# Arithmetic - Profit & Loss - Previous Year CAT/MBA Questions

You can practice all previous year OMET questions from the topic Arithmetic - Profit & Loss. This will help you understand the type of questions asked in OMET. It would be best if you clear your concepts before you practice previous year OMET questions.

**XAT 2019 QADI | Arithmetic - Profit & Loss**

An article is marked x% above the cost price. A discount of 2/3x% if given on the marked price. If the profit is 4% of the cost price and the value of x lies between 25 and 50, then the value of 50% of x is:

- A.
15

- B.
13

- C.
20

- D.
16

- E.
12

Answer: Option A

**Explanation** :

Let the CP of the article be Rs 100.

∴ M.P = 100 + x

As a discount of 2x/3 % is given on the Marked Price.

SP = (100 + x)$\left(1-\frac{2x/3}{100}\right)$ …(1)

Also, since profit is 4%, it means selling price = 100 + 4 = 104 …(2)

Equating (1) and (2)

⇒ (100 + x)$\left(1-\frac{2x/3}{100}\right)$ = 104

⇒ 100 + x – $\frac{2x}{3}$ – $\frac{2{x}^{2}}{300}$ = 104

⇒ $\frac{2{x}^{2}}{300}$ - $\frac{x}{3}$ + 4 = 0

⇒ x^{2} – 50x + 600 = 0

⇒ x = 20 or 30.

Since it is given that x is between 25 and 50 hence x = 30.

∴ 50% of 30 = 15.

Hence, option (a).

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**XAT 2017 QADI | Arithmetic - Profit & Loss**

A shop, which sold same marked price shirts, announced an offer - if one buys three shirts then the fourth shirt is sold at a discounted price of ₹ 100 only. Patel took the offer. He left the shop with 20 shirts after paying ₹ 20,000. What is the marked price of a shirt?

- A.
Rs. 1260

- B.
Rs. 1300

- C.
Rs. 1350

- D.
Rs. 1400

- E.
Rs. 1500

Answer: Option B

**Explanation** :

Let the marked price of a shirt = M

∴ If a customer buys 3 shirts then the fourth shirt would be given at a discounted price of 100 rupees.

⇒ Total cost of 4 shirts = 3M + 100

Customer bought a total of 20 shirts, hence he bought 15 shirts and marked price and got 5 shirts at the discounted price.

∴ Total amount paid by the customer = 15M + 500

⇒ 15M + 500 = 20,000

⇒ M = 1300

Hence, option (b).

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**XAT 2016 QADI | Arithmetic - Profit & Loss**

Rani bought more apples than oranges. She sells apples at Rs. 23 apiece and makes 15% profit. She sells oranges at Rs. 10 apiece and marks 25% profit. If she gets Rs. 653 after selling all the apples and oranges, find her profit percentage.

- A.
16.8%

- B.
17.4%

- C.
17.9%

- D.
18.5%

- E.
19.1%

Answer: Option B

**Explanation** :

Let the number of apples sold be ‘a’ and the number of oranges sold be ‘o’.

∴ Total Selling Price = 23a + 10b = 653

In R.H.S., there is a 3 in the unit’s place

∴ 23a + 10b should end with 3.

Now, unit’s digit of 10b will be ‘0’ hence units digit of 13a should be 3.

For this the values possible values of ‘a’ are 1, 11, 21, …

When a = 11, b = 40 [not possible since a should be more than b.]

When, a = 21, b = 17 which is in line with the condition of a > b

When a ≥ 31, b is negative, hence we will not consider those values.

∴ a = 21 and b = 17.

Now, the profit per apple is 15% and profit per orange is 25%

Cost price of each apple = 23/1.15 = Rs. 20

Cost price of each orange = 10/1.25 = Rs. 8

∴ Total Cost price = 20a + 8b = Rs.556

∴ Profit percent = ((653 - 556)/ 556) × 100 = 17.4%

Hence, option (b).

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**XAT 2016 QADI | Arithmetic - Profit & Loss**

Company ABC starts an educational program in collaboration with Institute XYZ. As per the agreement, ABC and XYZ will share profit in 60 : 40 ratio. The initial investment of Rs. 100,000 on infrastructure is borne entirely by ABC whereas the running cost of Rs. 400 per student is borne by XYZ. If each student pays Rs. 2000 for the program find the minimum number of students required to make the program profitable, assuming ABC wants to recover its investment in the very first year and the program has no seat limits.

- A.
63

- B.
84

- C.
105

- D.
157

- E.
167

Answer: Option C

**Explanation** :

Initial investment by ABC = 1,00,000

Let the total number of students be x.

Net profit from a student = 2000 – 400 = Rs. 1600

Net profit from ‘x’ students = 1600x

This will be divided between ABC and XYZ in the ratio of 60 : 40 i.e., 3 : 2.

∴ ABC will receive 1600x × 3/5

Hence, 1600x × 3/5 ≥ 1,00,000

⇒ x ≥ 104.2

∴ Minimum number of students should be 105.

Hence, option (c).

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**IIFT 2016 QA | Arithmetic - Profit & Loss**

In a local shop, as part of promotional measures, the shop owner sells three different varieties of soap, one at a loss of 13 percent, another at a profit of 23 percent and the third one at a loss of 26 percent. Assuming that the shop owner sells all three varieties of soap at the same price, the approximate percentage by which average cost price is lower or higher than the selling price is

- A.
10.5 higher

- B.
12.5 lower

- C.
14.5 lower

- D.
8.5 higher

Answer: Option A

**Explanation** :

Let the S.P. of each type be Rs. 100

C.P. of soap sold at 13% loss = 100/0.87 ≅ Rs. 115

C.P. of soap sold at 23% profit = 100/1.23 ≅ Rs. 81

C.P. of soap sold at 26% loss = 100/0.74 ≅ Rs. 135

∴ Average C.P. = (115 + 81 + 135)/3 = Rs. 110.3

∴ % by which average C.P. is higher = (10.3/100) × 100 = 10.3%

The closest value in the options is 10.5%

Hence, option 1.

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**IIFT 2015 QA | Arithmetic - Profit & Loss**

As a strategy towards retention of customers, the service centre of a split AC machine manufacturer offers discount as per the following rule: for the second service in a year, the customer can avail of a 10% discount; for the third and fourth servicing within a year, the customer can avail of 11% and 12% discounts respectively of the previous amount paid, Finally, if a customer gets more than four services within a year, he has to pay just 55% of the original servicing charges. If Rohan has availed 5 services from the same service centre in a given year, the total percentage discount availed by him is approximately:

- A.
16.52

- B.
20.88

- C.
22.33

- D.
24.08

Answer: Option B

**Explanation** :

Let original service charges be Rs. x.

Rohan has paid x, 0.9x, (0.9 × 0.89x =) 0.801x, (0.88 × 0.89 × 0.9x ≈ ) 0.705x, 0.55x for the five services.

Total payment done by Rohan ≈ 3.956x

Discount availed by Rohan ≈ 1.044x

Percentage discount ≈ (1.044 × 100)/5 = 20.88

Hence, option 2.

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**XAT 2015 QA | Arithmetic - Profit & Loss**

The Maximum Retail Price (MRP) of a product is 55% above its manufacturing cost. The product is sold through a retailer, who earns 23% profit on his purchase price. What is the profit percentage (expressed in nearest integer) for the manufacturer who sells his product to the retailer? The retailer gives 10% discount on MRP.

- A.
31%

- B.
22%

- C.
15%

- D.
13%

- E.
11%

Answer: Option D

**Explanation** :

Let Manufacturing Cost = Rs. 100

M.R.P = Rs. 155

Discount = 10%

S.P (of retailer) = 155 ×.9 = Rs. 139.5

Profit% (of retailer) = 23%

S.P. (of manufacturer) = 139.5 × (100/123) = Rs. 113

Profit % (of manufacturer) = 13%

Hence, option 4.

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**IIFT 2012 QA | Arithmetic - Profit & Loss**

Rohit bought 20 soaps and 12 toothpastes. He marked-up the soaps by 15% on the cost price of each, and the toothpastes by Rs.20 on the cost price each. He sold 75% of the soaps and 8 toothpastes and made a profit of Rs.385. If the cost of a toothpaste is 60% the cost of a soap and he got no return on unsold items, what was his overall profit or loss?

- A.
Loss of Rs. 355

- B.
Loss of Rs. 210

- C.
Loss of Rs. 250

- D.
None of the above

Answer: Option A

**Explanation** :

∴ 2.25s + 160 = 385

∴ s = 100

Cost of unsold items = 5s + 4 × 0.6s = 7.4s = 740, which is a loss.

Total cost = 20s + 12 × 0.6s = 27.2s

∴ Overall loss = 740 – 385 = 355

Hence, option 1.

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**IIFT 2011 QA | Arithmetic - Profit & Loss**

Sujoy, Mritunjoy and Paranjoy are three friends, who have worked in software firms Z Solutions, G Software’s and R Mindpower respectively for decade. The friends decided to float a new software firm named XY Infotech in January 2010. However, due to certain compulsions, Mritunjoy and Paranjoy were not able to immediately join the start-up in the appointed time. It was decided between friends that Sujoy will be running the venture as the full time director during 2010, and Mritunjoy and Paranjoy will be able to join the business only in January 2011. In order to compensate Sujoy for his efforts, it was decied that he will receive 10 percent of the profits and in the first year will invest lesser amount as compared to his friends. The remaining profit will be distributed among the friends in line with their contribution. Sujoy invested Rs. 35,000/- for 12 months, Mritunjoy invested Rs. 1,30,000/- for 6 months and Paranjoy invested Rs. 75,000/- for 8 months. If the total profit earned during 2010 was Rs. 4,50,000/-, then Paranjoy earned a profit of:

- A.
Rs. 1, 75, 500

- B.
Rs. 1, 35, 500

- C.
Rs. 1, 39, 500

- D.
None of the above

Answer: Option D

**Explanation** :

Sujoy receives 10% of the profit for his efforts.

Remaining 90% of the profit is distributed among the friends in the line with their contribution.

Now, Sujoy invested Rs. 35,000 for 12 months, Mritunjoy invested Rs. 1,30,000 for 6 months, and Paranjoy invested Rs. 75,000 for 8 months.

∴ Sujoy’s, Mritunjoy’s and Paranjoy’s investments are in the ratio

35000 × 12 : 130000 × 6 : 75000 × 8 ≡ 7 : 13 : 10

∴ Paranjoy's share = $\frac{0.9\times 450000}{7+13+10}$ × 10 = Rs. 135000

Hence, option 4.

Workspace:

**IIFT 2011 QA | Arithmetic - Profit & Loss**

In March 2011, EF Public Library purchased a total of 15 new books published in 2010 with a total expenditure of Rs. 4500. Of these books, 13 books were purchased from MN Distributors, while the remaining two were purchased from UV Publishers. It is observed that one-sixth of the average price of all the 15 books purchased is equal to one-fifth of the average price of the 13 books obtained from MN Distributors. Of the two books obtained from UV Publishers, if one-third of the price of one volume is equal to one-half of the price of the other, then the price of the two books are

- A.
Rs. 900/- and Rs. 600/-

- B.
Rs. 600/- and Rs. 400/-

- C.
Rs. 750/- and Rs. 500/-

- D.
None of the above

Answer: Option C

**Explanation** :

Average price of 15 books = 4500/15 = Rs. 300

Let the average price of 13 books purchased from MN distributors be a.

∴ 300/6 = a/5

∴ a = 250

∴ Price of books purchased from MN distributirs = 250 × 13 = 3250

∴ Price of books purchased from UV Publishers = 4500 – 3250 = Rs. 1250

Let the two books purchased from UV publishers cost Rs. x and Rs. y.

∴ x/3 = y/2

As x + y = 1250

∴ x = 750 and y = 500

Hence, option 3.

Workspace:

**IIFT 2011 QA | Arithmetic - Profit & Loss**

An old lady engaged a domestic help on the condition that she would pay him Rs. 90 and a gift after service of one year. He served only 9 months and received the gift and Rs. 65. Find the value of the gift.

- A.
Rs. 10

- B.
Rs. 12

- C.
Rs. 15

- D.
None of the above

Answer: Option A

**Explanation** :

Let the price of the gift be x.

Hence, total value to be paid to domestic help for one year = 90 + x

∴ Value of domestic help for 9 months = 3/4 × (90 + x)

∴ 65 + x = 3/4 × (90 + x)

∴ x = 10

Hence, option 1.

Workspace:

**IIFT 2010 QA | Arithmetic - Profit & Loss**

A metro train from Mehrauli to Gurgoan has capacity to board 900 people. The fare charged (in RS.) is defined by the function

f = ${\left(54-\frac{x}{32}\right)}^{2}$

where ‘x’ is the number of the people per trip. How many people per trip will make the marginal revenue equal to zero?

- A.
1728

- B.
576

- C.
484

- D.
364

Answer: Option B

**Explanation** :

Fare per person f = ${\left(54-\frac{x}{32}\right)}^{2}$

∴ Total fare f_{1} = x${\left(54-\frac{x}{32}\right)}^{2}$

∴ Marginal Revenue is the change in total fare due to change in number of people by one unit. It is given by

$\frac{d{f}_{1}}{dx}$ = x$\left[2\left(54-\frac{x}{32}\right)\left(-\frac{1}{32}\right)\right]$ + ${\left(54-\frac{x}{32}\right)}^{2}$

= $\frac{-x}{16}$$\left(54-\frac{x}{32}\right)$ + ${\left(54-\frac{x}{32}\right)}^{2}$

= $\left(54-\frac{x}{32}\right)$ $\left(\frac{-x}{16}+54-\frac{x}{32}\right)$

= $\left(54-\frac{x}{32}\right)$$\left(54-\frac{3x}{2}\right)$

Now $\frac{d{f}_{1}}{dx}$ = 0

∴ $\left(54-\frac{x}{32}\right)$ $\left(54-\frac{3x}{2}\right)$ = 0

∴ x = 1728 or x = 576

But x ≤ 900

∴ x = 576

Hence, option 2.

Workspace:

**IIFT 2010 QA | Arithmetic - Profit & Loss**

Shyam, Gopal and Madhur are three partners in a business. Their capitals are respectively Rs 4000, Rs 8000 and Rs 6000. Shyam gets 20% of total profit for managing the business. The remaining profit is divided among the three in the ratio of their capitals. At the end of the year, the profit of Shyam is Rs 2200 less than the sum of the profit of Gopal and Madhur. How much profit, Madhur will get?

- A.
Rs.1600

- B.
Rs.2400

- C.
Rs.3000

- D.
Rs.5000

Answer: Option B

**Explanation** :

Capitals of Shyam, Gopal and Madhur are in the ratio 2 : 4 : 3.

Let the total profit be x .

∴ By conditions,

0.8x × $\frac{7}{9}$ - $\left[0.8x\times \frac{2}{9}+0.2x\right]$ = 2200

∴ x = 9000

∴ Madhur’s share in the profit

= $\frac{3}{9}$ × 9000 × 0.8 = Rs. 2400

Hence, option 2.

Workspace:

**IIFT 2009 QA | Arithmetic - Profit & Loss**

Bennett distribution company, a subsidiary of a major cosmetics manufacturer Bavlon, is forecasting the zonal sales for the next year. Zone I with current yearly sales of Rs. 193.8 lakh is expected to achieve a sales growth of 7.25%; Zone II with current sales of Rs. 79.3 lakh is expected to grow by 8.2%; and Zone III with sales of Rs. 57.5 lakh is expected to increase sales by 7.15%. what is the Bennett’s expected sales growth for the next year?

- A.
7.46%

- B.
7.53%

- C.
7.88%

- D.
7.41%

Answer: Option A

**Explanation** :

Total sales this year = 193.8 + 79.3 + 57.5 = Rs. 330.6 lakhs

Expected sales next year = 193.8 × 1.0725 + 79.3 × 1.082 + 57.5 × 1.0715

≈ Rs. 355.26 lakhs

∴ Expected sales growth

= $\frac{355.26-330.6}{330.6}$ × 100

= 7.46%

Hence, option 1.

Workspace:

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