Ratio and Proportion MCQ Quiz - Objective Question with Answer for Ratio and Proportion - Download Free PDF

Last updated on Apr 21, 2025

Ratio and Proportion MCQs have been pestering exam candidates for ages with their tricky solutions. Almost every examination such as UPSC, SSC CGL, Bank Exams, etc. with the Quantitative Aptitude section features Ratio and Proportion Questions Answers. The ratio is defined as the comparison of sizes of two quantities of the same unit. Proportion, on the other hand, refers to the equality of two ratios. Ratio and Proportion Objective Questions are pretty easy to solve if there’s enough practice. Solving these questions can save a lot of time in the exams. Testbook has worked on this Ratio and Proportion Quiz for best practice of the candidates. Practice these Ratio and Proportion Questions Answers which will help you in improving your speed and accuracy of solving Ratio and Proportion Objective Questions. We have also provided solutions and explanations to each question in this article. Also, find tips to solve questions faster!

Latest Ratio and Proportion MCQ Objective Questions

Ratio and Proportion Question 1:

A certain amount of money is divided between A, B and C in the ratio 8 : 4 : 3. If A divides his share between D and E in the ratio of 9 : 7, what will be the ratio of C's share to D's?

  1. 4 : 5
  2. 3 : 4
  3. 2 : 3
  4. 6 : 7

Answer (Detailed Solution Below)

Option 3 : 2 : 3

Ratio and Proportion Question 1 Detailed Solution

Given:

The total amount is divided between A, B, and C in the ratio 8 : 4 : 3.

A divides his share between D and E in the ratio 9 : 7.

Formula used:

Profit = Time × Investment

Calculation:

Let the total amount of money be S.

A's share = (8 / (8 + 4 + 3)) × S = (8 / 15) × S

B's share = (4 / (8 + 4 + 3)) × S = (4 / 15) × S

C's share = (3 / (8 + 4 + 3)) × S = (3 / 15) × S

Now, A divides his share between D and E in the ratio 9 : 7.

So, D's share from A = (9 / (9 + 7)) × A's share = (9 / 16) × (8 / 15) × S

⇒ D's share = (72 / 240) × S = (3 / 10) × S

Now, we need to find the ratio of C's share to D's share:

C's share : D's share = (3 / 15) × S : (3 / 10) × S

⇒ Ratio = (3 / 15) × (10 / 3) = 2 / 3

∴ The ratio of C's share to D's share is 2 : 3.

Ratio and Proportion Question 2:

A certain sum of money was divided between x and y, in the ratio of 4 : 3. If y's share is ₹2,400, then the total initial capital is ___________.

  1. ₹7,200
  2. ₹5,600
  3. ₹8,000
  4. ₹6,000

Answer (Detailed Solution Below)

Option 2 : ₹5,600

Ratio and Proportion Question 2 Detailed Solution

Given:

The sum of money is divided between x and y in the ratio 4:3.

y's share = ₹2,400

Calculation:

Let the total sum of money be S.

y's share = (3 / (4 + 3)) × S

y's share = (3 / 7) × S = ₹2,400

⇒ (3 / 7) × S = ₹2,400

⇒ S = ₹2,400 × (7 / 3)

⇒ S = ₹5,600

∴ The total initial capital is ₹5,600.

Ratio and Proportion Question 3:

What will be the third ratio of (a+b) and (a+b)2?

  1. b
  2. (a + b)
  3. a
  4. (a + b)3

Answer (Detailed Solution Below)

Option 4 : (a + b)3

Ratio and Proportion Question 3 Detailed Solution

Given:

We are asked to find the third ratio of (a + b) and (a + b)2.

Formula used:

Third proportion of a and b = b²/a

Calculation:

Third ratio = ((a + b)2)2/(a + b)

Third ratio = (a + b)4/(a + b)

We can simplify this expression:

Third ratio = (a + b)3

∴ The third ratio is (a + b)3.

Ratio and Proportion Question 4:

The monthly incomes of two friends Chetan and Vipul, are in the ratio 5 : 7 respectively and each of them saves ₹96000 every month. If the ratio of their monthly expenditure is 1 : 3, find the monthly income of Chetan(in ₹).

  1. 120000
  2. 121000
  3. 168000
  4. 119000

Answer (Detailed Solution Below)

Option 1 : 120000

Ratio and Proportion Question 4 Detailed Solution

Given:

Monthly incomes of Chetan and Vipul are in the ratio 5 : 7

Each of them saves ₹96000 every month

The ratio of their monthly expenditure is 1 : 3

Formula used:

Income = Expenditure + Savings

Calculation:

Let the monthly income of Chetan be 5x and that of Vipul be 7x.

Let the monthly expenditure of Chetan be y and that of Vipul be 3y (since the ratio of their expenditures is 1:3).

For Chetan, Income = Expenditure + Savings

5x = y + 96000

For Vipul, Income = Expenditure + Savings

7x = 3y + 96000

Now, solve the system of equations:

1) 5x = y + 96000

⇒ y = 5x - 96000

2) 7x = 3y + 96000

Substitute y = 5x - 96000 into equation 2:

7x = 3(5x - 96000) + 96000

7x = 15x - 288000 + 96000

7x = 15x - 192000

⇒ 7x - 15x = -192000

⇒ -8x = -192000

⇒ x = 24000

Now, the monthly income of Chetan = 5x = 5 × 24000 = ₹120000

∴ The monthly income of Chetan is ₹120000.

Ratio and Proportion Question 5:

If 19 , 57 , 81 , and y are in proportion, then the value of y is:

  1. 252
  2. 248
  3. 249
  4. 243

Answer (Detailed Solution Below)

Option 4 : 243

Ratio and Proportion Question 5 Detailed Solution

Given:

19, 57, 81, and y are in proportion.

Formula Used:

If four numbers a, b, c, and d are in proportion, then a/b = c/d.

Calculation:

Here, a = 19, b = 57, c = 81, and d = y.

According to the formula:

⇒ 19 / 57 = 81 / y

Cross-multiplying:

⇒ 19y = 57 × 81

⇒ 19y = 4617

Dividing both sides by 19:

⇒ y = 4617 / 19

⇒ y = 243

The correct answer is option 4.

Top Ratio and Proportion MCQ Objective Questions

u : v = 4 : 7 and v : w = 9 : 7. If u = 72, then what is the value of w?

  1. 98
  2. 77
  3. 63
  4. 49

Answer (Detailed Solution Below)

Option 1 : 98

Ratio and Proportion Question 6 Detailed Solution

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Given:

u : v = 4 : 7 and v : w = 9 : 7

Concept Used: In this type of question, number can be calculated by using the below formulae

Calculation:

u : v = 4 : 7 and v : w = 9 : 7

To make ratio v equal in both cases

We have to multiply the 1st ratio by 9 and 2nd ratio by 7

u : v = 9 × 4 : 9 × 7 = 36 : 63 ----(i)

v : w = 9 × 7 : 7 × 7 = 63 : 49 ----(ii)

Form (i) and (ii), we can see that the ratio v is equal in both cases

So, Equating the ratios we get,

u v w = 36 63 49

u w = 36 49

When u = 72,

w = 49 × 72/36 = 98

Value of w is 98

A bag has ₹ 785 in the denomination of ₹ 2, ₹ 5 and ₹ 10 coins. The coins are in the ratio of 6 : 9 : 10. How many coins of ₹ 5 are in the bag?

  1. 60
  2. 12
  3. 45
  4. 24

Answer (Detailed Solution Below)

Option 3 : 45

Ratio and Proportion Question 7 Detailed Solution

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Given:

₹ 785 in the denomination of ₹ 2, ₹ 5 and ₹ 10 coins

The coins are in the ratio of 6 : 9 : 10

Calculation:

Let the number of coins of ₹ 2, ₹ 5 and ₹ 10 be 6x, 9x, and 10x respectively

⇒ (2 × 6x) + (5 × 9x) + (10 × 10x) = 785

⇒ 157x = 785

∴ x = 5

Number of coins of ₹ 5 = 9x = 9 × 5 = 45

∴ 45 coins of ₹ 5 are in the bag

If A : B = 7 : 8 and B : C = 7 : 9, then what is the ratio of A : B : C ?

  1. 56 : 49 : 72
  2. 49 : 56 : 72
  3. 56 : 72 : 49
  4. 72 : 56 : 49

Answer (Detailed Solution Below)

Option 2 : 49 : 56 : 72

Ratio and Proportion Question 8 Detailed Solution

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Given:

A : B = 7 : 8

B : C = 7 : 9

Concept:

If N is divided into a : b, then

First part = N × a/(a + b)

Second part = N × b/(a + b)

Calculation:

A/B = 7/8      ----(i)

Also B/C = 7/9      ----(ii)

Multiply equation (i) and (ii) we get,

⇒ (A/B) × (B/C) = (7/8) × (7/9)

⇒ A/C = 49/72

∵ A : B = 49 : 56

∴ A : B : C = 49 : 56 : 72

 Alternate Method

A : B = 7 : 8 = 49 : 56

B : C = 7 : 9 = 56 : 72

⇒ A : B : C = 49 : 56 : 72

A man has 25 paise, 50 paise and 1 Rupee coins. There are 220 coins in all and the total amount is 160. If there are thrice as many 1 Rupee coins as there are 25 paise coins, then what is the number of 50 paise coins?

  1. 60
  2. 120
  3. 40
  4. 80

Answer (Detailed Solution Below)

Option 1 : 60

Ratio and Proportion Question 9 Detailed Solution

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Given:

Total coin = 220

Total money = Rs. 160

There are thrice as many 1 Rupee coins as there are 25 paise coins.

Concept used:

Ratio method is used.

Calculation:

Let the 25 paise coins be 'x'

So, one rupees coins = 3x

50 paise coins = 220 – x – (3x) = 220 – (4x)

According to the questions,

3x + [(220 – 4x)/2] + x/4 =160

⇒ (12x + 440 – 8x + x)/4 = 160

⇒  5x + 440 = 640

⇒ 5x = 200

⇒ x = 40

So, 50 paise coins = 220 – (4x) = 220 – (4 × 40) = 60

∴ The number of 50 paise coin is 60.

If A is 25% less than B, then what will be the value of (2B - A)/A ?

  1. 5/4
  2. 3/2
  3. 3/4
  4. 5/3

Answer (Detailed Solution Below)

Option 4 : 5/3

Ratio and Proportion Question 10 Detailed Solution

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Given:

A = 75% of B

Calculation:

A = 3/4 of B

⇒ A/B = 3/4

Let the value of A be 3x and B be 4x

So (2B – A)/A = (2 × 4x – 3x)/3x

⇒ (2B – A)/A = 5x/3x

∴ (2B – A)/A = 5/3

Short Trick:

Ratio of A : B = 3 : 4

∴ (2B – A)/A = (8 – 3) /3 = 5/3

If x : y = 5 : 4, then what will be the ratio of \(\left( {\frac{x}{y}} \right):\left( {\frac{y}{x}} \right)\)?

  1. 25 : 16
  2. 16 : 25
  3. 4 : 5
  4. 5 : 4

Answer (Detailed Solution Below)

Option 1 : 25 : 16

Ratio and Proportion Question 11 Detailed Solution

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Given:

x : y = 5 : 4

Explanation:

(x/y) = (5/4)

(y/x) = (4/5)

Now, \(\left( {\frac{x}{y}} \right):\left( {\frac{y}{x}} \right)\) = (5/4)/(4/5) = 25/16

\(\left( {\frac{x}{y}} \right):\left( {\frac{y}{x}} \right)\) = 25 : 16

How much should be added to each term of 4 : 7 so that it becomes 2 : 3?

  1. 2
  2. 3
  3. 4
  4. 1

Answer (Detailed Solution Below)

Option 1 : 2

Ratio and Proportion Question 12 Detailed Solution

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Given :

Ratio of two numbers is 4 : 7 

Calculations :

Let the number added to denominator and numerator be 'x' 

Now according to the question 

(4 + x)/(7 + x) = 2 : 3 

⇒ 12 + 3x = 14 + 2x 

⇒ x = 2 

∴ 2 will be added to make the term in the ratio of 2 : 3.

The ratio of two numbers is 14 : 25. If the difference between them is 264, then which is the smaller of the two numbers?

  1. 316
  2. 294
  3. 336
  4. 282

Answer (Detailed Solution Below)

Option 3 : 336

Ratio and Proportion Question 13 Detailed Solution

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Given:

Ratio of two numbers is 14 : 25

Difference between them is 264

Calculation:

Let the numbers be 14x and 25x

⇒ 25x – 14x = 264

⇒ 11x = 264

∴ x = 24

⇒ Smaller number = 14x = 14 × 24 = 336

∴ The smaller of the two numbers is 336.

The ratio of salaries of A and B is 6 ∶ 7 respectively. If B’s salary is increased by \(5\frac{1}{2}\%\), his total salary becomes Rs. 1,47,700. Find the salary of A  (in Rs.).

  1. 1,10,000
  2. 1,20,000
  3. 1,40,000
  4. 1,35,000

Answer (Detailed Solution Below)

Option 2 : 1,20,000

Ratio and Proportion Question 14 Detailed Solution

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Given:

Ratio of salaries of A and B = 6 : 7

B's salary increased by \(5\frac{1}{2}\%\)

Total salary of B = Rs. 147700

Calculation:

Let salary of A and B be Rs. 60x and Rs. 70x

Now,

Increased salary of B = 70x + 70x × \(5\frac{1}{2}\%\)

⇒ Rs. 73.85x

According to the question,

73.85x = 147700

⇒ x = 147700/73.85

⇒ x = 2000

So, actual salary of A = 60 × 2000

⇒ Rs. 120000

∴ The salary (in Rs.) of A is 120000.

If x : y = 6 : 5 and z : y = 9 : 25, then what is the ratio of x : z?

  1. 50 : 33
  2. 54 : 125
  3. 10 : 3
  4. 48 : 25

Answer (Detailed Solution Below)

Option 3 : 10 : 3

Ratio and Proportion Question 15 Detailed Solution

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Given:

x : y = 6 : 5

And z : y = 9 : 25

Calculation :

x/y = 6/5     ---- (i)

And z/y = 9/25

⇒ y/z = 25/9     ---- (ii)

Multiply equation (i) and (ii) we get,

(x/y) × (y/z) = (6/5) × (25/9)

⇒ x/z = 10/3

∴ x : z = 10 : 3

Alternate Method 

x : y = 6 : 5     ----- (i)

And z : y = 9 : 25     ---- (ii)

As y is in both the ratios, Multiply (i) × 5 to make equal value of y in both the ratios

x : y = (6 : 5) × 5 = 30 : 25    ---- (iii)

from (ii) and (iii), Since y is same in both the ratios

x : z = 30 : 9 = 10 : 3
 

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