The angles of a quadrilateral are in ratio of 3 : 5 : 9 : 7. The second largest angle of the quadrilateral is equal to the largest angle of a triangle. One of the angles of the triangle is $25^∘$. What is the value-of second largest angle of the triangle?

Report

Report an issue

Name

Email

Message

Submit

Cancel

INSURANCE EXAMS (UIIC) 2011 click here to view all questions

The angles of a quadrilateral are in ratio of 3 : 5 : 9 : 7. The second largest angle of the quadrilateral is equal to the largest angle of a triangle. One of the angles of the triangle is $25^∘$. What is the value-of second largest angle of the triangle?

A$60^∘$

B$50^∘$

C$40^∘$

D$20^∘$

Nithin ? undefined

Correct answer is: \(50^o\)

Explanation:

Sum of ratios = 3 + 5 + 9 + 7 = 24

Second largest angle of quadrilateral = \(\frac{7}{24} \times 360 = 105 ^{\circ}\)

Largest angle of triangle
Therefore, Third angle of triangle = \(\frac{7}{24} \times 360 = 105 ^{\circ}\)

\(=180 ^{\circ} - 105 ^{\circ} - 25 ^{\circ}\)

\(= 50^∘ = \text{second largest angle of triangle.}\)

 

View Answer

Discuss

The cost of a diamond varies directly as the square of its weight. A diamond broke into four pieces with their weights in the ratio of 1:2:3:4. If the loss in total value of the diamond was the ₹ 70,000, what was the price of the original diamond?

Report

Report an issue

Name

Email

Message

Submit

Cancel

INSURANCE EXAMS (New India Assurance) 2009 click here to view all questions

The cost of a diamond varies directly as the square of its weight. A diamond broke into four pieces with their weights in the ratio of 1:2:3:4. If the loss in total value of the diamond was the ₹ 70,000, what was the price of the original diamond?

A₹ 1,00,000

B₹ 1,40,000

C₹ 1,50,000

D₹ 1,75,000

Nithin ? undefined

Correct answer is: ₹ 1,00,000

Explanation:

\(Cost ∝ (weight)^2\)

Total weight of original diamond = 1k + 2k + 3k + 4k = 10k, where k is positive integer

Cost of original diamond = \((10k)^2\) = \(100k^2\)

Total cost of four broken pieces = \(k^2\)(1 + 4 + 9 + 16) = 30\(k^2\)

The value of broken pieces is 70,000 less than the original diamond.

Difference in cost = 70,000

\(100k^2 - 30k^2 = 70,000\)

\(70k^2 = 70,000\)

\(k^2 = 1,000\)

Cost of original diamond = \(100k^2 = 100 × 1,000\)

= 1,00,000

View Answer

Discuss

The sides of a triangle are in the ratio $\frac{1}{2}: \frac{1}{3}: \frac{1}{4} and its perimeter is 104 cm. The length of the longest side (in cm) is -

Report

Report an issue

Name

Email

Message

Submit

Cancel

INSURANCE EXAMS (LIC) 2009 click here to view all questions

The sides of a triangle are in the ratio $\frac{1}{2}: \frac{1}{3}: \frac{1}{4}$ and its perimeter is 104 cm. The length of the longest side (in cm) is -

A26

B32

C48

D52

Nithin ? undefined

Correct answer is: 48

Explanation:

\(\eqalign{ & {\text{Ratio of sides}} \cr & = \frac{{\text{1}}}{{\text{2}}}:\frac{{\text{1}}}{{\text{3}}}:\frac{{\text{1}}}{{\text{4}}} \cr & = 6:4:3 \cr} \)

Let the sides be 6x, 4x and 3x
Then,
⇒ 6x + 4x + 3x = 104
or 13x = 104
or x = 8
∴ Longest side = 6x = (6 × 8)m = 48m

View Answer

Discuss

The sum of three numbers is 136. If the ratio between first and second be 2 : 3 and that between second and third be 5 : 3, then the second number is:

Report

Report an issue

Name

Email

Message

Submit

Cancel

INSURANCE EXAMS (LIC) 2009 click here to view all questions

The sum of three numbers is 136. If the ratio between first and second be 2 : 3 and that between second and third be 5 : 3, then the second number is:

A40

B48

C52

D60

Nithin ? undefined

Correct answer is: 60
Explanation:

Let the three numbers be a, b and c respectively.
Now.
a : b = 2 : 3
b : c = 5 : 3

Therefore, a : b : c =  \(\Large 2 \times 5:3 \times 5:3 \times 3\)

= 10 : 15 : 9
According to the question,
a + b + c = 136
=> 10x + 15x + 9x = 136

\(\implies 34x = 136 \implies x = \frac{136}{34}=4\)
\(\therefore b = 15x = 15×4 = 60\)

View Answer

Discuss

Three-fourth of a number is equal to 60% of another number. What is the difference between the numbers?

Report

Report an issue

Name

Email

Message

Submit

Cancel

INSURANCE EXAMS (LIC) 2008 click here to view all questions

Three-fourth of a number is equal to 60% of another number. What is the difference between the numbers?

A18

B32

C24

D Cannot be determined

Nithin ? undefined

Correct answre is:  Cannot be determined

Explanation:

Let the numbers be x and y respectively . Then,

\(\Large \frac{3}{4}x = \text{= 60% of y}\)

\(= \Large \frac{3}{4}x = \frac{60}{100}y \implies \frac{3}{4}x = \frac{3}{5}y\)

\(=\Large y = \frac{3}{4} \times \frac{5}{3}x = \frac{5}{4}x\)

\(\therefore \Large y - x = \frac{5}{4}x-x = \frac{x}{4}\)

Clearly, no unique answer is possible.

View Answer

Discuss

The present age of A, B, C are in the ratio 8:14:22 respectively.the present ages of B, C and D are in the ratio 21:33:44 respectively. Which of the following represents the ratio of he present ages of A, B, C and D respectively

Report

Report an issue

Name

Email

Message

Submit

Cancel

INSURANCE EXAMS (LIC) 2008 click here to view all questions

The present age of A, B, C are in the ratio 8:14:22 respectively.the present ages of B, C and D are in the ratio 21:33:44 respectively. Which of the following represents the ratio of he present ages of A, B, C and D respectively

A12:22:33:44

B12:22:31:44

C12:21:33:44

DNone of the these

Nithin ? undefined

Correct answer is: 12:21:33:44

Explanation:

A : B : C = 8 : 14 : 22
or 4 : 7 : 11
or 12 : 21 : 33
B : C : D = 21 : 33 : 44
Therefore, A : B : C : D
= 12 : 21 : 33 : 44

View Answer

Discuss

The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?

Report

Report an issue

Name

Email

Message

Submit

Cancel

INSURANCE EXAMS (LIC) 2006 click here to view all questions

The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?

A3 : 3 : 10

B10 : 11 : 20

C23 : 33 : 60

DCannot be determined

Nithin ? undefined

Correct answer is: 23 : 33 : 60

Explanation:

\(\eqalign{ & {\text{Let}}, \cr & A = 2k \cr & B = 3k\,{\text{and}} \cr & C\, = 5k \cr & A's\,{\text{new}}\,{\text{salary}} \cr & = \frac{{115}}{{100}}\,of\,2k = {\frac{{115}}{{100}} \times 2k} = \frac{{23k}}{{10}} \cr & B's\,{\text{new}}\,{\text{salary}} \cr & = \frac{{110}}{{100}}\,of\,3k = {\frac{{110}}{{100}} \times 3k} = \frac{{33k}}{{10}} \cr & C's\,{\text{new}}\,{\text{salary}} \cr & = \frac{{120}}{{100}}\,of\,5k = {\frac{{120}}{{100}} \times 5k} = 6k \cr & \therefore {\text{New}}\,{\text{ratio}} \cr & = {\frac{{23k}}{{10}}:\frac{{33k}}{{10}}:6k} \cr & = 23:33:60 \cr} \)

View Answer

Discuss