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

Given:

First three even natural numbers = 2, 4, 6

B = Sum of first three even natural numbers = 2 + 4 + 6 = 12

C is the third proportional of 57 and B.

Formula used:

If C is the third proportional of A and B, then:

⇒ C =

Calculation:

A = 57, B = 12

⇒ C =

⇒ C =

⇒ C = 2.53

∴ The correct answer is option (4).

Given:

C is the third proportional of 44 and B.

B = Sum of the first three even natural numbers = 2 + 4 + 6

Third proportional formula: If A, B, C are in proportion, then C = B²/A

Formula used:

C = B²/A

Calculation:

B = 2 + 4 + 6 = 12

⇒ C = (12)² / 44

⇒ C = 144 / 44

⇒ C = 3.27

∴ The correct answer is option (3).

Given Data:

a ∶ b = 4:6

b ∶ c = 10:11

Concept Used:

Ratios can be equated to find the ratio between different elements.

Solution:

⇒ a ∶ b = 4 ∶ 6 = 2 ∶ 3 (simplified)

⇒ b ∶ c = 10 ∶ 11

⇒ Therefore, a : c = 2 × 10 ∶ 3 x 10 ∶ 11 × 3 = 20 ∶ 33 (b got cancelled)

Therefore, the ratio c ∶ a is 33 ∶ 20.

Given:

Numbers = 4 and 28

Concept Used:

Third proportional of a and b = a : b = b : c

Calculation:

⇒ Let the third proportional be x.

⇒ So, According to the formula,

⇒ 4 : 28 = 28 : x

⇒ x =  = 196

Therefore, the third proportional of 4 and 28 is 196.

Given:

First pair: 12 and 42

Second pair: 16 and 56

Formula Used:

Third Proportional of two numbers a and b = (b × b) / a

Ratio = Third proportional of (12, 42) : Third proportional of (16, 56)

Calculation:

Third proportional of 12 and 42:

⇒ (42 × 42) / 12

⇒ 1764 / 12

⇒ 147

Third proportional of 16 and 56:

⇒ (56 × 56) / 16

⇒ 3136 / 16

⇒ 196

Ratio:

⇒ 147 : 196

⇒ (147 ÷ 49) : (196 ÷ 49)

⇒ 3 : 4

The ratio is 3 : 4.

Given:

We have to obtain the third proportional to 9 and 15

Concept Used:

Concept of ratio and proportion

Calculation:

Let, the third proportional be x

Then,

9 : 15 : : 15 : x

⇒ 9/15 = 15/x

⇒ x = (15 × 15) / 9

⇒ x = 25

∴ The required third proportional to 9 and 15 is 25.

Given:

First number (a) = (x2 - y2)

Second number (b) = (x - y)

Formula used:

Third proportional = {2nd number (b)}²/first number (a)

(x2 - y2) = (x - y) × (x + y)

Calculation:

Third proportional = (x - y)²/(x2 - y2)

⇒ {(x - y) × (x - y)}/{(x - y) × (x + y)} 

⇒ 

∴ The correct answer is .

Given data:

First term = b² - a²

Second term = b² - ab

Concept: Third proportional to two given terms x and y is (y² / x).

Step-by-step solution:

Third proportional = (b² - ab)² / (b² - a²) = 

Hence, the third proportional of (b² - a²) and (b² - ab) is .

Concept used:

The third proportional proportion is the second term of the mean terms.

For example, if we have a ∶ b = c ∶ d, then the term ‘c’ is the third proportional to ‘a’ and ‘b’.

Represented as:

a : b ∷ b : c

Calculation:

Let the third proportion to 16 and 24 be x

⇒ 16/24 = 24/x

⇒ x = (24 × 24)/16

⇒ x = 36

∴ The third proportional to 16 and 24 is 36

Concept used:

Third proportion- a ∶ b ∶ ∶ b ∶ c

Calculation:

Let the number added be x

16 ∶ 28 ∶∶ 28 ∶ (40 + x)

16/28 = 28/(40 + x)

40 + x = (28 × 28)/16

⇒ x = 9

Given:

Numbers = 12, 24 and 27

Calculation:

Forth proportions 12, 24 and 27 is n,

⇒ 12 : 24 :: 27 : n 

⇒ 12/24 = 27/n

⇒ n = 54

Then,

Third proportional to A and 36 is 54.

⇒ A : 36 = 36 : 54

⇒ 54A = 36²

⇒ A = 24

∴ The value of A is 24.

Given:

Find the third proportion of x and 30, when 45 : 12 : : 75 : x.

Formula used:

Third Proportional:

Let 'z' be the third proportional for a and b.

then, (a : b :: b : z)

Therefore, 

z = 

Calculation:

According to the question,

45 : 12 : : 75 : x.

It can be written as:

⇒ 

⇒ x =  = 20

Now, 

Let y be the third proportional of 20 and 30.

⇒ y = = 45

The third proportional of 20 and 30 = 45

Therefore, '45' is the required answer.

Additional Information

1. First Proportional:

Let 'x' be the first proportional for a, b and c.

then, (x : a :: b : c)

Therefore, 

x = 

2. Mean Proportional:

Let 'x' be the mean proportional for a and b.

then, (a : x :: x : b)

Therefore, 

x = 

3. Fourth Proportional:

Let 'x' be the first proportional for a, b and c.

then, (a : b :: c : x)

Therefore, 

x = 

Given:

a = 2

b = 3

Concept:

We need to find the third proportional to a³ + b³ and a² + ab + b².

Solution:

⇒ Substitute a and b into the two expressions to get the first and second numbers.

⇒ First number = a³ + b³ = 2³ + 3³ = 8 + 27 = 35

⇒ Second number = a2 + ab + b2 = 22 + 2*3 + 32 = 4 + 6 + 9 = 19

⇒ The third proportional (T) to two numbers (x and y) is given by the formula T = (y²)/x

So, substituting the first and second numbers:

⇒ T = (19²)/35 = 10.31

Therefore, the third proportional to a³ + b³ and a² + ab + b², when a = 2 and b = 3, is approximately 10.31 (correct to two decimal places).

Given:

The expression = 3x2, 4xy and 48

Concept:

If a, b, and c are in proportion.

Formula used:

If a, b, and c are in proportion then third proportion

Calculation:

According to the question

⇒ 48 = 

⇒ 3 × 3 = y2

⇒ y =√(3 × 3) = 3

∴ The required result will be 3.

Given:

p is the third proportional to 3, 9

Calculation:

Let the fourth proportion be x

p is the third proportional to 3, 9

⇒ 3/9 = 9/p

⇒ 3p = 81

⇒ p = 27

Now,

The fourth proportion is

⇒ 6/27 = 4/x

⇒ 6x = (27 × 4)

⇒ 6x = 108

⇒ x = 18

∴ The value of fourth proportion is 18