Third Proportional MCQ Quiz - Objective Question with Answer for Third Proportional - Download Free PDF
Last updated on May 30, 2025
Latest Third Proportional MCQ Objective Questions
Third Proportional Question 1:
What is the third proportional to 28 and 112?
Answer (Detailed Solution Below)
Third Proportional Question 1 Detailed Solution
Given:
First number = 28
Second number = 112
Formula used:
If a, b, and c are in proportion, then:
\(\dfrac{a}{b} = \dfrac{b}{c}\)
Third proportional (c) = \(\dfrac{b^2}{a}\)
Calculation:
Third proportional = \(\dfrac{b^2}{a}\)
⇒ c = \(\dfrac{112^2}{28}\)
⇒ c = \(\dfrac{12544}{28}\)
⇒ c = 448
∴ The third proportional is 448, and the correct answer is option (1).
Third Proportional Question 2:
Find the third proportional of 36 and 42.
Answer (Detailed Solution Below)
Third Proportional Question 2 Detailed Solution
Given:
First number = 36
Second number = 42
Concept:
If a : b = b : c, then c is called the third proportional to a and b.
Formula Used:
Third Proportional = (b × b) / a
Calculation:
Third Proportional = (42 × 42) / 36
= 1764 / 36
= 49
∴ The third proportional of 36 and 42 is 49.
Third Proportional Question 3:
The third proportional to x and x + 100 is 405, find the value of x (where x > 100).
Answer (Detailed Solution Below)
Third Proportional Question 3 Detailed Solution
Given:
First proportional = x
Second proportional = x + 100
Third proportional = 405
Condition: x > 100
Formula Used:
If a, b, and c are in continued proportion, then b2 = ac.
Here, a = x, b = x + 100, and c = 405.
Calculation:
Using the formula for continued proportion:
(x + 100)2 = x × 405
⇒ x2 + 2 × x × 100 + 1002 = 405x
⇒ x2 + 200x + 10000 = 405x
⇒ x2 + 200x - 405x + 10000 = 0
⇒ x2 - 205x + 10000 = 0
Solve the quadratic equation using the quadratic formula: x = [-b ± √(b2 - 4ac)] / 2a
Here, a = 1, b = -205, c = 10000.
Discriminant (D) = b2 - 4ac = (-205)2 - 4 × 1 × 10000
D = 42025 - 40000
D = 2025
√D = √2025 = 45
Now, find the values of x:
x1 = [-(-205) + 45] / (2 × 1) = (205 + 45) / 2 = 250 / 2 = 125
x2 = [-(-205) - 45] / (2 × 1) = (205 - 45) / 2 = 160 / 2 = 80
We are given that x > 100.
Therefore, the value of x is 125.
∴ The value of x is 125.
Third Proportional Question 4:
If the third proportional of 3x2 and 4xy is 48, then the positive value of y is:
Answer (Detailed Solution Below)
Third Proportional Question 4 Detailed Solution
Given:
First proportional = 3x2
Second proportional = 4xy
Third proportional = 48
Formula Used:
If a, b, and c are in continued proportion, then b2 = ac.
Here, a = 3x2, b = 4xy, and c = 48.
Calculation:
(4xy)2 = (3x2) × 48
⇒ 16x2y2 = 144x2
⇒ y2 = 144x2 / 16x2
⇒ y2 = 9
⇒ y = ±√9
⇒ y = ±3
We need the positive value of y.
∴ The positive value of y is 3.
Third Proportional Question 5:
Find the third proportional of (3 + √2) and 2√7.
Answer (Detailed Solution Below)
Third Proportional Question 5 Detailed Solution
Given:
First term (a) = (3 + √2)
Second term (b) = 2√7
Formula used:
If a, b, and c are in continued proportion, then b2 = a × c
Calculation:
Let the third proportional be c.
\(2√7)^2 = (3 + √2) \times c\)
⇒ 4 × 7 = (3 + √2) × c
⇒ 28 = (3 + √2) × c
⇒ c = \( \dfrac{28}{3 + √2} \)
Rationalize the denominator:
⇒ c = \( \dfrac{28}{3 + √2} \times \dfrac{3 - √2}{3 - √2} \)
⇒ c = \( \dfrac{28(3 - √2)}{9 - 2} \)
⇒ c = \( \dfrac{28(3 - √2)}{7} \)
⇒ c = 4(3 - √2)
∴ The correct answer is option (4).
Top Third Proportional MCQ Objective Questions
The third proportional to 9 and 15 is:
Answer (Detailed Solution Below)
Third Proportional Question 6 Detailed Solution
Download Solution PDFGiven:
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.
The third proportional to (x2 - y2) and (x - y) is:
Answer (Detailed Solution Below)
Third Proportional Question 7 Detailed Solution
Download Solution PDFGiven:
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)}
⇒ \(\rm \frac{x-y}{x+y}\)
∴ The correct answer is \(\rm \frac{x-y}{x+y}\).
What is the third proportional to 16 and 24 ?
Answer (Detailed Solution Below)
Third Proportional Question 8 Detailed Solution
Download Solution PDFConcept 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
What smallest number should be added to 40 so that is the third proportion to 16 and 28?
Answer (Detailed Solution Below)
Third Proportional Question 9 Detailed Solution
Download Solution PDFConcept 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
9 is the smallest numberFind the third proportional of (b2 - a2) and (b2 - ab).
Answer (Detailed Solution Below)
Third Proportional Question 10 Detailed Solution
Download Solution PDFGiven 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) = \(\rm \frac{b^2(b-a)}{(b+a)}\)
Hence, the third proportional of (b2 - a2) and (b2 - ab) is \(\rm \frac{b^2(b-a)}{(b+a)}\).
The fourth proportion to 12, 24 and 27 is the same as the third proportion to A and 36. What is the value of A?
Answer (Detailed Solution Below)
Third Proportional Question 11 Detailed Solution
Download Solution PDFGiven:
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.
Find the third proportion of x and 30, when 45 : 12 : : 75 : x.
Answer (Detailed Solution Below)
Third Proportional Question 12 Detailed Solution
Download Solution PDFGiven:
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 = \(\frac{b^2}{a}\)
Calculation:
According to the question,
45 : 12 : : 75 : x.
It can be written as:
⇒ \(\frac{45}{12} = \frac{75}{x}\)
⇒ x = \(\frac{12 \times 75}{45}\) = 20
Now,
Let y be the third proportional of 20 and 30.
⇒ y = \(\frac{30^2}{20}\)= 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 = \(\frac{ab}{c}\)
2. Mean Proportional:
Let 'x' be the mean proportional for a and b.
then, (a : x :: x : b)
Therefore,
x = \(\sqrt{ab}\)
3. Fourth Proportional:
Let 'x' be the first proportional for a, b and c.
then, (a : b :: c : x)
Therefore,
x = \(\frac{bc}{a}\)
The third proportional to a3 + b3 and a2 + ab + b2, when a = 2 and b = 3, is:
(correct to 2 decimal places)
Answer (Detailed Solution Below)
Third Proportional Question 13 Detailed Solution
Download Solution PDFGiven:
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).
If the third proportional of 3x2 and 4xy is 48, then find the positive value of y.
Answer (Detailed Solution Below)
Third Proportional Question 14 Detailed Solution
Download Solution PDFGiven:
The expression = 3x2, 4xy and 48
Concept:
If a, b, and c are in proportion.
\({a\over b}={b\over c}\)
Formula used:
If a, b, and c are in proportion then third proportion
\(c={b^2\over a}\)
Calculation:
According to the question
⇒ 48 = \({({4xy})^2\over 3x^2}={16x^2y^2\over3x^2}={16y^2\over3}\)
⇒ 3 × 3 = y2
⇒ y =√(3 × 3) = 3
∴ The required result will be 3.
If p is the third proportional to 3, 9, then what is the fourth proportional to 6, p, 4?
Answer (Detailed Solution Below)
Third Proportional Question 15 Detailed Solution
Download Solution PDFGiven:
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