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

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).

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).

Given:

If 30, 50, 96, and y are in proportion, then:

30 : 50 = 96 : y

Formula used:

In proportion, a : b = c : d is equivalent to:

a × d = b × c

Calculation:

30 : 50 = 96 : y

⇒ 30 × y = 50 × 96

⇒ y = (50 × 96) / 30

⇒ y = 4800 / 30

⇒ y = 160

∴ The correct answer is option (2).

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).

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.

Formula Used:

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

Calculation:

4^th proportional of 10, 12, 15

= (12 × 15)/10 = 18

∴ The fourth proportional is 18

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.

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.

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

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

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.

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.

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

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.

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

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.