Ratio and Proportion Questions for CMAT

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Instructions
For the following questions answer them individually

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

Answer: B

Explanation:
Let mixture in vessel A = x ml

and mixture in vessel B = y ml

4x
=> Milk in vessel A = 7
2y
Milk in vessel B = 5

Acc to ques,
4x 2y 1
=> 7 + 5 = 2 (x + y)
4x x y 2y
=> 7 − 2 = 2 − 5
x y
=> 14 = 10
x 14 7
=> y = 10 = 5

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

Answer: E

Explanation:
Let A ,B and C respectively = x, 2x, 3x

=> Sum of A , B and C = x + 2x + 3x = 3 × 600

=> 6x = 1800
1800
=> x = 6 = 300
=> A = 300, B = 600, C = 900

110
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 110
Value of A after increment = 100 × 300 = 330
80
Value of B after increment = 100 × 600 = 480
105
New value of average = 100 × 600 = 630

Acc to ques,
330+480+C′
=> 3 = 630
=> 810 + C ′ = 3 × 630 = 1890

=> C ′ = 1890 − 810 = 1080

∴ C is increased by = 1080 - 900 = 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

Answer: A

Explanation:
4
Quantity of milk in 27 litre mixture = 4+5 × 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,
X +12 7
=> 15 = 3

=> 3X + 36 = 15 × 7 = 105

=> 3X = 105 − 36 = 69
69
=> X = 3 = 23 litre

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

Answer: B

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Explanation:
Let the amount with Abhay , Vinay, Vinay's mother and grocer be A, V , VmandG respectively
From the data given in question
3
V = 10 A
2 2 3
Vm = 3 V = 3 × 10 A
5
C = 8 Vm
Vinay's mother has 600 left after giving money to the grocer.
3
8 Vm = 600
3 2 3
8 × 3 × 10 A = 600
A = 8000
Option B is the correct answer.

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

Answer: A

Explanation:
M's share = 3/8
N's share = 1/6 of remaining = 1/6 of 5/8 = 5/48

18+5
Remaining share = 1 - 48

3 25
O's share = 7 * 48 * 44352

Hence Rs 9900

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

Answer: B

Explanation:
Let the angles of the triangle be 19x, 10x, 7x

=> Sum of angles = 19x + 10x + 7x = 180∘

=> 36x = 180∘

180
=> x = 36 = 5∘
∘ ∘ ∘
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=> Angles are = 95∘ , 50∘ , 35∘

∴ Sum of thrice the smallest angle and the twice the largest angle
= (3 × 35∘ ) + (2 × 95∘ )

= 105 + 190 = 295∘

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

Answer: D

Explanation:
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,
3x+10 5
=> 4x+10 = 6

=> 18x + 60 = 20x + 50

=> 2x = 60 − 50 = 10
10
=> x = 2 = 5

∴ Present age of Meena = (3 × 5 + 5) = 20 years

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

Answer: A

Explanation:
Let Kajal's monthly salary = Rs. 100x
55
Amount spent by Kajal = 100 × 100x =Rs. 55x
2
=> Amount spent on clothes = (4+2+5) × 55x = 10x

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Acc to ques,

=> 10x = 5540

=> x = 554

∴ Kajal's monthly salary = 100 × 554 = Rs. 55,400

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

Answer: C

Explanation:
Let the number of 1 rupee, 50 paise and 25 paise coins = 10x, 8x, 5x
1 1
=> Total amount = (10x × 1) + (8x × 2 ) + (5x × 4 ) = 976
5x
=> 14x + 4 = 976
61x
=> 4 = 976
976×4
=> x = 61 = 64
∴ No. of 25 paise coins = 5 * 64 = 320

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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

Answer: A

Explanation:
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

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= [(18x × 4) + (18x + 2000) × 8] : [(7x × 4) + (7x + 7000) × 8]

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

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

54x+4000 2
Acc. to ques, => 21x+14000 = 1

=> 54x + 4000 = 42x + 28000

=> 54x − 42x = 12x = 28000 − 4000 = 24000

24000
=> x = 12 = 2000
∴ Total initial investment = 18x + 7x = 25x
= 25 × 2000 = Rs.50, 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?

1
A 78 2

1
B 79 6

5
C 72 6

D 76

1
E 77 2

Answer: B

Explanation:
22
Quantity of milk in vessel = 25 × 100 = 88 litres

=> Quantity of water = 100 − 88 = 12 litres

40 2
40 litres of the mixture is taken out, i.e., 100 = ( 5 )th
2
=> Milk left = 88 − 5 × 88 = 52.8 litres
2
Water left = 12 − 5 × 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

57.6−12
∴ Required % = 57.6 × 100
475 1
= 6 = 79 6 %
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

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C 22 litres

D 7 litres

E 1 litre

Answer: B

Explanation:
Jar A has 60 litres of mixture of milk and water in the respective ratio of 2 : 1
2
=> Quantity of milk in Jar A = 3 × 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

40+(40−x) 13
Acc. to ques, => 20+x = 7

=> 560 − 7x = 260 + 13x

=> 13x + 7x = 560 − 260

=> 20x = 300

300
=> x = 20 = 15 litres

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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

Answer: C

Explanation:
Let the numbers be 100x and 100y
100x x
We need to find = 100y = y =?

Acc to ques,
48 60
=> 100 ∗ 100x = 100 ∗ 100y

=> 48x = 60y

x 60 5
=> y = 48 = 4

=> x : y = 5 : 4

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?

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A Rs. 2,123/-

B Rs. 2,316/-

C Rs. 2,565/-

D Rs. 2,895/-

E None of these

Answer: D

Explanation:
Let the total amount to be divided = 27x

A : B : C : D = 4 : 5 : 7 : 11
7
=> Share of C = 27 ∗ 27x = 1351
1351
=> x = 7 = 193
Now, total amount of money with A & D together
4+11
= 27 ∗ 27x

= 15 ∗ 193 =Rs. 2, 895

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

Answer: C

Explanation:
Let the numbers be 100x and 100y
100x x
We need to find = 100y = y =?

Acc to ques,
38 52
=> 100 ∗ 100x = 100 ∗ 100y

=> 38x = 52y

x 52 26
=> y = 38 = 19

=> x : y = 26 : 19

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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?

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A 24

B 30

C 50

D Cannot determined

E None of these

Answer: A

Explanation:
Let present age of Jagannath = 9x years

=> Badri's present age = 5x years

According to ques, => (9x − 6) = 2 × (5x − 6)

=> 9x − 6 = 10x − 12

=> 10x − 9x = 12 − 6

=> x = 6

∴ Difference between their present ages = 9x − 5x = 4x

= 4 × 6 = 24

=> Ans - (A)

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

Answer: B

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

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

=> 10x = 125, 000

125,000
=> x = 10 = 12500
∴ Difference between Soni's and Sudhir's Share = 3x − 2x = x = Rs. 12, 500
=> Ans - (B)

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

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B 102

C 68

D 85

E 34

Answer: C

Explanation:
Let the total quantity of mixture in the vessel initially = 17x litres
14
=> Quantity of milk = 17 × 17x = 14x litres

Quantity of water = 17x − 14x = 3x litres

Acc. to ques,
14
14x−( 17 ×25.5)+5
3 80
=> 3x−( 17 ×25.5)+2.5 = 20

14x−21+5 4
=> 3x−4.5+2.5 = 1
14x−16 4
=> 3x−2 = 1

=> 14x − 16 = 12x − 8

=> 14x − 12x = 16 − 8

8
=> x = 2 = 4

∴ Initial quantity of mixture in the vessel before the replacement = 17 × 4 = 68 litres

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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

Answer: B

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

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

240
=> 15x = 2 = 120
120
=> x = 15 = 8

∴ Area of field = 8x × 7x = 56x2

= 56 × (8)2 = 3584m2

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Question 20
1 1
The respective ratio between the monthly salaries of Rene and Som is 5 : 3. Out of her monthly salary Rene gives 6 th as rent, 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

Answer: D

Explanation:
Let monthly salary of Rene = Rs.1500x

=> Monthly salary of Som = Rs.900x

1
Amount given as rent by Rene = 6 × 1500x = 250x
1
Amount given by Rene to her mother = 5 × 1500x = 300x
30
Amount for loan = 100 × 1500x = 450x
25
Amount kept aside = 100 × 1500x = 375x

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

=> 1500x − 1375x = 125x = 5000

5000
=> x = 125 = 40

∴ Som's salary = 900 × 40 = Rs.36, 000

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