Previous Year OMET Questions for Arithmetic

1. XAT 2023 QADI | Arithmetic - Profit & Loss

Rajnish bought an item at 25% discount on the printed price. He sold it at 10% discount on the printed price. What is his profit in percentage?

A.
10
B.
15
C.
17.5
D.
20
E.
None of the above

Answer: Option D

Explanation :

Let the printed price be Rs. 100.

Cost price for Rajnish after 25% discount = Rs. 75

Rajnish sold it at 10% discount in printed price i.e., at Rs. 90

∴ Required profit % = $\frac{90 - 75}{75} \times 100$ = $\frac{15}{75} \times 100$ = 20%

Hence, option (d).

2. 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) $(1 - \frac{2 x / 3}{100})$ …(1)

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

Equating (1) and (2)

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

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

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

⇒ x² – 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).

3. 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

4. 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%

5. 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

6. 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

7. 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

8. 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%

9. 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

10. 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 (d).

11. 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

12. 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

13. 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 = ${(54 - \frac{x}{32})}^{2}$

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

∴ Total fare f₁ = x ${(54 - \frac{x}{32})}^{2}$

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

$\frac{d f_{1}}{d x}$ = x $[2 (54 - \frac{x}{32}) (- \frac{1}{32})]$ + ${(54 - \frac{x}{32})}^{2}$

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

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

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

Now $\frac{d f_{1}}{d x}$ = 0

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

∴ x = 1728 or x = 576

But x ≤ 900

∴ x = 576

Hence, option (b).

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

∴ x = 9000

∴ Madhur’s share in the profit

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

Hence, option (b).

15. 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 (a).

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

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