The ratio between the three angles of a quadrilateral is 1 : 4 : 5 respectively. The value of the fourth angle of the quadrilateral is $60^∘$. What is the difference between the value of the largest and the smallest angles of the quadrilateral?

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The ratio between the three angles of a quadrilateral is 1 : 4 : 5 respectively. The value of the fourth angle of the quadrilateral is $60^∘$. What is the difference between the value of the largest and the smallest angles of the quadrilateral?

A$120^∘ $

B$90^∘$

C$110^∘$

D$100^∘$

Nithin ? Aug 13 '2022 at 10:54

Correct answer is: \(120^∘\)

Explanation:

\(x+ 4x+ 5x+ 60 = 360^∘ \)

\(\implies 10x = 300^∘\)

\(\implies x = 30\)

\(\text{Therefore, Required difference} = 5x - x = 4x\)

\(= \Large 4 \times 30 = 120 ^{\circ}\)

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The ratio between the angles of a quadrilateral is 3 : 4 : 6 : 7. Half the second largest angle of the quadrilateral is equal to the smaller angle of a parallelogram. What is the value of adjacent angle of the parallelogram?

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BANK PO Exam (Syndicate Bank) 2010 click here to view all questions

The ratio between the angles of a quadrilateral is 3 : 4 : 6 : 7. Half the second largest angle of the quadrilateral is equal to the smaller angle of a parallelogram. What is the value of adjacent angle of the parallelogram?

A$136^∘ $

B$126^∘$

C$94^∘$

D$96^∘$

Nithin ? Aug 13 '2022 at 10:45

Correct answer is: \(126^∘\)

Explanation:

\(3x + 4x + 6x + 7x = \Large 360 ^{\circ}\)

\(= 20x = 360^o\)

\(x = 18^o\)

Therefore, smaller angle of the parallelogram = \(\frac{6x}{2}\)

\(= 3x = 54^∘\)

Therefore, Adjacent angle of parallelogram

\(= 180^∘−54^∘=126^∘\)

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The angles of a quadrilateral are in the ratio of 2:4:7:5. The smallest angle of the quadrilateral is equal to the smallest angle of a triangle. One of the angles of the triangle is twice the smallest angle of the triangle. What is the second largest angle of the triangle ?

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BANK PO Exam (Central Bank) 2010 click here to view all questions

The angles of a quadrilateral are in the ratio of 2:4:7:5. The smallest angle of the quadrilateral is equal to the smallest angle of a triangle. One of the angles of the triangle is twice the smallest angle of the triangle. What is the second largest angle of the triangle ?

A80 degrees

B60 degrees

C120 degrees

D40 degrees

Nithin ? Aug 12 '2022 at 22:24

Correct answer is: 60 degrees

Explanation:

Given the angles of a quadrilateral are in the ratio of 2:4:7:5
Let the angles of a quadrilateral are 2x, 4x, 7x, 5x
But we know that sum of the angles = 360 degrees.
=> 2x + 4x + 7x + 5x = 360
=> x = 20
Therfore, the smallest angle of the quadrilateral = 2x = 2x20 = 40 degrees.
One of the angle of the triangle = 2 x 40 = 80 degrees
The other angle is 180 - (40 + 80) = 60 degrees.

Hence the second largest angle of the triangle is 60 degrees.

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The ratio between the angles of a quadrilateral is 7 : 2 : 5 : 6 respectively. What is the sum of double the smallest angle and half the largest angle of the quadrilateral?

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BANK PO Exam (Bank Of Baroda) 2010 click here to view all questions

The ratio between the angles of a quadrilateral is 7 : 2 : 5 : 6 respectively. What is the sum of double the smallest angle and half the largest angle of the quadrilateral?

A$162^∘$

B$198^∘$

C$99^∘$

D$135^∘$

Nithin ? Aug 12 '2022 at 22:18

Correct answer is: \(135^∘\)

Explanation:

\(7x + 2x +5x + 6x = 360^∘\)

\(\implies 20x = 360^∘\)

\(\implies x = \frac{360}{20} = 18\)

\(\text{Therefore, Required answer =} \Large \frac{15x}{2}\)

\(\text{Required answer}=\frac{15 \times 18}{2}=135 ^{\circ}\)

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The largest and the second largest angles of a triangle are in the ratio of 3 : 2 respectively. The smallest angle is 20% of the sum of the largest and the second largest angles. What is the sum of the smallest and the second largest angles?

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BANK PO Exam (Bank Of Baroda) 2010 click here to view all questions

The largest and the second largest angles of a triangle are in the ratio of 3 : 2 respectively. The smallest angle is 20% of the sum of the largest and the second largest angles. What is the sum of the smallest and the second largest angles?

A$80^∘$

B$60^∘$

C$100^∘$

D$90^∘$

Nithin ? Aug 12 '2022 at 22:10

Correct answer is: \(90^∘\)

Explanation:

If the largest and the second largest angles be 3x° and 2x°. respectively then, third angle = x

Threfore, x + 2x + 3x = 180°
Therefore, x = 30°

 

Therefore, Required sum = \(x + 2x = 3x = 90^∘\)

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When 30% of one number is subtracted from another number, the second number reduces to its own four-fifth. What is the ratio between the first and the second numbers respectively?

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BANK PO Exam (Allahabad Bank) 2010 click here to view all questions

When 30% of one number is subtracted from another number, the second number reduces to its own four-fifth. What is the ratio between the first and the second numbers respectively?

A 4 : 7

B3 : 2

C2 : 5

DNone of these

Nithin ? Aug 12 '2022 at 21:59

Correct answer is: None of these

Explanation:

let the numbers be x and y respectively.
According to the question,

\(\Large y-\frac{x \times 30}{100}=\frac{4}{5}y\)

\(\implies \frac{y}{5}=\frac{3x}{10}\)

\(= \Large x : y = \frac{10}{3 \times 5}\)

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The ratio of the number of students studying in school A, B and C is 5 : 8 : 4 respectively. If the number of students studying in each of the school is increased by 20%, 25% and 30% respectively, what will be the new respective ratio of the students in school A, B and C?

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BANK PO Exam (Indian Bank) 2010 click here to view all questions

The ratio of the number of students studying in school A, B and C is 5 : 8 : 4 respectively. If the number of students studying in each of the school is increased by 20%, 25% and 30% respectively, what will be the new respective ratio of the students in school A, B and C?

A3 : 25 : 15

B20 : 25 : 13

C15 : 25 : 13

DCannot be determined

Nithin ? Aug 12 '2022 at 21:48

Correct answer is: 15 : 25 : 13

Explanation:

Required ratio

\(\Large \frac{5 \times 120}{100}:\frac{8 \times 125}{100}:\frac{4 \times 130}{10}\)

\(\Large 5 \times 120 :\ 8 \times 125 :\ 4 \times 130\)

\(= 15 : 25 : 13\)

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