The problem involves calculating the cost price of an article based on two different selling scenarios with varying profit percentages and a given difference in selling price. We will use the concept of profit percentage, which is calculated on the cost price. By setting up equations based on the given information, we can find the cost price.
Let the cost price of the article be \( \text{CP} \).
In the first scenario, the man sold the article at a gain of 57%. The selling price (\( \text{SP}_1 \)) can be expressed as:
\[ \text{SP}_1 = \text{CP} + 57\% \text{ of CP} = \text{CP} \left(1 + \frac{57}{100}\right) = \text{CP} \left(\frac{157}{100}\right) = 1.57 \times \text{CP} \]In the second scenario, if he had sold it for ₹238 more, he would have gained 82%. This means the new selling price (\( \text{SP}_2 \)) would be \( \text{SP}_1 + 238 \). Also, \( \text{SP}_2 \) corresponds to an 82% gain on the cost price:
\[ \text{SP}_2 = \text{CP} + 82\% \text{ of CP} = \text{CP} \left(1 + \frac{82}{100}\right) = \text{CP} \left(\frac{182}{100}\right) = 1.82 \times \text{CP} \]We are given that \( \text{SP}_2 = \text{SP}_1 + 238 \). Substitute the expressions for \( \text{SP}_1 \) and \( \text{SP}_2 \) in terms of \( \text{CP} \):
\[ 1.82 \times \text{CP} = 1.57 \times \text{CP} + 238 \]Now, rearrange the equation to solve for \( \text{CP} \):
\[ 1.82 \times \text{CP} - 1.57 \times \text{CP} = 238 \]\[ (1.82 - 1.57) \times \text{CP} = 238 \]\[ 0.25 \times \text{CP} = 238 \]Calculate the cost price \( \text{CP} \):
\[ \text{CP} = \frac{238}{0.25} \]\[ \text{CP} = \frac{238}{\frac{1}{4}} \]\[ \text{CP} = 238 \times 4 \]\[ \text{CP} = 952 \]Alternatively, consider the difference in profit percentages. The gain increased from 57% to 82%. The difference in gain percentage is \( 82\% - 57\% = 25\% \). This 25% gain corresponds to the additional ₹238. Therefore, 25% of the cost price is ₹238.
\[ 25\% \text{ of CP} = 238 \]\[ \frac{25}{100} \times \text{CP} = 238 \]\[ \frac{1}{4} \times \text{CP} = 238 \]\[ \text{CP} = 238 \times 4 \]\[ \text{CP} = 952 \]The cost price of the article is ₹952.
B) 952
The problem presents a series of three-letter combinations and asks us to find the next combination in the sequence. We need to identify the pattern in how the letters change from one combination to the next, considering their positions in the English alphabet.
The pattern for the first letter is a decrease of 2 positions each time: \(25 - 2 = 23\), \(23 - 2 = 21\), \(21 - 2 = 19\). Following this pattern, the next first letter should be \(19 - 2 = 17\), which is Q.
The pattern for the second letter is also a decrease of 2 positions each time: \(18 - 2 = 16\), \(16 - 2 = 14\), \(14 - 2 = 12\). Following this pattern, the next second letter should be \(12 - 2 = 10\), which is J.
The pattern for the third letter is also a decrease of 2 positions each time: \(21 - 2 = 19\), \(19 - 2 = 17\), \(17 - 2 = 15\). Following this pattern, the next third letter should be \(15 - 2 = 13\), which is M.
The next combination in the series is QJM.
C) QJM – This option correctly follows the established pattern for all three letters.
To determine the total approximate latitudinal extent of India, we need to find the difference between its southernmost and northernmost latitudinal points. This calculation will give us the angular distance in degrees from south to north.
Correct Option: C) 30°
The latitudinal extent of India from its southernmost point (mainland) at approximately \(8^\circ \text{ N}\) to its northernmost point at approximately \(37^\circ \text{ N}\) is about \(29^\circ\). This value is best approximated by \(30^\circ\).
The question asks to identify the trading company that was formed in 1600 with an exclusive charter for trade east of the Cape of Good Hope for 15 years. This requires knowledge of the history of European East India Companies.
Correct Option: C) English East India Company
The English East India Company, formally known as "The Governor and Company of Merchants of London Trading into the East Indies," was chartered by Queen Elizabeth I on December 31, 1600. This charter granted the company an exclusive monopoly on trade with all countries east of the Cape of Good Hope and west of the Straits of Magellan for a period of 15 years. This aligns perfectly with the details provided in the question.
The question asks about the region where Wing Commander Akshay Saxena was awarded the Vayu Sena Medal for anti-piracy operations. This requires knowledge of recent defense news and geographical locations of such operations.
Correct Option: C) Arabian Sea
The question asks to identify which of the given options is NOT a part of Carnatic style composition. This requires knowledge of the typical compositional forms found in Carnatic music.
B) Chaturang is a compositional form primarily found in Hindustani classical music, not Carnatic music. It typically comprises four sections: Tarana, Sargam, Sahitya, and Bols.
To evaluate the product \(81 \times 112\), we can use the standard multiplication method. Alternatively, we can break down one of the numbers into simpler parts to make the multiplication easier, for example, by using the distributive property of multiplication over addition.
Multiply 81 by 112 directly:
112
x 81
-----
112 (112 × 1)
8960 (112 × 80)
-----
9072
We can write \(112\) as \(100 + 10 + 2\). Then multiply \(81\) by each part:
\[ 81 \times 112 = 81 \times (100 + 10 + 2) \]Apply the distributive property:
\[ = (81 \times 100) + (81 \times 10) + (81 \times 2) \]Calculate each product:
Now, add these results:
\[ 8100 + 810 + 162 \] \[ 8100 +\ 810 +\ 162 ----- 9072 \]Both methods yield the same result.
Correct Option: A) 9072
This question tests general knowledge about recent sports events, specifically the winner of the Ranji Trophy for the 2024-25 season. To answer this, one needs to recall the outcome of the latest Ranji Trophy final.
Correct Option: A) Vidarbha
Explanation based on the provided correct answer: Assuming the question implies a future outcome or has a specific context not provided, and given that 'A) Vidarbha' is marked as correct, we proceed with this. Historically, Vidarbha has been a strong team, winning the Ranji Trophy twice in recent years (2017-18 and 2018-19) and reaching the final in 2023-24. If they were to win the 2024-25 season, it would be a significant achievement. However, as of the current date, the 2024-25 season has not concluded, and thus no champion has been crowned.
This problem can be solved using a system of two linear equations based on the given information: the total number of notes and the total value of the withdrawal. We will define variables for the number of ₹50 and ₹100 notes and set up the equations accordingly.
Let \(x\) be the number of ₹50 notes.
Let \(y\) be the number of ₹100 notes.
According to the problem, Mahesh received a total of 34 notes. So, the first equation is:
\[ x + y = 34 \quad \text{(Equation 1)} \]The total amount withdrawn is ₹3,100. The value from ₹50 notes is \(50x\) and from ₹100 notes is \(100y\). So, the second equation is:
\[ 50x + 100y = 3100 \quad \text{(Equation 2)} \]We need to find the number of ₹50 notes, which is \(x\). We can solve this system of equations. From Equation 1, express \(y\) in terms of \(x\):
\[ y = 34 - x \]Substitute this expression for \(y\) into Equation 2:
\[ 50x + 100(34 - x) = 3100 \]Now, simplify and solve for \(x\):
\[ 50x + 3400 - 100x = 3100 \]\[ -50x = 3100 - 3400 \]\[ -50x = -300 \]\[ x = \frac{-300}{-50} \]\[ x = 6 \]So, the number of ₹50 notes is 6.
To verify, we can find \(y\): \(y = 34 - 6 = 28\). Check the total value: \(50 \times 6 + 100 \times 28 = 300 + 2800 = 3100\). This matches the given total amount.
A) 6 is the correct number of ₹50 notes received by Mahesh.
The question asks to identify the specific clause under Article 51A of the Indian Constitution that mandates the Fundamental Duty of safeguarding public property and abjuring violence. This requires knowledge of the various clauses of Article 51A, which lists the Fundamental Duties of Indian citizens.
D) Article 51A (i) is the correct answer because this clause explicitly states the Fundamental Duty of every citizen to safeguard public property and to abjure violence.