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

Given:

Numbers: 22, 26, 19, 21

When x is added, they are in proportion: (22 + x) : (26 + x) :: (19 + x) : (21 + x)

Second proportion: 2x : y :: y : (4x - 8), with y > 0

Formula used:

If a : b :: c : d, then a/b = c/d or ad = bc

If a : b :: b : c, then b² = ac (for mean proportion)

Calculations:

First, find x using the first proportion:

(22 + x)/(26 + x) = (19 + x)/(21 + x)

⇒ (22 + x)(21 + x) = (26 + x)(19 + x)

⇒ 22 × 21 + 22x + 21x + x² = 26 × 19 + 26x + 19x + x²

⇒ 462 + 43x + x² = 494 + 45x + x²

⇒ 462 + 43x = 494 + 45x

⇒ 43x - 45x = 494 - 462

⇒ -2x = 32

⇒ x = -16

Now, use the second proportion with the value of x:

2x : y :: y : (4x - 8)

Since y is the mean proportional, y² = (2x)(4x - 8)

Substitute x = -16:

⇒ y² = (2 × -16) × (4 × -16 - 8)

⇒ y² = (-32) × (-64 - 8)

⇒ y² = (-32) × (-72)

⇒ y² = 2304

⇒ y = \(\sqrt{2304}\)

⇒ y = 48 (Since y > 0)

∴ The value of y is 48.

Given Proportions:

1) 7 : 63 :: 6.2 : x

2) 2 : 6 :: 9 : y

Calculations:

Find the value of x.

For the first proportion, the product of the extremes equals the product of the means.

⇒ 7 × x = 63 × 6.2

⇒ x = (63 × 6.2) / 7

⇒ x = 55.8

Find the value of y.

For the second proportion, the product of the extremes equals the product of the means.

⇒ 2 × y = 6 × 9

⇒ y = 54 / 2

⇒ y = 27

Find the ratio of x to y.

⇒ Ratio = x : y = 55.8 : 27

⇒ To simplify, remove the decimal by multiplying both sides by 10: 558 : 270

⇒ Simplify the ratio by dividing both numbers by their Highest Common Factor, which is 18.

⇒ 558 ÷ 18 = 31

⇒ 270 ÷ 18 = 15

∴ The ratio of x to y is 31 : 15.

Given:

First number = 5

Second number = 8

Third number = 15

Formula Used:

The fourth proportional to a, b, c is given by: \(\text{Fourth proportional} = \frac{(b × c)}{a}\)

Calculation:

⇒ Fourth proportional = (8 × 15) / 5

⇒ Fourth proportional = 120 / 5

⇒ Fourth proportional = 24

The fourth proportional to 5, 8, 15 is: 24

Correct Option: Option 4

Given:

Numbers: 3, 7, and 9

Formula used:

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

d = (b × c) / a

Calculation:

d = (7 × 9) / 3

⇒ d = 63 / 3

⇒ d = 21

∴ The correct answer is option (3).

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).

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

Given

Proportional numbers: 11.6 m, 9.2 m, 32.8 m

Concept:

If a:b = c:d, then d = b * c / a (fourth proportional)

Solution:

Substitute the values into the formula: d = 9.2 × 32.8/11.6 ⇒ d = 26.01 m

Therefore, the fourth proportional is 26.01 m.