Arithmetic - Percentage - Previous Year CAT/MBA Questions

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26. CAT 2017 QA Slot 2 | Arithmetic - Percentage CAT Question

In a village, the production of food grains increased by 40% and the per capita production of food grains increased by 27% during a certain period. The percentage by which the population of the village increased during the same period is nearest to

(a)
16
(b)
13
(c)
10
(d)
7

Answer: Option C

Video Explanation

Text Explanation :

Total Food Production = Total Population × Per Capita Food Production

Let the initial population be ‘p’ and the initial per capita food production be ‘c’

If f is the total food production, f = pc

This can also be rewritten as p = $\frac{f}{c}$

Now, as per given information, f increases to 1.4f and c increases to 1.27c.

So, if p₁ is population after increase.

1.4f = p₁(1.27c)

$\frac{1.4 f}{1.27 c}$ = p₁

⇒ p₁ = $(\frac{1.4}{1.27}) (\frac{f}{c})$

or p₁ = $(\frac{1.4}{1.27})$ (p) [ $(∵ p = \frac{f}{c})$ ]

$\Rightarrow$ p₁ ≃ 1.1p

This means that the population of the village has increased by approximately 10%.

Hence, option (c).

Answer the next 2 questions based on the information given below.

Shabnam is considering three alternatives to invest her surplus cash for a week. She wishes to guarantee maximum returns on her investment. She has three options, each of which can be utilized fully or partially in conjunction with others.

Option A: Invest in a public sector bank. It promises a return of +0.10%

Option B: Invest in mutual funds of ABC Ltd. A rise in the stock market will result in a return of +5%, while a fall will entail a return of –3%

Option C: Invest in mutual funds of CBA Ltd. A rise in the stock market will result in a return of –2.5%, while a fall will entail a return of +2%

27. CAT 2007 QA | Arithmetic - Percentage CAT Question

The maximum guaranteed return to Shabnam is:

(a)
0.25%
(b)
0.10%
(c)
0.20%
(d)
0.15%
(e)
0.30%

28. CAT 2007 QA | Arithmetic - Percentage CAT Question

What strategy will maximize the guaranteed return to Shabnam?

(a)
100% in option A
(b)
36% in option B and 64% in option C
(c)
64% in option B and 36% in option C
(d)
1/3 in each of the three options
(e)
30% in option A, 32% in option B and 38% in option C

29. CAT 2007 QA | Arithmetic - Percentage CAT Question

Each question is followed by two statements, I and II. Answer each question using the following instructions:

Mark (1) if the question can be answered by using statement I alone but not by using statement II alone.
Mark (2) if the question can be answered by using statement II alone but not by using statement I alone.
Mark (3) if the question can be answered by using either of the statements alone.
Mark (4) if the question can be answered by using both the statements together but not by either of the statements alone.
Mark (5) if the question cannot be answered by using any of the statements.

Thirty percent of the employees of a call centre are males. Ten per cent of the female employees have an engineering background. What is the percentage of male employees with engineering background?

I. Twenty five per cent of the employees have engineering background.
II. Number of male employees having an engineering background is 20% more than the number of female employees having an engineering background.

(a)
1
(b)
2
(c)
3
(d)
4
(e)
5

Answer the following question based on the information given below.

In an examination, there are 100 questions divided into three groups A, B and C such that each group contains at least one question. Each question in group A carries 1 mark, each question in group B carries 2 marks and each question in group C carries 3 marks. It is known that the questions in group A together carry at least 60% of the total marks.

30. CAT 2004 QA | Arithmetic - Percentage CAT Question

If group B contains 23 questions, then how many questions are there in group C?

(a)
1
(b)
2
(c)
3
(d)
Cannot be determined

Answer: Option A

Video Explanation

Text Explanation :

Let there be a, b and c questions in groups A, B and C respectively.

Then, a + b + c =100

Total marks = a + 2b + 3c

Also, $\frac{a}{a + 2 b + 3 c} \geq \frac{60}{100}$

b = 23

⇒ a + c = 77

⇒ a = 77 – c

⇒ $\frac{a}{a + 46 + 3 c} \geq 0.6$

⇒ a ≥ 0.6a + 27.6 + 1.8c

⇒ 4a ≥ 276 + 18c

⇒ a ≥ 69 + 4.5c

⇒ a – 4.5c ≥ 69

⇒ 77 – c – 4.5c ≥ 69

⇒ 77 ≥ 69 + 5.5c

⇒ c ≤ 8/5.5

⇒ c = 1

Hence, option (a).

Alternatively,
Evaluating options,

If C has 1 question then B and A have 23 and 76 questions respectively.
The total number of marks = 125
⇒ Group A has 60.8% marks.
⇒ Option (a) is possible.

If C has 2 questions then B and A have 23 and 75 questions respectively.
The total number of marks = 127
⇒ Group A has 59.05% marks.
⇒ Option (b) is not possible.

If C has 3 questions then B and A have 23 and 74 questions respectively.
The total number of marks = 129
⇒ Group A has 57.36% marks.
⇒ Option (c) is not possible.

Hence, option (a).

31. CAT 2004 QA | Arithmetic - Percentage CAT Question

If group C contains 8 questions and group B carries at least 20% of the total marks, which of the following best describes the number of questions in group B?

(a)
11 or 12
(b)
12 or 13
(c)
13 or 14
(d)
14 or 15

Answer: Option C

Video Explanation

Text Explanation :

c = 8
∴ a + b = 92 ...(1)

Also, $\frac{2 b}{a + 2 b + 3 c} \geq 0.2$

⇒ $\frac{2 b}{92 - b + 2 b + 24} \geq 0.2$

⇒ 2b ≥ 23.2 + 0.2b

⇒ $b \geq \frac{232}{18}$

⇒ b ≥ 13 ...(2)

Also, as group A carries at least 60% of the total marks,

$\frac{a}{a + 2 b + 3 c} \geq 0.6$

⇒ $\frac{a}{a + 2 (92 - a) + 24} \geq 0.6$

⇒ aa ≥ 0.6a + 110.4 - 1.2a + 14.4

⇒ 1.6a ≥ 124.8

⇒ a ≥ 78 ...(3)

From (1), (2) and (3)
⇒ b can be 13 or 14.

Hence, option (c).

Alternately,
Consider options.

For c = 8 and b = 11, a = 81. The total marks = 127.
Group B has 17.32% marks, which is not possible.

For c = 8 and b = 12, a = 80. The total marks = 128.
Group B has 18.75% marks, which is not possible.

For c = 8 and b = 13, a = 79. The total marks = 129.
Group B has 20.15% marks and group A has 61.24% marks, which is possible.

For c = 8 and b = 14, a = 78. The total marks = 130.
Group B has 21.53% marks and group A has 60% marks, which is possible.

For c = 8 and b = 15, a = 77. The total marks = 131.
Group B has 22.9% marks and group A has 58.77 marks, which is not possible.

Hence, option (c).

32. CAT 2004 QA | Arithmetic - Percentage CAT Question

Each question is followed by two statements, A and B. Answer each question using the following instructions

Choose 1 if the question can be answered by using one of the statements alone but not by using the other statement alone.
Choose 2 if the question can be answered by using either of the statements alone.
Choose 3 if the question can be answered by using both statements together but not by either statement alone.
Choose 4 if the question cannot be answered on the basis of the two statements.

Zakib spends 30% of his income on his children’s education, 20% on recreation and 10% on healthcare. The corresponding percentages for Supriyo are 40%, 25%, and 13%. Who spends more on children’s education?

A. Zakib spends more on recreation than Supriyo.
B. Supriyo spends more on healthcare than Zakib.

(a)
1
(b)
2
(c)
3
(d)
4

Answer: Option A

Text Explanation :

Let Zakib’s and Supriyo’s incomes be z and s respectively.

Consider statement A:

0.2z > 0.25s

$∴ \frac{z}{s} < 1.25$

∴ z > s

Zakib and Supriyo spend 0.3z and 0.4s on children’s education.

$\frac{0.3 z}{0.4 s} > 0.3 \times \frac{1.25}{0.4} \frac{0.3 z}{0.4 s} > 0.9375$

∴ Statement A alone is not sufficient.

Consider statement B:

0.13s > 0.1z

$∴ \frac{z}{s} < 1.3$

$\frac{0.3 z}{0.4 s} < 0.975$

∴ Supriyo spends more than Zakib on children’s education.

∴ Statement B alone is sufficient.

Hence, option (a).

33. CAT 2003 QA - Leaked | Arithmetic - Percentage CAT Question

At the end of year 1998, Shepard bought nine dozen goats. Henceforth, every year he added p% of the goats at the beginning of the year and sold q% of the goats at the end of the year where p > 0 and q > 0. If Shepard had nine dozen goats at the end of year 2002, after making the sales for that year, which of the following is true?

(a)
p = q
(b)
p < q
(c)
p > q
(d)
p = q/2

34. CAT 2001 QA | Arithmetic - Percentage CAT Question

A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than 50% marks is

(a)
2
(b)
3
(c)
4
(d)
5

Answer: Option C

Video Explanation

Text Explanation :

Let the maximum marks for each of the paper = 100

∴ Total maximum marks = 5 × 100 = 500

Let the marks obtained by the student be 6x, 7x, 8x, 9x and 10x in each of the paper.

∴ 6x + 7x + 8x + 9x + 10x = 60% of 500

40x = 300

∴ x = 7.5

∴ The marks obtained in each of the paper will be 45, 52.5, 60, 67.5 and 75.

∴ In 4 papers he got more than 50% marks.

Hence, option (c).

Alternatively

Average of 6, 7, 8, 9 and 10 = $\frac{6 + 7 + 8 + 9 + 10}{5} = 8$

∵ 60% of marks = 8

∴ 50% of marks = $\frac{8}{60} \times 50$

= 6.67

∴ The score in 4 of the subjects is more than 6.67.

Hence, option (c).

35. CAT 2001 QA | Arithmetic - Percentage CAT Question

A college has raised 75% of the amount it needs for a new building by receiving an average donation of Rs. 600 from the people already solicited. The people already solicited represent 60% of the people the college will ask for donations. If the college is to raise exactly the amount needed for the new building, what should be the average donation from the remaining people to be solicited?

(a)
Rs. 300
(b)
Rs. 250
(c)
Rs. 400
(d)
Rs. 500

36. CAT 2001 QA | Arithmetic - Percentage CAT Question

The owner of an art shop conducts his business in the following manner: Every once in a while he raises his prices by X%, then a while later he reduces all the new prices by X%. After one such up-down cycle, the price of a painting decreased by Rs. 441. After a second up-down cycle the painting was sold for Rs. 1,944.81. What was the original price of the painting?

(a)
Rs. 2,756.25
(b)
Rs. 2,256.25
(c)
Rs. 2,500
(d)
Rs. 2,000

Answer: Option A

Video Explanation

Text Explanation :

As the price decreases after the first cycle, it has to decrease after the second cycle too. Also the decrease in the second cycle will be less than 441 as the original price for the second cycle is less than the original price for the first cycle.

∴ Price after First Cycle – 1944.81 < 441

Now we consider options.

So, options 2 and 4 are eliminated.

As the percentage change in the price in the first and second cycles is equal,

$\frac{O r i g i n a l p r i c e}{D e c r e a s e i n p r i c e a f t e r t h e f i r s t c y c l e}$ should be equal to

$\frac{P r i c e a f t e r f i r s t c y c l e}{D e c r e a s e i n p r i c e a f t e r t h e s e c o n d c y c l e}$

Only option 1 satisfies this.

Hence, option (a).

37. CAT 2001 QA | Arithmetic - Percentage CAT Question

Choose 1; if the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.
Choose 2; if the question can be answered by using either statement alone.
Choose 3; if the question can be answered by using both statements together, but cannot be answered using either statement alone.
Choose 4; if the question cannot be answered even by using both statements together.

Is Country X's GDP higher than country Y's GDP?

GDPs of the countries X and Y have grown over the past five years at compounded annual rate of 5% and 6% respectively.
Five years ago, GDP of country X was higher than that of country Y.

(a)
1
(b)
2
(c)
3
(d)
4

38. CAT 2000 QA | Arithmetic - Percentage CAT Question

The table below shows the age-wise distribution of the population of Reposia. The number of people aged below 35 years is 400 million.

If the ratio of females to males in the ‘below 15 years’ age group is 0.96, then what is the number of females (in millions) in that age group?

(a)
82.8
(b)
90.8
(c)
80.0
(d)
90.0

Answer: Option B

Text Explanation :

Population below 35 years of age = 30 + 17.75 + 17 = 64.75% of the total population = 400 million

∴ 30% of the total population $= \frac{30 \times 400}{64.75}$ million ≈ 185 million

The ratio of females to males in the ‘below 15 years’ age group is 0.96.

i.e. if the total population is 196, then there are 96 females.

Approximately, the number of females (in millions) in the ‘below 15 years’ age group

$= \frac{185 \times 96}{196} = 90.6$

Hence, option (b).

39. CAT 1999 QA | Arithmetic - Percentage CAT Question

Forty per cent of the employees of a certain company are men, and 75% of the men earn more than Rs. 25,000 per year. If 45% of the company’s employees earn more than Rs. 25,000 per year, what fraction of the women employed by the company earn less than or equal to Rs. 25,000 per year?

(a)
$\frac{2}{11}$
(b)
$\frac{1}{4}$
(c)
$\frac{1}{3}$
(d)
$\frac{3}{4}$

Answer: Option D

Video Explanation

Text Explanation :

Men Women
40% 60%

Out of 40% men, 75% earn more than Rs. 25,000.

Hence, 30% of the company (men) earn more than Rs. 25,000.

But, in all 45% of the employees earn more than Rs. 25,000.

Hence, among women 15% earn more than Rs. 25,000 and the remaining (60 – 15)% earn less than or equal to Rs. 25,000.

Therefore, the fraction of women = $\frac{45}{60} = \frac{3}{4}$

Hence, option (d).

40. CAT 1998 QA | Arithmetic - Percentage CAT Question

One bacterium splits into eight bacteria of the next generation. But due to environmental condition only 50% survives and remaining 50% dies after producing next generation. If the seventh generation number is 4,096 million, what is the number in first generation?

(a)
1 million
(b)
2 million
(c)
4 million
(d)
8 million

Answer: Option A

Video Explanation

Text Explanation :

Let there be x bacteria in the first generation i.e. n₁ = x

∴ n₂ = 8x, but only 50% survives

⇒ n_{2, survived} = $\frac{8 x}{2} = 4 x$

n₃ = 8(4x), but only 50% survives

n_{3, survived} = 4² x

n_{3, survived} = 4^7-1 x = 4096 million

∴ x = 1 million

41. CAT 1998 QA | Arithmetic - Percentage CAT Question

Direction: Each question is followed by two statements, I and II. Answer the questions based on the statements and mark the answer as
1. if the question can be answered with the help of any one statement alone but not by the other statement.
2. if the question can be answered with the help of either of the statements taken individually.
3. if the question can be answered with the help of both statements together.
4. if the question cannot be answered even with the help of both statements together.

Radha and Rani appeared in an examination. What was the total number of questions?
I. Radha and Rani together solved 20% of the paper.
II. Radha alone solved $\frac{3}{5}$ of the paper solved by Rani.

Backspace

7 8 9 4 5 6 1 2 3 0 . -

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42. CAT 1997 QA | Arithmetic - Percentage CAT Question

A student gets an aggregate of 60% marks in five subjects in the ratio 10 : 9 : 8 : 7 : 6. If the passing marks are 50% of the maximum marks and each subject has the same maximum marks, in how many subjects did he pass the examination?

(a)
2
(b)
3
(c)
4
(d)
5

Answer: Option C

Video Explanation

Text Explanation :

Let his marks be 100, 90, 80, 70 and 60 in the five subjects. Hence, totally he has scored 400 marks. This constitutes only 60% of the total marks. Hence, total marks = $\frac{400}{0.6} = 667,$ Since the total marks in each subject is the same, hence maximum marks in each subject will be $(\frac{667}{5})$ ≃ 133. Out of this 50% is the passing marks. In other words, to pass in a subject he needs to score 66.5 marks. We can see that only in
one subject he scored less than this, viz. 60. Hence, he passed in 4 subjects.

43. CAT 1997 QA | Arithmetic - Percentage CAT Question

A man earns x% on the first Rs. 2,000 and y% on the rest of his income. If he earns Rs. 700 from income of Rs. 4,000 and Rs. 900 from if his income is Rs. 5,000, find x%.

(a)
20%
(b)
15%
(c)
25%
(d)
None of these

Answer: Option B

Video Explanation

Text Explanation :

The two equations can be written
2000 $(\frac{x}{100})$ + 2000 $(\frac{y}{100})$ = 700 and 2000 $(\frac{x}{100})$ + 3000 $(\frac{y}{100}) = 900$

The equations can be simplified to x + y = 35 and 2x + 3y = 90. Solving these two equations simultaneously, we get x = 15%.

44. CAT 1996 QA | Arithmetic - Percentage CAT Question

I bought 5 pens, 7 pencils and 4 erasers. Rajan bought 6 pens, 8 erasers and 14 pencils for an amount which was half more what I had paid. What per cent of the total amount paid by me was paid for the pens?

(a)
37.5%
(b)
62.5%
(c)
50%
(d)
None of these

45. CAT 1996 QA | Arithmetic - Percentage CAT Question

The price of a Maruti car rises by 30% while the sales of the car come down by 20%. What is the percentage change in the total revenue?

(a)
-4%
(b)
-2%
(c)
+4%
(d)
+2%

Answer: Option C

Video Explanation

Text Explanation :

This can simply be solved by multiplying the two multiplication factors to get the effective multiplication factor. e.g. multiplication factor for 30% increase = 1.30. Multiplication factor for 20% decrease = 0.8. Hence, 1.30 × 0.8 = 1.04. This multiplication factor (i.e. 1.04) indicates that there is a 4% increase in total revenue. So the answer is +4.

Alternative method:
By using the formula x + y + $\frac{x y}{100}$

∴ x = +30%; y = – 20%

⇒ 30 + 60 + $\frac{50 (- 20)}{100}$

= 30 – 20 – 6 = +4%

46. CAT 1995 QA | Arithmetic - Percentage CAT Question

Ram purchased a flat at Rs.1 lakh and Prem purchased a plot of land worth Rs.1.1 lakh. The respective annual rates at which the prices of the flat and the plot increased were 10% and 5%. After two years they exchanged their belongings and one paid the other the difference. Then

(a)
Ram paid Rs.275 to Prem
(b)
Ram paid Rs.475 to Prem
(c)
Ram paid Rs.375 to Prem
(d)
Prem paid Rs.475 to Ram

47. CAT 1995 QA | Arithmetic - Percentage CAT Question

A person who has a certain amount with him goes to market. He can buy 50 oranges or 40 mangoes. He retains 10% of the amount for taxi fares and buys 20 mangoes and of the balance he purchases oranges. Number of oranges he can purchase is

(a)
36
(b)
40
(c)
15
(d)
20

48. CAT 1995 QA | Arithmetic - Percentage CAT Question

$\frac{2}{5}$ of the voters promise to vote for P and the rest promised to vote for Q. Of these, on the last day 15% of the voters went back of their promise to vote for P and 25% of voters went back of their promise to vote for Q, and P lost by 2 votes. Then the total number of voters is

(a)
100
(b)
110
(c)
90
(d)
95

49. CAT 1995 QA | Arithmetic - Percentage CAT Question

The rate of inflation was 1000%. Then what will be the cost of an article, which costs 6 units of currency now, 2 years from now?

(a)
666
(b)
660
(c)
720
(d)
726

Answer: Option D

Video Explanation

Text Explanation :

Required cost = $6 {[1 + \frac{1000}{100}]}^{2}$ = 6(11)² = 121 × 6 = 726.

50. CAT 1994 QA | Arithmetic - Percentage CAT Question

The number of votes not cast for the Praja Party increased by 25% in the National General Election over those not cast for it in the previous Assembly Polls, and the Praja Party lost by a majority twice as large as that by which it had won the Assembly Polls. If a total 2,60,000 people voted each time. How many voted for the Praja Party in the Assembly Elections.

(a)
1,10,000
(b)
1,50,000
(c)
1,40,000
(d)
1,20,000

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