**Introduction:**

### Profit and Loss is an important topic in CAT Arithmetic. This topic is one that is something that is based on our transactions of everyday life and is frequently uses terms such as: cost price, selling price, marked price, discounts, profit, gain and loss. If you think closely, then every deal you make related to the sale or purchase of something has the sentiment of profit and loss attached to it. When we shop online, we look at the marked prices of products which different online stores offer and then check the discounts offered by these stores.

**Question 1:** Alphonso, on his death bed, keeps half his property for this wife and divides the rest equally among his three sons : Ben, Carl and Dave. Some years later, Ben dies leaving half his property to his widow and half to his brothers Carl and Dave together, sharing equally. When Carl makes his will, he keeps half his property for his widow and the rest he bequeaths to his younger brother Dave. When Dave dies some years later, he keeps half his property for his widow and the remaining for his mother. The mother now has Rs. 1,575,000.What was the worth of the total property?

(a) Rs. 30 lakh

(b) Rs. 8 lakh

(c) Rs. 18 lakh

(d) Rs. 24 lakh

### Answer and Explanation

**Option d**

Let the total property of the Alphonso be Rs.x.

After Alphonso’s death, money possessed by the family members would be

Wife = x/2, Ben = x/6, Carl =x/6, Dave =x/6

After Ben’s death, money possessed by each of them would be

Alphonso’s wife = x/2, Ben = 0,Ben’s wife = x/6, Carl = x/6 + x/24 = 5x/24, Dave = x/6 + x/24 = 5x/24

After Carl’s death, money possessed by them

Alphonso’s wife has x/2, Ben has 0, Ben’s wife has x/12, Carl has 0, Carl’s wife has 5x/48, Dave has

5x/24 + 5x/48 = 15x/48

After Dave’s death, money possessed by them is:

Alphonso’s wife has x/2 + 15x/96 = 63x/96, Ben has 0, Ben’s wife has x/12, Carl’s has 0, Carl’s wife has

5x/48, Dave has 0 and Dave’s wife has 15x/96

Now, given that 63x/96 = 1575000

x= 2400000

**Alternative Method:**

You can also solve this question by using options.

If we take total amount to be Rs 2400000, then after Alphonso’s death, the money with the family members will be:

Alphonso’s wife = 1200000, Ben = Carl = Dave = 400000, Ben will leave 100000 each for Carl and Dave.

So, Carl and Dave have 50000 each, Carl will leave 250000 for Dave, so Dave has 750000.

Dave left 750000/2 = 375000 for his mother, so his mother has 1200000 + 375000 = 1575000, which is given in the question. hence option 4 is the answer.

**Question 2:** Two oranges, three bananas and four apples cost Rs. 15. Three oranges, two bananas and one apple cost Rs. 10. I bought 3 oranges, 3 bananas and 3 apples. How much did I pay?

(a) Rs. 10

(b) Rs. 8

(c) Rs. 15

(d) Cannot be determined

### Answer and Explanation

**Option c**

It is given that

2O + 3B + 4A = 15 …..(1)

3O + 2B + A = 10…….(2)

The answer to this question seems to be cannot be determined as we are given three variables but we can form two equations only. But the question is not asking about the individual price of 3 oranges, 3 bananas and 3 apples but it asks the cost of 3O + 3B + 3A. For that, if we add the two equations, we get

5O+5B+5A=25

O+B+A=5

Therefore 3O +3B+3A = 3×5 = 15

**Question 3: **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 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?

(a) 500

(b) 700

(c) 800

(d) 1000

### Answer and Explanation

**Option b**

Total cost to produce 1500 watches = (1500 × 150 + 30000) = Rs. 2,55,000

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

number of watches sold after the season = (1500 – *x*)

∴Revenue earned on the sale of 1500 watches

= 250 × *x* + (1500 – *x*) × 100 = 150*x* + 150000

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

∴ 150*x* + 150000 = 2,55,000 ⇒*x* = 700

**Question 4:** A stockist wants to make some profit by selling sugar. He contemplates about various methods. Which of the following would maximize his profit?

1. Sell sugar at 10% profit.

2. Use 900 g of weight instead of 1 kg.

3. Mix 10% impurities in sugar and selling sugar at cost price.

4. Increase the price by *5% *and reduce weights by 5%.

(a) I or III

(b) II

(c) II, III and IV

(d) Profits are same

### Answer and Explanation

**Option b**

We will solve this question by taking all the cases one by one.

In the first case it is given that the profit is 10%.

For second case, let the CP of 1 kg of sugar be Rs. 100

Then CP of 900 g of sugar= (100/1000 )x 900 = Rs. 90

Hence, profit % in Case II= [{(100-90)/90}x100] = 11.11%

For case III, If he adds 10% impurity then his CP for 1 kg

= {(100/1100) x 100} = Rs. 90.90

Hence, profit % in Case III = [{(100-90.90)/90.90} x 100] = 10.01%

and in the last case, If he reduces weight by 5%

Then cost price of 950 g = {(100/1000) x 950} = Rs. 95 and SP = Rs. 105

Hence, profit % in Case IV = {(105 – 95 )/95} X 100 = 10.52%

Hence, the profit is maximum in second case.

**Question** **5**: A dealer offers a cash discount of 20% and still makes a profit of 20%, when he further allows 16 articles to a dozen to a particularly sticky bargainer. How much per cent above the cost price were his wares listed ?

(a) 100%

(b) 80%

(c)75%

(d) 66%

### Answer and Explanation

**Option a**

Let the CP of the article be Rs. x, since he earns a profit of 20%, hence SP = 1.2x.

It is given that he is selling 16 articles to a dozen, so he a incurs loss by

selling 16 articles at the cost of 12 articles [loss = {(16-12)/16} x 100 = 25%]

∴ His selling price = SP × 0.75

Now SP × 0.75 = 1.2 *x*⇒ SP = (1.2/0.75)x = 1.6x.

This SP is arrived after giving a discount of 20% on MP.

Hence, MP = (1.6/0.8)x = 2x

It means that article has been marked 100% above the cost price.

**Alternative Method:**

Let the cost price = Rs 100. Since the profit is 20%, so the SP = Rs 120.

This SP = Rs 120 is arrived after giving a discount of 20%, i.e. MP = 120/0.8 = Rs 150.

Now he is selling 16 goods to a dozen, so his loss in this case = {(16-12)/16} x100 = 25%.

It means that Rs 150 were arrived after losing 25%. Hence the actual MP = 150/0.75 = Rs 200.

Hence, he has marked the MP 100% above the CP.

**Extra tips for CAT Profit and Loss Questions**

• As you can see from the Profit and Loss questions above, this topic is all about practical application of basic Arithmetic concepts. In fact, most of the situations you encounter in these problems are often encountered by us in our everyday lives.

• This is one topic which finds its roots in school mathematics. In case you which you study the absolute basics for this topic, then you should refer to NCERT books for this topic. These books explain the basic concepts for this topic in detail and you will be able to understand all the important concepts that form part of this topic.

• In case you want problems for bulk practice for this topic, then you should refer to RS Agarwal. The book provides you enough problems for this topic and you can solve these easy to medium level problems to improve your confidence in the topic.

• Remember, this is one topic where you can literally force yourself to learn the topic by sheer brute force solving of problems and can make sure you improve in the topic by solving lots and lots of problems. By solving similar kinds of questions, you will essentially build up your recall value for this topic and be able to solve questions easily in the exam.