# 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).

Workspace:

**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).

Workspace:

**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).

Workspace:

**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).

Workspace:

**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).

Workspace:

**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.

Workspace:

**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.

Workspace:

**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.

Workspace:

**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.

Workspace:

**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.

Workspace:

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