Fourth Proportional MCQ Quiz - Objective Question with Answer for Fourth Proportional - Download Free PDF

Last updated on Jun 3, 2025

Testbook is committed to providing the best practice material for our candidates. Practice these Fourth Proportional MCQs Quiz that Testbook has brought to the candidates and improve your grasp of the concept better. This article has full solutions and explanations to all the Fourth Proportion objective questions listed here. You will also find a list of tips, tricks and ways to solve Fourth Proportinal question answers in an easier manner. So, Solve away!

Latest Fourth Proportional MCQ Objective Questions

Fourth Proportional Question 1:

If 2 , 64 , 86 , and y are in proportion, then the value of y is:

  1. 2767
  2. 2762
  3. 2752
  4. 2757

Answer (Detailed Solution Below)

Option 3 : 2752

Fourth Proportional Question 1 Detailed Solution

Given:

2, 64, 86, and y are in proportion.

Formula used:

If a, b, c, and d are in proportion, then \(\frac{a}{b} = \frac{c}{d}\).

Calculation:

\(\frac{2}{64} = \frac{86}{y}\)

\(\frac{2}{64} = \frac{86}{y}\)

\(\frac{1}{32} = \frac{86}{y}\)

⇒ y = 86 × 32

⇒ y = 2752

∴ The correct answer is option (3).

Fourth Proportional Question 2:

If 4 , 31 , 92 , and y are in proportion, then the value of y is:

  1. 713
  2. 722
  3. 718
  4. 715

Answer (Detailed Solution Below)

Option 1 : 713

Fourth Proportional Question 2 Detailed Solution

Given:

4, 31, 92, and y are in proportion.

Formula used:

If a, b, c, and d are in proportion: (a/b = c/d)

Calculation:

⇒ (4/31 = 92/y)

⇒ y = (92 × 31) / 4

⇒ y = 2852 / 4

⇒ y = 713

∴ The correct answer is option (1).

Fourth Proportional Question 3:

If 3 , 60 , 62 , and y are in proportion, then the value of y is:

  1. 1245
  2. 1234
  3. 1249
  4. 1240

Answer (Detailed Solution Below)

Option 4 : 1240

Fourth Proportional Question 3 Detailed Solution

Given:

3, 60, 62, and y are in proportion

Formula used:

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

Calculation:

3/60 = 62/y

⇒ 3 × y = 60 × 62

⇒ 3y = 3720

⇒ y = 3720 / 3

⇒ y = 1240

∴ The correct answer is option (4).

Fourth Proportional Question 4:

If F1 and F2 are the fourth proportional to \(\frac{2}{7}, \frac{7}{12}, 8\) and \(\frac{5}{6}, \frac{4}{3}, 10\) , respectively, then what is F1 : F2?

  1. 49 : 48
  2. 49 : 16
  3. 25 : 16
  4. 16 : 9

Answer (Detailed Solution Below)

Option 1 : 49 : 48

Fourth Proportional Question 4 Detailed Solution

Given:

F1 is the fourth proportional to (2/7), (7/12), 8.

F2 is the fourth proportional to (5/6), (4/3), 10.

Formula Used:

If a, b, c are given, and d is the fourth proportional, then:

d = (b × c) / a

F1 : F2 = F1 / F2

Calculation:

For F1:

a = 2/7, b = 7/12, c = 8

Using the formula,

⇒ F1 = (b × c) / a

⇒ F1 = ((7/12) × 8) / (2/7)

⇒ F1 = (56/12) ÷ (2/7)

⇒ F1 = (56/12) × (7/2)

⇒ F1 = (56 × 7) / (12 × 2)

⇒ F1 = 392 / 24

⇒ F1 = 49 / 3

For F2:

a = 5/6, b = 4/3, c = 10

Using the formula,

⇒ F2 = (b × c) / a

⇒ F2 = ((4/3) × 10) / (5/6)

⇒ F2 = (40/3) ÷ (5/6)

⇒ F2 = (40/3) × (6/5)

⇒ F2 = (40 × 6) / (3 × 5)

⇒ F2 = 240 / 15

⇒ F2 = 16

Now, F1 : F2 = F1 / F2

⇒ F1 : F2 = (49 / 3) ÷ 16

⇒ F1 : F2 = (49 / 3) × (1 / 16)

⇒ F1 : F2 = 49 / 48

The ratio F1 : F2 is 49 : 48.

Fourth Proportional Question 5:

Find the fourth proportional to the numbers x + 6, 3x + 6, 8x, if x = 6.

  1. 80
  2. 98
  3. 96
  4. 88

Answer (Detailed Solution Below)

Option 3 : 96

Fourth Proportional Question 5 Detailed Solution

Given:

Numbers: x + 6 , 3x + 6 , 8x

x = 6

Formula Used:

To find the fourth proportional to the numbers a, b, and c is given by:

\(\frac{a}{b} = \frac{c}{d}\)

Calculation:

Substitute the values x = 6 into the numbers:

a = x + 6 = 6 + 6 = 12

b = 3x + 6 = 3(6) + 6 = 18 + 6 = 24

c = 8x = 8(6) = 48

Fourth proportional d using the formula:

\(\frac{a}{b} = \frac{c}{d}\)

\(\frac{12}{24} = \frac{48}{d}\)

⇒ 12d = 24 × 48

⇒ d = 96

The correct answer is option 3.

Top Fourth Proportional MCQ Objective Questions

The fourth proportional to 10, 12, 15 is :

  1. 20
  2. 18
  3. 22
  4. 24

Answer (Detailed Solution Below)

Option 2 : 18

Fourth Proportional Question 6 Detailed Solution

Download Solution PDF

Formula Used:

Fourth proportional of a, b, c = (b × c)/a

Calculation:

4th proportional of 10, 12, 15

= (12 × 15)/10 = 18

∴ The fourth proportional is 18

Additional Information Sunny 28.7.21

  1. Mean Proportional - Mean proportional between a and b = √ab
  2. Third Proportional - If a ∶ b = b ∶ c, then c is called the third proportional to a and b.
  3. Fourth Proportional - If a ∶ b = c ∶ d; then d is called the fourth proportional to a, b, and c.

The ratio between the fourth proportional of 7, 5 and 3 to the third proportional of 7 and 13 is:

  1. 75 ∶ 448
  2. 15 ∶ 169
  3. 21 ∶ 25
  4. 25 ∶ 21

Answer (Detailed Solution Below)

Option 2 : 15 ∶ 169

Fourth Proportional Question 7 Detailed Solution

Download Solution PDF

We know that,

Fourth proportional of a, b, c is bc/a

⇒ Fourth proportional to 7, 5 and 3 = 5 × 3/7 = 15/7

We know that,

Third proportional to x, y is y2/x

⇒ Third proportional of 7, 13 = 132/7

∴ Required ratio = (15/7)/132/7 = 15/169 = 15 ∶ 169

A certain number is subtracted from each of the numbers 20, 24 and 29. After subtraction, those numbers are in proportional. What is the number subtracted?

  1. 6
  2. 4
  3. 5
  4. 3

Answer (Detailed Solution Below)

Option 2 : 4

Fourth Proportional Question 8 Detailed Solution

Download Solution PDF

Given:

Numbers are 20, 24, and 29. After subtracting a certain number, the numbers are in proportion.

Concept:

If two pairs of numbers (a:b and b:c) are in proportion,

then the cross products are equal (i.e., b2 = ac).

Solution:

Let the number to be subtracted be x.

then

​a = 20 - x

b = 24 - x

and

c = 29 - x

⇒ (24 - x)2 = (20 - x)(29 - x)

⇒ x2 + 576 - 48x = x2 - 49x + 580 

⇒ x = 4 

Therefore, the number subtracted is 4.

If p is the third proportional to 8, 20 and q is the fourth proportional to 3, 5, 24, then find the value of (2p + q).

  1. 126
  2. 104
  3. 140
  4. 90

Answer (Detailed Solution Below)

Option 3 : 140

Fourth Proportional Question 9 Detailed Solution

Download Solution PDF

Given:

p is the third proportional to 8, 20

q is the fourth proportional to 3, 5, 24

Concept used:

If x is the third proportional to a, b then x = b2/a

If x is the fourth proportional to a, b, c then a/b = c/x

Calculation:

Here, p = 202/8 = 400/8 = 50

Also, 3/5 = 24/q

⇒ q = (5 × 24)/3 = 40

Then, (2p + q) = (2 × 50) + 40 = 100 + 40 = 140

∴ The value of (2p + q) is 140

The fourth proportional to the numbers 5, 6 and 8 is:

  1. 9.8
  2. 9.6
  3. 9
  4. 9.5

Answer (Detailed Solution Below)

Option 2 : 9.6

Fourth Proportional Question 10 Detailed Solution

Download Solution PDF

GIVEN:

Numbers 5,6 and 8

FORMULA USED:

If a, b, c, and d are in proportional 

then , a/b = c/d.

CALCULATION:

Let the fourth number be x 

⇒ 5/6 = 8/x 

⇒ 5 × x = 6 × 8 

⇒ x = 48/5 

 x = 9.6.

∴The fourth proportion is 9.6.

If K + 3, k + 2, 3k – 7, 2k – 3 are in proportion in the given order, then what will be the minimum value of the fourth proportion?

  1. 7
  2. -5
  3. 5
  4. -7

Answer (Detailed Solution Below)

Option 2 : -5

Fourth Proportional Question 11 Detailed Solution

Download Solution PDF

Given

K + 3, k + 2, 3k – 7, 2k – 3 

Calculation

⇒ K + 3/k + 2 = 3k – 7/2k – 3 

⇒ (K + 3)(2k – 3) = (k + 2)(3k - 7)

⇒ 2k2 - 3k + 6k -9 = 3k2 - 7k + 6k - 14

⇒ k2 - 4k - 5 = 0

⇒ (K + 1)(k – 5)

⇒ (K + 1) = 0 or (k – 5) = 0

⇒ k = -1 or K = 5

Since minimum value is asked we will consider k = -1

The fourth proportional = 2k - 3 = -2 - 3 = -5

The answer is -5.

The fourth proportion to 12, 18, 6 is equal to the third proportion to 4, k. What is the value of k?

  1. 6.5
  2. 4
  3. 6
  4. 4√3

Answer (Detailed Solution Below)

Option 3 : 6

Fourth Proportional Question 12 Detailed Solution

Download Solution PDF

Given:

Fourth proportion to 12, 18, 6 is equal to the third proportion to 4, k.

Calculation:

According to the question

Let the fourth proportion be x

⇒ 12/18 = 6/x

⇒ x = (6 × 18)/12

⇒ x = 9

Now,

Third proportion is

⇒ 4/k = k/9

⇒ k2 = 36

⇒ k = 6

∴ The required value of k is 6

Fourth proportion to 12, 18 and 6 is same as the third proportion to k and 6. What is the value of k?

  1. 13.5
  2. 3√6
  3. 3
  4. 4

Answer (Detailed Solution Below)

Option 4 : 4

Fourth Proportional Question 13 Detailed Solution

Download Solution PDF

Given:

Numbers = 12, 18 and 6

Calculation:

Forth proportion 12, 18 and 6 is n,

⇒ 12 : 18 :: 6 : n

⇒ 12/18 = 6/n

⇒ n = 9

Then,

Third proportional to k and 6 is 9.

⇒ k : 6 = 6 : 9

⇒ 9k = 36

⇒ k = 4

∴ Value of k is 4.

What is the ratio of the fourth proportional to 2, 5, 4 and the mean proportional between 2.5 and 0.016?

  1. 5 ∶ 1
  2. 10 ∶ 1
  3. 50 ∶ 1
  4. 25 ∶ 1

Answer (Detailed Solution Below)

Option 3 : 50 ∶ 1

Fourth Proportional Question 14 Detailed Solution

Download Solution PDF

Concept used:

Fourth proportion,

a/b = c/d

Mean proportion of a,b is √ab

Calculation:

Now,

2/5 = 4/d

⇒ d = 20/2 = 10 i.e fourth proportion

Again

Mean proportional of 2.5 and 0.016 = √(2.5 × 0.016)

⇒ √0.04

⇒ 0.2

Ratio = 10 : 0.2

⇒ 100 : 2 = 50 : 1

∴ Required ratio is 50 : 1.

The fourth proportional of the numbers 8, 12 and 14 is:

  1. 15
  2. 18
  3. 24
  4. 21

Answer (Detailed Solution Below)

Option 4 : 21

Fourth Proportional Question 15 Detailed Solution

Download Solution PDF

Concept used:

If four number a,b,c,d are in proportion

Then we can say that

a / b = c / d 

⇒ a × d  = b × c

Calculation:

Let the number be x 

As per the question,

8 × x = 12 × 14

⇒ x = (12 × 14) / 8

⇒ x = 21

The fourth proportion is 21

Get Free Access Now
Hot Links: teen patti club apk teen patti 3a teen patti flush teen patti bodhi