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?

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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

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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 -

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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

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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:

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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

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

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

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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.

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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

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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

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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?

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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:

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

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The ratio of the earnings of A and B is 4:7. If the earnings A increase by 50% and those of B decrease by 25%, the new ratio of their earnings becomes 8:7. What areA's earnings?

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The ratio of the earnings of A and B is 4:7. If the earnings A increase by 50% and those of B decrease by 25%, the new ratio of their earnings becomes 8:7. What areA's earnings?

ARs 26,000

BRs 28, 000

CRs 21,000

DData inadequate

Nithin ? undefined

Correct answer is: Data inadequate

Explanation:

The ratio of the earnings of A and BB is 4:7

Let Earnings of A=4k

Earnings of B=7k

Earnings of A now becomes 4k+\(\frac{1}{2}​\)×4k=4k+2k=6k

Earnings of B now becomes 7k−\(\frac{1}{4}\)​×7k=\(\frac{3}{4}\)​×7k=\(\frac{21k​}{4}\)

Now ratio of earnings are \(\frac{6}{\frac{21}{4}}\)​=\(\frac{24}{21}\)​=\(\frac{8}{7}\)

Hence the Data is Inadequate.

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