will face similar problems in the exam. You will get more idea of the type of questions you need to practice through past year CAT papers. This is a very important topic. Every year around 3-4 questions come in the exam on profit and loss. So, practice this topic thoroughly.

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Quantitative Aptitude – Arithmetic – Profit and Loss – Q1: Mayank buys some candies for Rs 15 a dozen and an equal number of different candies for Rs 12 a dozen. He sells all for Rs 16.50 a dozen and makes a profit of Rs 150. How many dozens of candies did he buy altogether?

Quantitative Aptitude – Arithmetic – Profit and Loss – Q2: The manufacturer of a table sells it to a wholesale dealer at a profit of 10%. The wholesale dealer sells the table to a retailer at a profit of 30%.

Quantitative Aptitude – Arithmetic – Profit and Loss – Q3: If Fatima sells 60 identical toys at a 40% discount on the printed price, then she makes 20% profit.

Quantitative Aptitude – Arithmetic – Profit and Loss – Q4: In a market, the price of medium quality mangoes is half that of good mangoes.

Quantitative Aptitude – Arithmetic – Profit and Loss – Q5: If a seller gives a discount of 15% on retail price, she still makes a profit of 2%. Which of the following ensures that she makes a profit of 20%?

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