# Arithmetic - Percentage - Previous Year CAT/MBA Questions

You can practice all previous year OMET questions from the topic Arithmetic - Percentage. 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 2020 QADI | Arithmetic - Percentage**

Nalini has received a total of 600 WhatsApp messages from four friends Anita, Bina, Chaitra and Divya. Bina and Divya have respectively sent 30% and 20% of these messages, while Anita has sent an equal number of messages as Chaitra. Moreover, Nalini finds that of Anita’s, Bina’s, Chaitra’s and Divya’s messages, 60%, 40%, 80% and 50% respectively are jokes. What percentage of the jokes, received by Nalini, have been sent neither by Divya nor by Bina?

- A.
65.12

- B.
61.4

- C.
57

- D.
38.6

- E.
34.88

Answer: Option B

**Explanation** :

Number of messages send by Bina = 30% of 600 = 180

Number of messages send by Divya = 20% of 600 = 120

Remaining messages (300) are sent by Anita and Chitra equally i.e., Anita and Chitra sent 150 messages each.

Jokes sent by Anita = 60% of 150 = 90

Jokes sent by Bina = 40% of 180 = 72

Jokes sent by Chitra = 80% of 150 = 120

Jokes sent by Divya = 50% of 120 = 60

Total Jokes sent = 90 + 72 + 120 + 60 = 342

∴ Percentage of jokes that were neither sent by Bina or Divya = 210/342 × 100 = 61.4%

Hence, option (b).

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**XAT 2019 QADI | Arithmetic - Percentage**

A, B, C, D and E are five employees working in a company. In two successive years, each of them got hikes in his salary as follows:

A : p% and (p + 1)%,

B : (p + 2)% and (p - 1)%,

C : (p + 3)% and (p - 2)%,

D : (p + 4)% and (p - 3)%,

E : (p + 5)% and (p - 4)%.

If all of them have the same salary at the end of two years, who got the least hike in his salary?

- A.
E

- B.
B

- C.
D

- D.
A

- E.
C

Answer: Option A

**Explanation** :

Since final salary for all five employees is same, least hike will be for that employee who has the highest initial salary.

Again, since final salary for all five employees is same, initial salary will be highest for that employee who has least overall % change.

Let us calculate % change for all the employees.

We know when a number is successively increased b a% and then b%, overall % change is a + b + ab/100.

Here let us assume the value of p as 10%

Therefore, % change for

A: 10 + 11 + 10 × 11/100 = 21 + 1.1 = 22.1%

B: 12 + 9 + 12 × 9/100 = 21 + 1.08 = 22.08%

C: 13 + 8 + 13 × 8/100 = 21 + 1.04 = 22.04%

D: 14 + 7 + 14 × 7/100 = 21 + 0.98 = 21.98%

E: 15 + 6 + 15 × 6/100 = 21 + 0.90 = 21.90%

∴ Least % change is for E, hence E has the highest initial salary hence the least hike.

Hence, option (a).

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**IIFT 2019 QA | Arithmetic - Percentage**

Joseph is in a dilemma. He has been offered a job which would pay him ₹ 80,000 per month for first three years and ₹ 1,20,000 per month for the next three years, and ₹ 1,50,000 per month for the remaining four years. He has also been offered an MBA at a prestigious place and he is considering whether to accept the job or go for the MBA. The first year tuition fee for the MBA program is ₹ 16,00,000 and the second year tuition fee for the MBA program is ₹ 20,00,000. After MBA, he'll get a salary of ₹ 2,00,000 per month for the first four years and then ₹ 2,50,000 per month for the remaining four years. What will be the approximate percentage gain for Joseph in opting for the MBA instead of the job in the 10 years horizon considering no discounting of money?

- A.
23%

- B.
25%

- C.
27%

- D.
29%

Answer: Option B

**Explanation** :

Total amount earned through job = [(80000 × 3) + (120000 × 3) + (150000 × 4)] × 12

= 1200000 × 12 = Rs. 144 lakhs

Net amount earned through MBA = salary earned in 8 years (after MBA) − MBA fees paid for 2 years

= [(200000 + 250000) × 4 × 12] − (1600000 + 2000000)

= 21600000 − 3600000

= Rs. 180 lakhs

∴ Percentage benefit = [(180 − 144)/144] × 100

= 25%

Hence, option (b).

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**IIFT 2019 QA | Arithmetic - Percentage**

KBC restaurant chain regularly conducts survey of its customers. The customers are asked to rate the food quality, service and price as Excellent, Good and Fair. Customers are also asked whether they would come back. It was found that 76% of customers say that they will come back. Amongst those who say that they will come back, 57% rate the restaurant as Excellent, 36% rate it as Good and remainder rate it as Fair. Of those who say that they will not return, the respective values are 14%, 32% and 54%. What percentage of customers rated the restaurant as good?

- A.
27.4%

- B.
35%

- C.
51%

- D.
30.7%

Answer: Option B

**Explanation** :

Let the total number of customers be 100x.

So, customers who said they will return and who said that they will not return is 76x and 24x respectively.

Of the 76x customers, the number of customers who rate it as good = 36% of 76x = 0.36 × 76x = 27.36x.

Of the 24x customers, the number of customers who rate it as good = 32% of 24x = 0.32 × 24x = 7.68x.

So, total customers who rated the restaurant as good = 27.36x + 7.68x = 35.04x.

Required percentage = (35.04x/100x) × 100 = 35.04 ≈ 35%.

Hence option (b).

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**XAT 2018 QADI | Arithmetic - Percentage**

The price of a product is P. A shopkeeper raises its price by X% and then offers a discount of Y% on the raised price. The discounted price again becomes P. If Y is the difference between X and Y, then find X.

- A.
20

- B.
25

- C.
50

- D.
100

- E.
None of the above

Answer: Option D

**Explanation** :

Given, $P\left(1+\frac{X}{100}\right)\left(1-\frac{Y}{100}\right)$ = P

⇒ $\left(1+\frac{X}{100}\right)\left(1-\frac{Y}{100}\right)$ = 1 …(1)

⇒ X > Y

It is also given that X – Y = Y.

⇒ X = 2Y

Substituting this in (1)

⇒ $\left(1+\frac{2Y}{100}\right)\left(1-\frac{Y}{100}\right)$ = 1

⇒ 1 - ($\frac{2{Y}^{2}}{10000}$ + $\frac{Y}{100}$ = 1

⇒ Y = 50

∴ X = 100

Hence, option (d).

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**IIFT 2018 QA | Arithmetic - Percentage**

A Business Group has 3 Companies X, Y, Z and a Trust P which is engaged in charitable activities. Each group company has to donate 5% of its own funds to the Trust, excluding the loan which the company has taken from other companies of the group. X has given a loan to Y which is equivalent to 10% of the funds of Y. After receiving the loan, Y has funds which are 2 times the funds of Z. If Z gave Rs. 10,000 as donation to the Trust P, how much is the approximate contribution of Y to the Trust P?

- A.
Rs. 17,000

- B.
Rs. 18,000

- C.
Rs. 19,000

- D.
Rs. 20,000

Answer: Option B

**Explanation** :

Let the initial amount (in Rs.) with companies X, Y and Z be x, y and z respectively.

X has given an amount equivalent to 10% of the amount originally with Y. Hence, X has given Rs. (0.1y) to Y.

∴ Amount now with Y = y + 0.1y = Rs. (1.1y)

The amount with Y is twice the amount with Z. Hence, the amount with Z is Rs. (0.55y).

Z gave Rs. 10,000 i.e. 5% of his funds to the Trust.

∴ 0.05 × 0.55y = 10000

Amount given by Y = 0.05y

= 0.05 × (10000)/(0.55 × 0.05)

= 10000/0.55

= 18181 i.e. approx. Rs. 18,000

Hence, option 2.

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**IIFT 2017 QA | Arithmetic - Percentage**

A mobile company that sells two models ACN-I and ACN-II of mobile, reported that revenues from ACN-I in 2016 were down 12% from 2015 and revenue from ACN-II sales in 2016 were up by 9% from 2015. If the total revenues from sales of both the mobile models ACN-I and ACN-II in 2016 were up by 3% from 2015, what is the ratio of revenue from ACN-I sales in 2015 to revenue from ACN-II sales in 2015?

- A.
5 : 2

- B.
2 : 5

- C.
3 : 4

- D.
None of the above

Answer: Option B

**Explanation** :

Let the revenues of ACN-I and ACN-II in 2015 be a and b respectively.

∴ Total revenues in 2015 = (a + b)

Since total revenues grew by 3% in 2016, total revenue in 2016 = 1.03(a + b).

Also, revenue of ACN-I dropped by 12% while those of ACN-II increased by 9%

∴ Revenue of ACN-I in 2016 = 0.88a and Revenue of ACN-II in 2016 = 1.09b

∴ Total revenue in 2016 = (0.88a + 1.09b)

∴ 0.88a + 1.09b = 1.03(a + b)

∴ 0.06b = 0.15a i.e. a : b = 2 : 5

Hence, option 2.

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**IIFT 2015 QA | Arithmetic - Percentage**

The pre-paid recharge of Airtel gives 21% less talktime than the same price pre-paid recharge of Vodafone. The post-paid talktime of Airtel is 12% more than its pre-paid recharge, having the same price. Further, the post-paid talktime of same price of Vodafone is 15% less than its pre-paid recharge. How much percent less / more talktime can one get from the Airtel post-paid service compared to the post-paid service of Vodafone?

- A.
3.9% more

- B.
4.7% less

- C.
4.7% more

- D.
2.8% less

Answer: Option A

**Explanation** :

Assume that for price P, assume that Vodafone gives talk time of 100 seconds.

So, for the same price P, Airtel gives talk time of 79 (= 21% less than 100) seconds.

The post-paid talk time for the same price by Airtel and Vodafone is 1.12 × 79 and 100 × 0.85, i.e., 88.48 seconds and 85 seconds respectively.

One can get 88.48 – 85 = 3.48 seconds more from Airtel post-paid service compared to the Vodafone post-paid service.

Required percentage = 3.48/85 = 4.07

The closest option is option 1.

Hence, option 1.

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**XAT 2015 QA | Arithmetic - Percentage**

The tax rates for various income slabs are given below.

There are 15 persons working in an organization. Out of them, 3 to 5 persons are falling in each of the income slabs mentioned above. Which of the following is the correct tax range of the 15 persons? (E.g. If one is earning Rs. 2000, the tax would be: 500 × 0 + 1500 × 0.05)

- A.
1350 to 7350, both excluded

- B.
1350 to 9800, both included

- C.
2175 to 7350, both excluded

- D.
2175 to 9800, both included

- E.
None of the above

Answer: Option A

**Explanation** :

Total tax will be minimum if income of 5 persons is not more than 500 and income of 4 persons is minimum and also in the range (500, 2000]. Total tax will be maximum if income of 5 persons is maximum possible and income of 4 persons is maximum in the range (2000, 5000].

Minimum tax > (5 × 0) + (4 × 0) + (3 × 75) + (3 × 375) = Rs. 1350

Maximum tax range < (3 × 0) + (3 × 75) + (4 × 375) + (5 × 1125) = Rs. 7350

Hence, option 1.

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**IIFT 2014 QA | Arithmetic - Percentage**

A pharmaceutical company manufactures 6000 strips of prescribed diabetic drugs for Rs. 8,00,000 every month. In July 2014, the company supplied 600 strips of free medicines to the doctors at various hospitals. Of the remaining medicines, it was able to sell 4/5^{th} of the strips at 25 pecent discount and the balance at the printed price of Rs. 250. Assuming vendor’s discount at the rate of a uniform 30 percent of the total revenue, the approximate percentage profit / loss of the pharmaceutical company in July 2014 is:

- A.
5.5 percent (profit)

- B.
4 percent (loss)

- C.
5.5 percent (loss)

- D.
None of the above

Answer: Option C

**Explanation** :

600 strips were given free to doctors.

Of 5400 strips, (4/5) × 5400 = 4320 strips were sold at 25% discount.

Revenue generated from these strips

= 250 × 0.75 × 4320 = Rs. 8,10,000

Revenue generated from (5400 – 4320 =) 1080 strips = 250 × 1080 = Rs. 2,70,000

Total revenue = Rs. 10,80,000

Vendor’s discount = 30% of the total revenue.

∴ Total earning = 70% of 1080000 = Rs. 7,56,000

Loss = Rs. 44,000

% loss = 5.5

Hence, option 3.

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**IIFT 2013 QA | Arithmetic - Percentage**

A survey was conducted to test relative aptitudes in quantitative and logical reasoning of MBA applicants. It is perceived (prior to the survey) that 80 percent of MBA applicants are extremely good in logical reasoning, while only 20 percent are extremely good in quantitative aptitude. Further, it is believed that those with strong quantitative knowledge are also sound in data interpretation, with conditional probability as high as 0.87. However, some MBA applicants who are extremely good in logical reasoning can be also good in data interpretation, with conditional probability 0.15. An applicant surveyed is found to be strong in data interpretation. The probability that the applicant is also strong in quantitative aptitude is

- A.
0.4

- B.
0.6

- C.
0.8

- D.
0.9

Answer: Option B

**Explanation** :

Suppose 100 MBA applicants were surveyed.

80 of them are good in logical reasoning and 20 are good in quantitative aptitude.

0.87 × 20 ≈ 17 are good in quantitative aptitude and in data interpretation as well.

0.15 × 80 = 12 are good in logical reasoning and in data interpretation as well.

Thus, there are 17 + 12 = 29 MBA applicants those are strong in data interpretation.

Of the 29 MBA applicants 17 are strong in quantitative aptitude.

The required probability = $\frac{17}{29}$ = 0.58

Hence, option 2.

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**IIFT 2013 QA | Arithmetic - Percentage**

If decreasing 70 by X percent yields the same result as increasing 60 by X percent, then X percent of 50 is

- A.
3.84

- B.
4.82

- C.
7.10

- D.
The data is insufficient to answer the question

Answer: Option A

**Explanation** :

70 - $\frac{x}{100}$ × 70 = 60 + $\frac{x}{100}$ × 60

∴ 10 = $\frac{70x}{100}$ + $\frac{60x}{100}$

∴ x = $\frac{100}{13}$

Calculating x % of 50,

$\frac{100}{13}$ × $\frac{1}{100}$ × 50 = 3.84

Hence, option 1.

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**IIFT 2013 QA | Arithmetic - Percentage**

Three years ago, your close friend had won a lottery of Rs. 1 crore. He purchased a flat for Rs. 40 lakhs, a car for Rs. 20 lakhs and shares worth Rs. 10 lakhs. He put the remaining money in a bank deposit that pays compound interest @ 12 percent per annum. If today, he sells off the flat, the car and the shares at certain percentage of their original value and withdraws his entire money from the bank, the total gain in his assets is 5%. The closest approximate percentage of the original value at which he sold off the three items is

- A.
60 percent

- B.
75 percent

- C.
90 percent

- D.
105 percent

Answer: Option C

**Explanation** :

Principal put in bank deposit

= 1,00,00,000 – 40,00,000 – 20,00,000 – 10,00,000

= Rs. 30,00,000

Amount after three years

= 3000000 × (1.12)^{3} = Rs. 42,14,784

Total gain after 3 years is 5%.

Total value = 10000000 × 1.05 = Rs. 1,05,00,000

10500000 − 4214784 = 6285216

Let *x* be the percentage at which he sold off the three items.

∴ $\frac{x\times 7000000}{100}$ = 6285216

Solving this, x ≈ 90%

Hence, option 3.

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**XAT 2012 QA | Arithmetic - Percentage**

Tina, Mina, Gina, Lina and Bina are 5 sisters, aged in that order, with Tina being the eldest. Each of them had to carry a bucket of water from a well to their house. Their buckets’ capacities were proportional to their ages. While returning, equal amount of water got splashed out of their buckets. Who lost maximum amount of water as a percentage of the bucket capacity?

- A.
Tina

- B.
Mina

- C.
Gina

- D.
Lina

- E.
Bina

Answer: Option E

**Explanation** :

Let T, M, G, L and B be the capacities of Tina’s, Mina’s, Gina’s, Lina’s and Bina’s bucket.

Hence, T > M > G > L > B

Assume that they spill x litres of water.

Hence, the percentages of the water spilled by them are;

(x/T) × 100, (x/M) × 100, (x/G) × 100, (x/L) × 100 and (x/B) × 100 respectively.

As, , T > M > G > L > B, this implies that x/ T < x/M < x/G < x/L < x/B

Hence, percentage of water spilled is highest for Bina.

Hence, option 5.

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**IIFT 2012 QA | Arithmetic - Percentage**

The annual production in cement industry is subject to business cycles. The production increases for two consecutive years consistently by 18% and decreases by 12% in the third year. Again in the next two years, it increases by 18% each year and decreases by 12% in the third year. Talking 2008 as the base year, what will be the approximate effect on cement production in 2012?

- A.
24% increase

- B.
37% decrease

- C.
45% increase

- D.
60% decrease

Answer: Option C

**Explanation** :

In the given time period, there would be an increase of 18% from 2008-2009, followed by a compounded increase of 18% from 2009-2010, followed by a compounded decrease of 12% from 2010-2011. Finally, there is a compounded increase of 18%.

Hence, it is clear that effectively the production has increased. Hence, options 2 and 4 are ruled out.

Also, even if the increase is not compounded, there would have been a net increase of 18 + 18 – 12 + 18 = 42%.

Since the increase is compounded, the net effect would be more than 42%.

The exact value in 2012, if the base value is x in 2008 is x × 1.18 × 1.18 × 0.88 × 1.18 = 1.445x

This is an increase of approximately 45%.

Hence, option 3.

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**IIFT 2012 QA | Arithmetic - Percentage**

In 2011, Plasma – a pharmaceutical company – allocated Rs.4.5 × 10^{7} for Research and Development. In 2012, the company allocated Rs.60,000,000 for Research and Development. If each year the funds are evenly divided among 2 × 10^{2} departments, how much more will each department receive this year than it did last year?

- A.
Rs.2.0 × 10

^{5} - B.
Rs.7.5 × 10

^{5} - C.
Rs.7.5 × 10

^{4} - D.
Rs.2.5 × 10

^{7}

Answer: Option C

**Explanation** :

Funds allocated for Research & Development in 2011

= Rs. 4.5 × 10^{7}

Funds allocated for Research & Development in 2012

= Rs. 6 × 10^{7}

Difference in the funds = Rs. 1.5 × 10^{7}

= $\frac{1.5\times {10}^{7}}{2\times {10}^{2}}$ = 7.5 × 10^{4}

Hence, option 3.

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**IIFT 2011 QA | Arithmetic - Percentage**

Mr. Sinha received a certain amount of money by winning a lottery contest. He purchased a new vehicle with 40 percent of the money received. He then gave 20 percent of the remaining amount to each of his two sons for investing in their business. Thereafter, Mr. Sinha spent half of the remaining amount for renovation of his house. One-fourth of the remaining amount was then used for purchasing a LCD TV and the remaining amount – Rs. 1,35,000/- was deposited in a bank. What was the amount of his cash prize?

- A.
Rs. 10,00,000/-

- B.
Rs. 9,00,000/-

- C.
Rs. 8,00,000/-

- D.
None of the above

Answer: Option A

**Explanation** :

Without loss of generality, we can assume that Mr. Sinha received Rs. 100 from the lottery.

After purchasing a vehicle he was left with Rs. 60.

After giving 20% of the remaining to each of the sons, he was left with 0.6 × 60 = Rs. 36

After spending half of the remaining amount on renovation, he is left with Rs. 18.

After spending on the LCD, he is left with Rs. (3 × 18/4) = 54/4

Now, this corresponds to Rs. 135000

∴ The original amount = 135000 × 100/(54/4) = Rs. 10,00,000

Hence, option 1.

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**IIFT 2011 QA | Arithmetic - Percentage**

The ratio of number of male and female journalists in a newspaper office is 5:4. The newspaper has two sections, political and sports. If 30 percent of the male journalists and 40 percent of the female journalists are covering political news, what percentage of the journalists (approx.) in the newspaper is currently involved in sports reporting?

- A.
65 percent

- B.
60 percent

- C.
70 percent

- D.
None of the above

Answer: Option A

**Explanation** :

Let there be 90 journalists in all.

∴ There are 50 males and 40 female journalists.

Now, 30% of males and 40% of females cover politics.

∴ 15 males and 16 females cover politics.

∴ (90 – 15 – 16) = 59 cover sports news.

∴ Required percentage = 59 × $\frac{100}{90}$ ≈ 65%

Hence, option 1.

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**IIFT 2010 QA | Arithmetic - Percentage**

A Techno company has 14 machines of equal efficiency in its factory. The annual manufacturing costs are Rs. 42,000 and establishment charges are Rs. 12,000. The annual output of the company is Rs. 70,000. The annual output and manufacturing costs are directly proportional to the no. of machines. The share holders get 12.5% profit, which is directly proportional to the annual output of the company. If 7.14% machines remain closed throughout the year, then the percentage decrease in the amount of profit of the share holders would be:

- A.
12%

- B.
12.5%

- C.
13.0%

- D.
None of these

Answer: Option D

**Explanation** :

Profit is directly proportional to the annual output and the annual output is directly proportional to the number of machines.

∴ We can say that the profit is directly proportional to the number of machines.

∴ If 7.14% machines remain closed, the percentage decrease in profit is also 7.14%.

Hence, option 4.

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**IIFT 2010 QA | Arithmetic - Percentage**

Sun Life Insurance Company issues standard, preferred, and ultra-preferred policies. Among the company’s policy holders of a certain age, 50% are standard with a probability of 0.01 of dying in the next year, 30% are preferred with a probability 0.008 of dying in the next year, and 20% are ultra-preferred with a probability of 0.007 of dying in the next year. If a policy holder of that age dies in the next year, what is the probability of the deceased being a preferred policy holder?

- A.
0.1591

- B.
0.2727

- C.
0.375

- D.
None of these

Answer: Option B

**Explanation** :

Required probability

= $\frac{0.3\times 0.008}{0.5\times 0.01+0.3\times 0.008+0.2\times 0.007}$

= $\frac{0.0024}{0.005+0.0024+0.0014}$

= $\frac{0.0024}{0.0088}$ ≈ 0.2727

Hence, option 2.

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**IIFT 2010 QA | Arithmetic - Percentage**

A survey shows that 61%, 46% and 29% of the people watched “3 idiots”, “Rajneeti” and “Avatar” respectively. 25% people watched exactly two of the three movies and 3% watched none. What percentage of people watched all the three movies?

- A.
39%

- B.
11%

- C.
14%

- D.
7%

Answer: Option D

**Explanation** :

n(A ⋃ B ⋃ C) = n(A) + n(B) + n(C) – n(A ⋂ B) – n(B ⋂ C) – n(A ⋂ C) – 2n(A ⋂ B ⋂ C)

∴ 100 – 3 = 61 + 46 + 29 –25 – 2(x)

∴ 2x = 14

∴ x = 7

Hence, option 4.

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**IIFT 2010 QA | Arithmetic - Percentage**

A small and medium enterprise imports two components A and B from Taiwan and China respectively and assembles them with other components to form a toy. Component A contributes to 10% of production cost. Component B contributes to 20% of the production cost. Usually the company sells this toy at 20% above the production cost. Due to increase in the raw material and labour cost in both the countries, component A became 20% costlier and component B became 40% costlier. Owing to these reasons the company increased its selling price by 15%. Considering that cost of other components does not change, what will be the profit percentage, if the toy is sold at the new price?

- A.
15.5%

- B.
25.5%

- C.
35.5%

- D.
40%

Answer: Option B

**Explanation** :

Let initial production cost be 100.

Then cost of A = 10 and cost of B = 20

Selling price = 120

∴ Cost of rest =100 – Cost of A – Cost of B

= 100 – 10 – 20 = 70

New cost of A = 1 + $\frac{20}{100}$ × 10 = 12

New cost of B = 1 + $\frac{40}{100}$ × 20 = 28

∴ New cost = 28 + 12 + 70= 110

New selling price = $\left(1+\frac{15}{100}\right)$ × original selling price

= $\left(1+\frac{15}{100}\right)$ × 120

= 138

New profit = $\frac{NewSP-NewCP}{NewCP}$ × 100

= $\frac{138-110}{110}$ × 100

≈ 25.5%

Hence, option 2.

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**IIFT 2009 QA | Arithmetic - Percentage**

In 2006, Raveendra was allotted 650 shares of Sun Systems Ltd in the initial public offer, at the face value of Rs.10 per share. In 2007, Sun Systems declared the bonus at the rate of 3: 13. In 2008, the company again declared the bonus at the rate of 2: 4. In 2009, the company declared a dividend of 12.5%. How much dividend does Raveendra get in 2009 as a percentage of his initial investment?

- A.
24.5%

- B.
23.9%

- C.
24.1%

- D.
23%

Answer: Option D

**Explanation** :

∴ Dividend in 2009 = 1200 × 12.5 × $\frac{10}{100}$ = 1500

∴ Dividend as a percentage of initial investment = $\frac{1500}{6500}$ × 100 = 23%

Hence, option 4.

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**IIFT 2009 QA | Arithmetic - Percentage**

A cylindrical overhead tank is filled by two pumps – P1 and P2. P1 can fill the tank in 8 hours while P2 can fill the tank in 12 hours. There is a pipe P3 which can empty the tank in 8 hours. Both the pumps are opened simultaneously. The supervisor of the tank, before going out on a work, sets a timer to open P3 when the tank is half filled so that tank is exactly filled up by the time he is back. Due to technical fault P3 opens when tank is one third filled. If the supervisor comes back as per the plan what percent of the tank is still empty?

- A.
25% tank

- B.
12% tank

- C.
10% tank

- D.
None of the above

Answer: Option C

**Explanation** :

Time required by P1 and P2 to fill the tank = $\frac{8\times 12}{8+12}$ = $\frac{24}{5}$ hrs.

∴ Time required by P1 and P2 to fill half the tank = $\frac{12}{5}$hrs.

The remaining half of the tank will be filled by P1 and P2 along with P3 with the rate of P2 only, because P3 will empty the tank with the rate of P1.

∴ Time required to fill the remaining half of the tank = 12/2 = 6 hrs.

∴ Time after which supervisor return as per the plan = $\frac{12}{5}$ + 6 = $\frac{42}{5}$ hrs.

Time required by P1 and P2 to fill $\frac{1}{3}$rd of the tank = $\frac{8}{5}$ hrs.

Time required to fill the remaining $\frac{2}{3}$rd of the tank (rate of P2) = 12 × $\frac{2}{3}$ = 8 hrs.

∴ Time after which tank will be full = $\frac{8}{5}$ + 8 = $\frac{48}{5}$ hrs.

∴ Difference in time = $\frac{48}{5}$ - $\frac{42}{5}$ = $\frac{6}{5}$ hrs.

With the rate of P2 (i.e. in 12 hrs.), 1 tank can be filled.

∴ In $\frac{6}{5}$ hrs. the part of the tank still remaining empty = $\frac{6}{5}$ × $\frac{1}{12}$ = $\frac{1}{10}$ = 10%

Hence, option 3.

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