Previous Year CAT Questions for Arithmetic - Ratio, Proportion & Variation

1. CAT 2021 QA Slot 1 | Arithmetic - Ratio, Proportion & Variation

The amount Neeta and Geeta together earn in a day equals what Sita alone earns in 6 days. The amount Sita and Neeta together earn in a day equals what Geeta alone earns in 2 days. The ratio of the daily earnings of the one who earns the most to that of the one who earns the least is

A.
7 : 3
B.
3 : 2
C.
11 : 3
D.
11 : 7

2. CAT 2021 QA Slot 2 | Arithmetic - Ratio, Proportion & Variation

Anil, Bobby and Chintu jointly invest in a business and agree to share the overall profit in proportion to their investments. Anil’s share of investment is 70%. His share of profit decreases by ₹ 420 if the overall profit goes down from 18% to 15%. Chintu’s share of profit increases by ₹ 80 if the overall profit goes up from 15% to 17%. The amount, in INR, invested by Bobby is

A.
2000
B.
2400
C.
2200
D.
1800

3. CAT 2021 QA Slot 3 | Arithmetic - Ratio, Proportion & Variation

One part of a hostel’s monthly expenses is fixed, and the other part is proportional to the number of its boarders. The hostel collects ₹ 1600 per month from each boarder. When the number of boarders is 50, the profit of the hostel is ₹ 200 per boarder, and when the number of boarders is 75, the profit of the hostel is ₹ 250 per boarder. When the number of boarders is 80, the total profit of the hostel, in INR, will be

A.
20000
B.
20200
C.
20800
D.
20500

4. CAT 2020 QA Slot 2 | Arithmetic - Ratio, Proportion & Variation

A sum of money is split among Amal, Sunil and Mita so that the ratio of the shares of Amal and Sunil is 3 : 2, while the ratio of the shares of Sunil and Mita is 4 : 5. If the difference between the largest and the smallest of these three shares is Rs 400, then Sunil’s share, in rupees, is

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5. CAT 2019 QA Slot 2 | Arithmetic - Ratio, Proportion & Variation

In an examination, Rama's score was one-twelfth of the sum of the scores of Mohan and Anjali. After a review, the score of each of them increased by 6. The revised scores of Anjali, Mohan, and Rama were in the ratio 11 : 10 : 3. Then Anjali's score exceeded Rama's score by

A.
26
B.
32
C.
24
D.
35

6. CAT 2018 QA Slot 1 | Arithmetic - Ratio, Proportion & Variation

Raju and Lalitha originally had marbles in the ratio 4 : 9. Then Lalitha gave some of her marbles to Raju. As a result, the ratio of the number of marbles with Raju to that with Lalitha became 5 : 6. What fraction of her original number of marbles was given by Lalitha to Raju?

A.
6/19
B.
1/5
C.
7/33
D.
1/4

Answer: Option C

Explanation :

Let Raju and Lalitha originally had (4x) and (9x) marbles. Later Lalitha gave (y) marbles to Raju.

Therefore, $\frac{4 x + y}{9 x - y}$ = $\frac{5}{6}$

Solving this, we get

y = 21x/11

The required fraction = $\frac{\frac{21}{11} x}{9 x}$ = $\frac{7}{33}$

Hence, option 3.

7. CAT 2018 QA Slot 2 | Arithmetic - Ratio, Proportion & Variation

The scores of Amal and Bimal in an examination are in the ratio 11 : 14. After an appeal, their scores increase by the same amount and their new scores are in the ratio 47 : 56. The ratio of Bimal’s new score to that of his original score is

A.
4 : 3
B.
3 : 2
C.
8 : 5
D.
5 : 4

Answer: Option A

Explanation :

Suppose the original scores of Amal and Bimal are 11x and 14x respectively.

Suppose ‘y’ is the increase in their marks.

Therefore the new marks of Amal and Bimal are ‘11x + y’ and ‘14x + y’ respectively.

Therefore, we have $\frac{11 x + y}{14 x + y} = \frac{47}{56}$

∴ 616x + 56y = 658x + 47y

Solving for x and y, we get 14x = 3y

Therefore Bimal’s old marks = 14x = 3y and his new marks = 14x + y = 4y. Therefore the required ratio = 4:3.

Hence, option 1.

8. CAT 2017 QA Slot 1 | Arithmetic - Ratio, Proportion & Variation

Suppose, C₁, C₂, C₃, C₄, and C₅ are five companies. The profits made by C₁, C₂, and C₃ are in the ratio 9 : 10 : 8 while the profits made by C₂, C₄, and C₅ are in the ratio 18 : 19 : 20. If C₅ has made a profit of Rs 19 crore more than C1, then the total profit (in Rs) made by all five companies is:

A.
438 crore
B.
435 crore
C.
348 crore
D.
345 crore

9. CAT 2017 QA Slot 1 | Arithmetic - Ratio, Proportion & Variation

A stall sells popcorn and chips in packets of three sizes: large, super, and jumbo. The numbers of large, super, and jumbo packets in its stock are in the ratio 7 : 17 : 16 for popcorn and 6 : 15 : 14 for chips. If the total number of popcorn packets in its stock is the same as that of chips packets, then the numbers of jumbo popcorn packets and jumbo chips packets are in the ratio:

A.
1 : 1
B.
8 : 7
C.
4 : 3
D.
6 : 5

Answer: Option A

Explanation :

Let the total number of popcorn packets in stock be T.

Total number of chips packets in stock = T

Required ratio = $\frac{16}{40} T : \frac{14}{35} T$ = 1 : 1.

Hence, option 1.

10. CAT 2017 QA Slot 2 | Arithmetic - Ratio, Proportion & Variation

If a, b, c are three positive integers such that a and b are in the ratio 3 : 4 while b and c are in the ratio 2 : 1, then which one of the following is a possible value of (a + b + c)?

A.
201
B.
205
C.
207
D.
210

11. CAT 2006 QA | Arithmetic - Ratio, Proportion & Variation

If $\frac{a}{b} = \frac{1}{3}, \frac{b}{c} = 2, \frac{c}{d} = \frac{1}{2}, \frac{d}{e} = 3$ and $\frac{e}{f} = \frac{1}{4}$ then what is the value of $\frac{a b c}{d e f}$ ?

A.
$\frac{3}{8}$
B.
$\frac{27}{8}$
C.
$\frac{3}{4}$
D.
$\frac{27}{4}$
E.
$\frac{1}{4}$

Answer: Option A

Explanation :

$\frac{a}{d} = \frac{a}{b} \times \frac{b}{c} \times \frac{c}{d} = \frac{1}{3} \times 2 \times \frac{1}{2} = \frac{1}{3}$

$\frac{b}{e} = \frac{b}{c} \times \frac{c}{d} \times \frac{d}{e} = 2 \times \frac{1}{2} \times 3 = 3$

$\frac{c}{f} = \frac{c}{d} \times \frac{d}{e} \times \frac{e}{f} = \frac{1}{2} \times 3 \times \frac{1}{4} = \frac{3}{8}$

$∴ \frac{a b c}{d e f} = \frac{1}{3} \times 3 \times \frac{3}{8} = \frac{3}{8}$

Hence, option (c).

12. CAT 2006 QA | Arithmetic - Ratio, Proportion & Variation

What is the weight of Praja‘s luggage?

A.
20 kg
B.
25 kg
C.
30 kg
D.
35 kg
E.
40 kg

13. CAT 2006 QA | Arithmetic - Ratio, Proportion & Variation

What is the free luggage allowance?

A.
10 kg
B.
15 kg
C.
20 kg
D.
25 kg
E.
30 kg

14. CAT 2004 QA | Arithmetic - Ratio, Proportion & Variation

If $\frac{a}{b + c} = \frac{b}{c + a} = \frac{c}{a + b} = r,$ then r cannot take any value except _________.

A.
$\frac{1}{2}$
B.
-1
C.
$\frac{1}{2}$ or -1
D.
$- \frac{1}{2}$ or -1

Answer: Option C

Explanation :

$\frac{a}{b + c} = \frac{b}{c + a} = \frac{c}{c + a} = r$

By property of equal ratios,

$\frac{a + b + c}{b + c + c + a + a + b} = r$

$∴ \frac{a + b + c}{2 (a + b + c)} = r$

Assuming (a + b + c ≠ 0),

∴ r = $\frac{1}{2}$

If a + b + c = 0, a = –(b + c)

Then, $r = \frac{a}{b + c} = \frac{- (b + c)}{(b + c)} = - 1$

Hence, option 3.

15. CAT 2003 QA - Retake | Arithmetic - Ratio, Proportion & Variation

In a coastal village, every year floods destroy exactly half of the huts. After the flood water recedes, twice the number of huts destroyed are rebuilt. The floods occurred consecutively in the last three years namely 2001, 2002 and 2003. If floods are again expected in 2004, the number of huts expected to be destroyed is:

A.
Less than the number of huts existing at the beginning of 2001.
B.
Less than the total number of huts destroyed by floods in 2001 and 2003.
C.
Less than the total number of huts destroyed by floods in 2002 and 2003.
D.
More than the total number of huts built in 2001 and 2002.

16. CAT 2003 QA - Retake | Arithmetic - Ratio, Proportion & Variation

Let a, b, c, d and e be integers such that a = 6b = 12c, and 2b = 9d = 12e. Then which of the following pairs contains a number that is not an integer?

A.
$[\frac{a}{27}, \frac{b}{e}]$
B.
$[\frac{a}{36}, \frac{c}{e}]$
C.
$[\frac{a}{12}, \frac{b d}{18}]$
D.
$[\frac{a}{6}, \frac{c}{d}]$

Answer: Option D

Explanation :

Since a = 6b = 12c and 2b = 9d = 12e

∴ a : b : c = 12 : 2 : 1 and b : d : e = 18 : 4 : 3

∴ a : b : c : d : e = 108 : 18 : 9 : 4 : 3

∴ a = 108k; b = 18k; c = 9k; d = 4k and e = 3k where ‘k’ is an integer

Option 1 is: $(\frac{a}{27}, \frac{b}{e})$ = (4k, 6)

Option 2 is: $(\frac{a}{36}, \frac{c}{e})$ = (3k, 3)

Option 3 is: $(\frac{a}{12}, \frac{b d}{18})$ = (9k, 4k²)

Option 4 is: $(\frac{a}{6}, \frac{c}{d}) = (18 k, \frac{9}{4})$

The 4th option contains $\frac{9}{4}$ , which is not an integer.

Hence, option 4.

17. CAT 2002 QA | Arithmetic - Ratio, Proportion & Variation

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

Answer (1) if the question can be solved by any one of the statements, but not the other one.
Answer (2) if the question can be solved by using either of the two statements.
Answer (3) if the question can be solved by using both the statements together and not by any one of them.
Answer (4) if the question cannot be solved with the help of the given data and more data is required.

A sum of Rs. 38,500 was divided among Jagdish, Punit and Girish. Who received the minimum amount?

A. Jagdish received 2/9 of what Punit and Girish together received.
B. Punit received 3/11 of what Jagdish and Girish together received.

A.
1
B.
2
C.
3
D.
4

Answer: Option C

Explanation :

Consider statement A:

Jagdish : (Punit + Girish) = 2 : 9

∴ Jagdish's share = $\frac{2}{11}$ × Total = 18.18% of the total

However, we don’t know the percentage distribution between Punit and Girish.

∴ Statement A alone is not sufficient.

Consider statement B:

Punit : (Jagdish + Girish) = 3 : 11

∴ Punit's share = $\frac{3}{14}$ × Total = 21.4% of the total

However, we do not know the percentage distribution between Jagdish and Girish.

∴ Statement B alone is not sufficient.

Consider both statements together:

Jagdish = 18.18% of the total amount

Punit = 21.4% of the total amount

Girish = 100 − 18.18 − 21.4 = 60.42% of the total amount

∴ Jagdish received the minimum amount.

Hence, option 3.

18. CAT 2001 QA | Arithmetic - Ratio, Proportion & Variation

Three friends, returning from a movie, stopped to eat at a restaurant. After dinner, they paid their bill and noticed a bowl of mints at the front counter. Sita took 1/3 of the mints, but returned four because she had a momentary pang of guilt. Fatima then took 1/4 of what was left but returned three for similar reasons. Eswari then took half of the remainder but threw two back into the bowl. The bowl had only 17 mints left when the raid was over. How many mints were originally in the bowl?

A.
38
B.
31
C.
41
D.
None of these

Answer: Option D

Explanation :

Sita takes 1/3rd of the total mints which implies that the total number of mints in the bowl should be a multiple of 3. None of the options is a multiple of 3.

Hence, option 4.

Alternatively

This problem can be best solved by working backwards.

Number of mints before Eswari = (17 − 2) × 2 = 30

∴ Number of mints before a Fatima = $\frac{(30 - 3) \times 4}{3} = 36$

∴ Number of mints before Sita = $\frac{(36 - 4) \times 3}{2} = 48$

∴ Total number of mints in the bowl = 48

Hence, option 4.

19. CAT 2000 QA | Arithmetic - Ratio, Proportion & Variation

A truck travelling at 70 kilometres per hour uses 30% more diesel to travel a certain distance than it does when it travels at the speed of 50 kilometres per hour. If the truck can travel 19.5 kilometres on a litre of diesel at 50 kilometres per hour, how far can the truck travel on 10 litres of diesel at a speed of 70 kilometres per hour?

A.
130
B.
140
C.
150
D.
175

20. CAT 1999 QA | Arithmetic - Ratio, Proportion & Variation

The speed of a railway engine is 42 kmph when no compartment is attached, and the reduction in speed is directly proportional to the square root of the number of compartments attached. If the speed of the train carried by this engine is 24 kmph when 9 compartments are attached, the maximum number of compartments that can be carried by the engine is

A.
49
B.
48
C.
46
D.
47

Answer: Option B

Explanation :

18 ∝ $\sqrt{9}$

42 ∝ $\sqrt{x};$ Here x = number of compartments

$\frac{18}{42} = \frac{\sqrt{9}}{\sqrt{x}}$

Simplifying, x = 49, but this is with reference to maximum speed. Hence number of compartments would be one less in order to run i.e. 48.

Hence, option (b).

21. CAT 1999 QA | Arithmetic - Ratio, Proportion & Variation

Total expenses of a boarding house are partly fixed and partly varying linearly with the number of boarders. The average expense per boarder is Rs. 700 when there are 25 boarders and Rs. 600 when there are 50 boarders. What is the average expense per boarder when there are 100 boarders?

A.
550
B.
580
C.
540
D.
570

22. CAT 1998 QA | Arithmetic - Ratio, Proportion & Variation

I have one-rupee coins, 50-paisa coins and 25-paisa coins. The number of coins are in the ratio 2.5 : 3 : 4. If the total amount with me is Rs. 210, find the number of one-rupee coins.

A.
90
B.
85
C.
100
D.
105

Answer: Option D

Explanation :

Since the number of coins are in the ratio 2.5 : 3 : 4, the values of the coins will be in the ratio
(1 × 2.5) : (0.5 × 3) : (0.25 × 4) = 2.5 : 1.5 : 1 or 5 : 3 : 2
Since they totally amount to Rs. 210, if the value of each type of coins are assumed to be 5x, 3x and 2x, the average value per coin will be $\frac{210}{10 x}$ .

So the total value of one-rupee coins will be $5 \times (\frac{210}{10 x})$ = Rs. 105

So the total number of one-rupee coins will be 105.

23. CAT 1998 QA | Arithmetic - Ratio, Proportion & Variation

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.

What is the value of ‘a’?
I. Ratio of a and b is 3 : 5, where b is positive.
II. Ratio of 2a and b is $\frac{12}{10},$ where a is positive.

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24. CAT 1997 QA | Arithmetic - Ratio, Proportion & Variation

A student instead of finding the value of $\frac{7}{8}$ of a number, found the value of $\frac{7}{18}$ of the number. If his answer differed from the actual one by 770, find the number.

A.
1584
B.
2520
C.
1728
D.
1656

Answer: Option A

Explanation :

This equation is very straightforward. If the number is 'x', then $\frac{7 x}{8} - \frac{7 x}{18} = 770 .$ On solving this equation, we get x = 1584. Hint: Students please note that if the difference in $\frac{7}{8}$ and $\frac{7}{18}$ of a number is 770, then the difference in $\frac{1}{8}$ and $\frac{1}{18}$ of the number should be 110. If we express this as an equation, we get $\frac{x}{8} - \frac{x}{18} = 110$

or 10x = 110 × 18 × 8
or x = 11 × 18 × 8
You can further proceed from here in two ways: (i) the last digit of the required answer should be (1 × 8 × 8) = 4, (ii) number should be divisible by 11. In both cases, the answer that is obtained from the given choices is 1584.

25. CAT 1997 QA | Arithmetic - Ratio, Proportion & Variation

The value of each of a set of coins varies as the square of its diameter, if its thickness remains constant, and it varies as the thickness, if the diameter remains constant. If the diameter of two coins are in the ratio 4 : 3, what should be the ratio of their thickness if the value of the first is four times that of the second?

A.
16 : 9
B.
9 : 4
C.
9 : 16
D.
4 : 9

Answer: Option B

Explanation :

Let D₁, T₁ and D₂, T₂ denote the diameters and the thickness of the two coins respectively. If V₁ and V₂are the values of the two coins.

$\frac{V_{1}}{V_{2}} = (\frac{{D_{1}}^{2} T_{1}}{{D_{2}}^{2} T_{2}}) = {(\frac{D_{1}}{D_{2}})}^{2} (\frac{T_{1}}{T_{2}})$

Therefore, $\frac{4}{1} = {(\frac{4}{3})}^{2} (\frac{T_{1}}{T_{2}}) \Rightarrow (\frac{T_{1}}{T_{2}}) = \frac{9}{4}$

Arithmetic - Ratio, Proportion & Variation - Previous Year CAT/MBA Questions

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