Mr. Pandit owned 950 gold coins all of which he distributed amongst his three daughters Lalita, Amita and Neeta. Lalita gave 25 gold coins to her husband, Amita donated 15 gold coins and Neeta made jewellery out of 30 gold coins. The new respective ratio of the coins left with them was 20 : 73 : 83. How many gold coins did Amita receive from Mr. Pandit?

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Mr. Pandit owned 950 gold coins all of which he distributed amongst his three daughters Lalita, Amita and Neeta. Lalita gave 25 gold coins to her husband, Amita donated 15 gold coins and Neeta made jewellery out of 30 gold coins. The new respective ratio of the coins left with them was 20 : 73 : 83. How many gold coins did Amita receive from Mr. Pandit?

A380

B415

C400

D350

Nithin ? Aug 13 '2022 at 11:0

Correct answer is: 380

Explanation:

\(20x + 73x + 83x\)

\(= 950 - 25 - 15 - 30\)

\(\implies 176x = 880\)

\(\implies x = \frac{880}{176}=5\)

Therefore, Number of coins got by Amita

\(= \Large 73x+15=73 \times 5+15=380\)

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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?

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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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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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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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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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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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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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