Ratio and Proportion Questions for CMAT 2022 – Download PDF

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Ratio & Proportion Questions for CMAT
Ratio & Proportion Questions for CMAT

Ratio and Proportion Questions for CMAT 2022 – Download PDF

Download CMAT 2022 Ratio and Proportion Questions pdf by Cracku. Very Important Ratio and Proportion Questions for CMAT 2022 based on asked questions in previous exam papers. These questions will help your CMAT preparation. So kindly download the PDF for reference and do more practice.

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Question 1: The milk and water in two vessels A and B are in the ratio 4 : 3 and 2 : 3 respectively. In what ratio the liquids in both the vessels be mixed to obtain a new mixture in vessel C consisting half milk and half water?

a) 8 : 3

b) 7 : 5

c) 4 : 3

d) 2 : 3

e) None of these

Question 2: Three numbers are A, B and C are in the ratio 1 : 2 : 3 and their average is 600. If A is increases by 10% and B is decrease by 20%, then the average increased by 5%, C will be increase by :

a) 250

b) 150

c) 200

d) 160

e) 180

Question 3: Jar A contains ‘X’ litre of pure milk only. A 27 litre mixture of milk and water in the respective ratio of 4 : 5, is added to jar A. The new mixture thus formed in jar A contains 70% milk, what is the value of X ?

a) 23

b) 30

c) 27

d) 48

e) 28

Question 4: Abhay gave 30% of his money 2 to Vijay. Vijay gave 2/3rd of what he received to his mother. Vijay’s mother gave 5/8th of the money she received from Vijay, to the grocer. Vijay s mother is now left with Rs. 600. How much money did Abhay have initially ?

a) Rs: 6,200

b) Rs. 8,000

c) Rs. 6,000

d) Rs. 8,200

e) Rs 10.200

Question 5: M, N. O and P divided Rs. 44352 among themselves. M took 3/8 th of money. N took 1/6th of the remaining amount and the rest was divided among 0 and P in the ratio of 3 : 4 respectively. How much did 0 get as his share ?

a) Rs. 9900

b) Rs. 10,600

c) Rs. 10,300

d) Rs. 8700

e) Rs. 9000

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Question 6: The angles in a triangle are in a ratio of 19 : 10 : 7. What is the sum of thrice the smallest angle and the twice the largest angle ?

a) 275°

b) 295°

c) 280°

d) 273°

e) None of these

Question 7: Five years ago, the ratio between ages of Meena and Sita was 3 : 4. After five years from now the ratio between their ages will be 5 : 6. Find the present age of Meena ?

a) 22 years

b) 25 years

c) 15 years

d) 20 years

e) None of these

Question 8: Kajal spends 55% of her monthly income on grocery, clothes and education in the ratio of 4 : 2 : 5 respectively. If the amount spent on clothes is Rs. 5,540, what is Kajal’s monthly income

a) Rs. 55,400

b) Rs. 54,500

c) Rs. 55,450

d) Rs.55.650

e) None of these

Question 9: In a piggy bank there are 1 rupee, 50 paise and 25 paise coins. The respective ratio of their numbers is 10 : 8 : 5. In piggy bank there is a total sum of Rs. 976. How many 25 paise coins are there in the piggy bank ?

a) 256

b) 360

c) 320

d) 640

e) None of these

Question 10: A and B started a business with initial investments in the respective ratio of 18 : 7. After four months from the start of the business, A invested Rs. 2000 more and B invested Rs. 7000 more. At the end of one year, if the profit was distributed among them in the ratio of 2 : 1 respectively, what was the total initial investment with which A and B started the business?

a) Rs. 50,000

b) Rs. 25,000

c) Rs. 1,50,000

d) Rs. 75,000

e) Rs. 1,25,000

Question 11: A vessel contains 100 litres mixture of milk and water in the respective ratio of 22 : 3. 40 litres of the mixture is taken out from the vessel and 4.8 litres of pure milk and pure water each is added to the mixture. By what percent is the quantity of water in the final mixture less than the quantity of milk?

a) 78${1 \over 2}$

b) 79${1 \over 6}$

c) 72${5 \over 6}$

d) 76

e) 77${1 \over 2}$

Question 12: Jar A has 60 litres of mixture of milk and water in the respective ratio of 2 : 1. Jar B which had 40 litres of mixture of milk and water was emptied into jar A, as a result in jar A, the respective ratio of milk and water became 13 : 7. What was the quantity of water in jar B?

a) 8 litres

b) 15 litres

c) 22 litres

d) 7 litres

e) 1 litre

Question 13: Of the two numbers, 48 per cent of first number is 60 per cent of the second number. What is the respective ratio of the first number to the second number ?

a) 4 : 7

b) 3 : 4

c) 5 : 4

d) Cannot be determined

e) None of these

Question 14: A sum of money is divided among A, B, C and D in the ratio of 4 : 5 : 7 : 11 respectively. If the share of C is Rs. 1,351/- then what is the total amount of money of A and D together?

a) Rs. 2,123/-

b) Rs. 2,316/-

c) Rs. 2,565/-

d) Rs. 2,895/-

e) None of these

Question 15: 38 per cent of first number is 52 per cent of the second number. What is the respective ratio of the first number to the second number?

a) 5 : 4

b) 16 : 9

c) 26 : 19

d) Cannot be determined

e) None of these

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Question 16: Six years ago Jagannath was twice as old as Badri if the ratio of their present age is 9:5 respectively .What is the difference between their present ages?

a) 24

b) 30

c) 50

d) Cannot determined

e) None of these

Question 17: An amount of Rs 1,25,000 is to be distributed among the Sudhir,Soni,Shakunthala in the respective ratio of 2 : 3 : 5.What will be the difference between Soni’s and Sudhir’s  Share?

a) 25000

b) 12500

c) 18750

d) 2500

e) None of these

Question 18: A vessel contains a mixture of milk and water in the respective ratio of 14 : 3. 25.5 litres of the mixture is taken out from the vessel and 2.5 litres of pure water and 5 litres of pure milk is added to the mixture. If the resultant mixture contains 20% water, what was the initial quantity of mixture in the vessel before the replacement? (in litres)

a) 51

b) 102

c) 68

d) 85

e) 34

Question 19: The perimeter of a rectangular field is 240 metre. The ratio between the length and breadth of the field is 8:7. Find the area of the field.

a) 3854 sq. m.

b) 3584 sq. m.

c) 3684 sq. m.

d) 3666 sq. m.

e) None of these

Question 20: The respective ratio between the monthly salaries of Rene and Som is 5 : 3. Out of her monthly salary Rene gives ${1 \over 6}$th as rent, ${1 \over 5}$th to her mother, 30% as her education loan and keeps 25% aside for miscellaneous expenditure. Remaining Rs. 5000 she keeps as savings. What is Som’s monthly salary?

a) Rs. 21000

b) Rs. 24000

c) Rs. 27000

d) Rs. 36000

e) Rs. 18000

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Answers & Solutions:

1) Answer (B)

Let mixture in vessel A = $x$ ml

and mixture in vessel B = $y$ ml

=> Milk in vessel A = $\frac{4x}{7}$

Milk in vessel B = $\frac{2y}{5}$

Acc to ques,

=> $\frac{4x}{7} + \frac{2y}{5} = \frac{1}{2} (x + y)$

=> $\frac{4x}{7} – \frac{x}{2} = \frac{y}{2} – \frac{2y}{5}$

=> $\frac{x}{14} = \frac{y}{10}$

=> $\frac{x}{y} = \frac{14}{10} = \frac{7}{5}$

2) Answer (E)

Let A ,B and C respectively = $x , 2x , 3x$

=> Sum of A , B and C = $x + 2x + 3x = 3 \times 600$

=> $6x = 1800$

=> $x = \frac{1800}{6} = 300$

=> $A = 300 , B = 600 , C = 900$

Value of A after increment = $\frac{110}{100} \times 300 = 330$

Value of B after increment = $\frac{80}{100} \times 600 = 480$

New value of average = $\frac{105}{100} \times 600 = 630$

Acc to ques,

=> $\frac{330 + 480 + C’}{3} = 630$

=> $810 + C’ = 3 \times 630 = 1890$

=> $C’ = 1890 – 810 = 1080$

$\therefore$ C is increased by = 1080 – 900 = 180

3) Answer (A)

Quantity of milk in 27 litre mixture = $\frac{4}{4 + 5} \times 27 = 12$ litre

Quantity of water = $27 – 12 = 15$ litre

Ratio of milk and water in the new mixture = $70 : 30 = 7 : 3$

Acc to ques,

=> $\frac{X + 12}{15} = \frac{7}{3}$

=> $3X + 36 = 15 \times 7 = 105$

=> $3X = 105 – 36 = 69$

=> $X = \frac{69}{3} = 23$ litre

4) Answer (B)

Let the amount with Abhay , Vinay, Vinay’s mother and grocer be $A, V , V_m and G $ respectively
From the data given in question
$V = \frac{3}{10} A$
$ V_m = \frac{2}{3} V = \frac{2}{3} \times \frac{3}{10} A $
$C = \frac{5}{8} V_m$
Vinay’s mother has 600 left after giving money to the grocer.
$\frac{3}{8} V_m =600$
$\frac{3}{8} \times \frac{2}{3} \times \frac{3}{10} A =600$
$A = 8000$
Option B is the correct answer.

5) Answer (A)

M’s share = 3/8
N’s share = 1/6 of remaining = 1/6 of 5/8 = 5/48

Remaining share = 1 – $\frac{18+5}{48}$

O’s share = $\frac{3}{7}$ * $\frac{25}{48}$ * 44352

Hence Rs 9900

6) Answer (B)

Let the angles of the triangle be $19x , 10x , 7x$

=> Sum of angles = $19x + 10x + 7x = 180^{\circ}$

=> $36x = 180^{\circ}$

=> $x = \frac{180}{36} = 5^{\circ}$

=> Angles are = $95^{\circ} , 50^{\circ} , 35^{\circ}$

$\therefore$ Sum of thrice the smallest angle and the twice the largest angle

= $(3 \times 35^{\circ}) + (2 \times 95^{\circ})$

= $105 + 190 = 295^{\circ}$

7) Answer (D)

Let the ages of Meena and Sita 5 years ago be $3x$ and $4x$ years

=> Present age of Meena = $(3x + 5)$ years

Present age of Sita = $(4x + 5)$ years

Acc. to ques,

=> $\frac{3x + 10}{4x + 10} = \frac{5}{6}$

=> $18x + 60 = 20x + 50$

=> $2x = 60 – 50 = 10$

=> $x = \frac{10}{2} = 5$

$\therefore$ Present age of Meena = $(3 \times 5 + 5) = 20$ years

8) Answer (A)

Let Kajal’s monthly salary = Rs. $100x$

Amount spent by Kajal = $\frac{55}{100} \times 100x = $Rs. $55x$

=> Amount spent on clothes = $\frac{2}{(4 + 2 + 5)} \times 55x = 10x$

Acc to ques,

=> $10x = 5540$

=> $x = 554$

$\therefore$ Kajal’s monthly salary = $100 \times 554$ = Rs. 55,400

9) Answer (C)

Let the number of 1 rupee, 50 paise and 25 paise coins = $10x , 8x , 5x$

=> Total amount = $(10x \times 1) + (8x \times \frac{1}{2}) + (5x \times \frac{1}{4}) = 976$

=> $14x + \frac{5x}{4} = 976$

=> $\frac{61x}{4} = 976$

=> $x = \frac{976 \times 4}{61} = 64$

$\therefore$ No. of 25 paise coins = 5 * 64 = 320

10) Answer (A)

Let amount invested by A = $Rs. 18x$

=> Amount invested by B = $Rs. 7x$

After four months from the start of the business, A invested Rs. 2000 more and B invested Rs. 7000 more

Thus, ratio of profit received by A : B

= $[(18x \times 4) + (18x + 2000) \times 8] : [(7x \times 4) + (7x + 7000) \times 8]$

= $(72x + 144x + 16000) : (28x + 56x + 56000)$

= $(216x + 16000) : (84x + 56000) = (54x + 4000) : (21x + 14000)$

Acc. to ques, => $\frac{54x + 4000}{21x + 14000} = \frac{2}{1}$

=> $54x + 4000 = 42x + 28000$

=> $54x – 42x = 12x = 28000 – 4000 = 24000$

=> $x = \frac{24000}{12} = 2000$

$\therefore$ Total initial investment = $18x + 7x = 25x$

= $25 \times 2000 = Rs. 50,000$

11) Answer (B)

Quantity of milk in vessel = $\frac{22}{25} \times 100 = 88$ litres

=> Quantity of water = $100 – 88 = 12$ litres

40 litres of the mixture is taken out, i.e., $\frac{40}{100} = (\frac{2}{5})^{th}$

=> Milk left = $88 – \frac{2}{5} \times 88 = 52.8$ litres

Water left = $12 – \frac{2}{5} \times 12 = 7.2$ litres

Now, 4.8 lires of milk and water are added.

=> Quantity of milk in the vessel = 52.8 + 4.8 = 57.6 litres

Quantity of water in the vessel = 7.2 + 4.8 = 12 litres

$\therefore$ Required % = $\frac{57.6 – 12}{57.6} \times 100$

= $\frac{475}{6} = 79 \frac{1}{6} \%$

12) Answer (B)

Jar A has 60 litres of mixture of milk and water in the respective ratio of 2 : 1

=> Quantity of milk in Jar A = $\frac{2}{3} \times 60 = 40$ litres

Quantity of water in Jar A = $60 – 40 = 20$ itres

Let quantity of water in Jar B = $x$ litres

=> Quantity of milk in Jar B = $(40 – x)$ litres

Acc. to ques, => $\frac{40 + (40 – x)}{20 + x} = \frac{13}{7}$

=> $560 – 7x = 260 + 13x$

=> $13x + 7x = 560 – 260$

=> $20x = 300$

=> $x = \frac{300}{20} = 15$ litres

13) Answer (C)

Let the numbers be $100x$ and $100y$

We need to find = $\frac{100x}{100y} = \frac{x}{y} = ?$

Acc to ques,

=> $\frac{48}{100} * 100x = \frac{60}{100} * 100y$

=> $48x = 60y$

=> $\frac{x}{y} = \frac{60}{48} = \frac{5}{4}$

=> $x:y = 5:4$

14) Answer (D)

Let the total amount to be divided = $27x$

A : B : C : D = 4 : 5 : 7 : 11

=> Share of C = $\frac{7}{27} * 27x = 1351$

=> $x = \frac{1351}{7} = 193$

Now, total amount of money with A & D together

= $\frac{4 + 11}{27} * 27x$

= $15 * 193 = $Rs. $2,895$

15) Answer (C)

Let the numbers be $100x$ and $100y$

We need to find = $\frac{100x}{100y} = \frac{x}{y} = ?$

Acc to ques,

=> $\frac{38}{100} * 100x = \frac{52}{100} * 100y$

=> $38x = 52y$

=> $\frac{x}{y} = \frac{52}{38} = \frac{26}{19}$

=> $x : y = 26 : 19$

16) Answer (A)

Let present age of Jagannath = $9x$ years

=> Badri’s present age = $5x$ years

According to ques, => $(9x-6)=2 \times (5x-6)$

=> $9x-6=10x-12$

=> $10x-9x=12-6$

=> $x=6$

$\therefore$ Difference between their present ages = $9x-5x=4x$

= $4 \times 6=24$

=> Ans – (A)

17) Answer (B)

Let amount received by Sudhir,Soni and Shakunthala be $2x,3x$ and $5x$ respectively.

=> Total amount = $(2x+3x+5x)=125,000$

=> $10x=125,000$

=> $x=\frac{125,000}{10}=12500$

$\therefore$ Difference between Soni’s and Sudhir’s  Share = $3x-2x=x = Rs.$ $12,500$

=> Ans – (B)

18) Answer (C)

Let the total quantity of mixture in the vessel initially = $17x$ litres

=> Quantity of milk = $\frac{14}{17} \times 17x = 14x$ litres

Quantity of water = $17x – 14x = 3x$ litres

Acc. to ques,

=> $\frac{14x – (\frac{14}{17} \times 25.5) + 5}{3x – (\frac{3}{17} \times 25.5) + 2.5} = \frac{80}{20}$

=> $\frac{14x – 21 + 5}{3x – 4.5 + 2.5} = \frac{4}{1}$

=> $\frac{14x – 16}{3x – 2} = \frac{4}{1}$

=> $14x – 16 = 12x – 8$

=> $14x – 12x = 16 – 8$

=> $x = \frac{8}{2} = 4$

$\therefore$ Initial quantity of mixture in the vessel before the replacement = $17 \times 4 = 68$ litres

19) Answer (B)

Let the length and breadth of the rectangular field be $8x$ m and $7x$ m respectively.

Perimeter = $2 (8x + 7x) = 240$

=> $15x = \frac{240}{2} = 120$

=> $x = \frac{120}{15} = 8$

$\therefore$ Area of field = $8x \times 7x = 56 x^2$

= $56 \times (8)^2 = 3584 m^2$

20) Answer (D)

Let monthly salary of Rene = $Rs. 1500x$

=> Monthly salary of Som = $Rs. 900x$

Amount given as rent by Rene = $\frac{1}{6} \times 1500x = 250x$

Amount given by Rene to her mother = $\frac{1}{5} \times 1500x = 300x$

Amount for loan = $\frac{30}{100} \times 1500x = 450x$

Amount kept aside = $\frac{25}{100} \times 1500x = 375x$

=> Amount left = $1500x – (250x + 300x + 450x + 375x) = 5000$

=> $1500x – 1375x = 125x = 5000$

=> $x = \frac{5000}{125} = 40$

$\therefore$ Som’s salary = $900 \times 40 = Rs. 36,000$

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