# 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).

Workspace:

**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).

Workspace:

**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).

Workspace:

**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).

Workspace:

**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.

Workspace:

**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.

Workspace:

**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.

Workspace:

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