The problem asks us to find a number that relates to 98 in the same way that 12 relates to 72. We need to identify the pattern or relationship between the first pair of numbers and then apply that same pattern to the second pair.
Analyze the relationship between 12 and 72:
Let the first number be \(N_1 = 12\) and the second number be \(N_2 = 72\).
We can observe that \(72\) is a multiple of \(12\).
\[ 72 = 12 \times 6 \]Alternatively, we can express the relationship using division:
\[ \frac{N_2}{N_1} = \frac{72}{12} = 6 \]So, the second number is 6 times the first number.
Identify another possible relationship:
Consider the relationship using the number itself. If we divide the first number by 2 and then multiply by the first number:
\[ \frac{12}{2} \times 12 = 6 \times 12 = 72 \]This pattern seems plausible: \(N_2 = \left( \frac{N_1}{2} \right) \times N_1\).
Apply the identified pattern to the second pair:
Let the unknown number be \(X\) and the fourth number be \(98\).
Using the pattern \(N_2 = \left( \frac{N_1}{2} \right) \times N_1\), we have:
\[ 98 = \left( \frac{X}{2} \right) \times X \] \[ 98 = \frac{X^2}{2} \]Multiply both sides by 2:
\[ X^2 = 98 \times 2 \] \[ X^2 = 196 \]Take the square root of both sides:
\[ X = \sqrt{196} \] \[ X = 14 \]Thus, the missing number is 14.
D) 14 — Following the pattern \(N_2 = (N_1/2) \times N_1\), if \(N_2 = 98\), then \(98 = (X/2) \times X\), which leads to \(X^2 = 196\), and \(X = 14\).
The question asks to identify which of the given options is NOT an Indian research base in Antarctica. This requires knowledge of the names of India's research stations on the Antarctic continent.
Correct Option: A) Dakshin Yamunotri is NOT an Indian research base at Antarctica. It is a pilgrimage site in the Himalayas.
The question asks to identify the odd one out from a list of organs. This requires classifying the organs based on their primary function or system they belong to.
Correct Option: A) Kidney. The kidney is part of the excretory system, whereas the liver, large intestine, and stomach are all integral parts of the digestive system.
The question asks to identify the British official known as the 'Father of Communal Electorate' in India. This title is associated with the introduction of separate electorates for Muslims, a significant feature of the Morley-Minto Reforms.
Correct Option: D) Lord Minto is widely regarded as the 'Father of Communal Electorate' in India due to his pivotal role in introducing separate electorates for Muslims through the Morley-Minto Reforms (Indian Councils Act of 1909).
To solve this series problem, we need to identify the pattern or rule that transforms each number into the next. We will examine the relationship between consecutive terms to find a consistent mathematical operation.
Correct Option: A) 839 is the number that replaces the question mark, following the established pattern.
The question asks to identify the primary architectural technique used for decoration in the Taj Mahal. We need to recall the distinctive decorative methods employed in Mughal architecture, specifically in the Taj Mahal, and compare them with the given options.
Correct Option: B) Pietra dura is an inlay technique of using cut and fitted, highly polished colored stones to create images. It is the primary decorative technique used in the Taj Mahal, where precious and semi-precious stones like lapis lazuli, jade, crystal, turquoise, and sapphire are inlaid into white marble to form intricate floral patterns and calligraphic verses from the Quran.
We are given a scenario where doubling the selling price triples the original profit. We need to find the new profit percentage. We will use the basic formulas for profit and profit percentage, representing the cost price, selling price, and profit with variables.
Let the original Cost Price be \( \text{CP} \).
Let the original Selling Price be \( \text{SP} \).
Let the original Profit be \( P_1 \).
The formula for profit is:
\[ P_1 = \text{SP} - \text{CP} \quad \text{(Equation 1)} \]According to the problem, the selling price is doubled. So, the new Selling Price is \( 2 \times \text{SP} \).
The profit becomes three times the original profit. So, the new Profit, \( P_2 \), is \( 3 \times P_1 \).
Using the profit formula for the new scenario:
\[ P_2 = (2 \times \text{SP}) - \text{CP} \]Substitute \( P_2 = 3 \times P_1 \) into the equation:
\[ 3 \times P_1 = (2 \times \text{SP}) - \text{CP} \quad \text{(Equation 2)} \]Now, substitute \( P_1 = \text{SP} - \text{CP} \) from Equation 1 into Equation 2:
\[ 3 \times (\text{SP} - \text{CP}) = 2 \times \text{SP} - \text{CP} \]Expand and solve for the relationship between SP and CP:
\[ 3 \times \text{SP} - 3 \times \text{CP} = 2 \times \text{SP} - \text{CP} \]\[ 3 \times \text{SP} - 2 \times \text{SP} = 3 \times \text{CP} - \text{CP} \]\[ \text{SP} = 2 \times \text{CP} \]This means the original selling price is twice the cost price. Now we can find the original profit percentage and the new profit percentage.
Original Profit Percentage (\( \%P_1 \)):
\[ \%P_1 = \frac{P_1}{\text{CP}} \times 100 \]\[ \%P_1 = \frac{\text{SP} - \text{CP}}{\text{CP}} \times 100 \]\[ \%P_1 = \frac{2 \times \text{CP} - \text{CP}}{\text{CP}} \times 100 \]\[ \%P_1 = \frac{\text{CP}}{\text{CP}} \times 100 = 100\% \]New Profit (\( P_2 \)):
\[ P_2 = 3 \times P_1 \]Since \( P_1 = \text{SP} - \text{CP} = 2 \times \text{CP} - \text{CP} = \text{CP} \), then \( P_2 = 3 \times \text{CP} \).New Selling Price (\( \text{SP}_2 \)):
\[ \text{SP}_2 = 2 \times \text{SP} = 2 \times (2 \times \text{CP}) = 4 \times \text{CP} \]New Profit Percentage (\( \%P_2 \)):
\[ \%P_2 = \frac{P_2}{\text{CP}} \times 100 \]\[ \%P_2 = \frac{3 \times \text{CP}}{\text{CP}} \times 100 \]\[ \%P_2 = 3 \times 100 = 300\% \]Correct Option: D) 300%
The question asks to identify the phylum of animals characterized by having jointed legs. This requires knowledge of the distinguishing features of major animal phyla.
Correct Option: B) Arthropod — The phylum Arthropoda is characterized by the presence of an exoskeleton and jointed appendages, which include jointed legs. This is a defining feature of this diverse group of animals, which includes insects, arachnids, and crustaceans.
Find the value of x.
6(8x + 25) - 70 = 5(8x + 25)
x = 5 \( \frac{5}{7} \)
x = 5 \( \frac{5}{8} \)
x = \( \frac{5}{8} \)
x = 5 \( \frac{15}{8} \)
The problem asks us to find the value of \(x\) from the given linear equation. We can simplify the equation by treating the expression \((8x + 25)\) as a single variable, or by expanding the terms using the distributive property. The former approach is generally quicker.
Write down the given equation:
\[ 6(8x + 25) - 70 = 5(8x + 25) \]Let \(y = 8x + 25\). Substitute \(y\) into the equation:
\[ 6y - 70 = 5y \]Rearrange the equation to isolate \(y\). Subtract \(5y\) from both sides:
\[ 6y - 5y - 70 = 0 \]\[ y - 70 = 0 \]Add \(70\) to both sides to find the value of \(y\):
\[ y = 70 \]Now, substitute back \(y = 8x + 25\):
\[ 8x + 25 = 70 \]Subtract \(25\) from both sides to isolate the term with \(x\):
\[ 8x = 70 - 25 \]\[ 8x = 45 \]Divide by \(8\) to find the value of \(x\):
\[ x = \frac{45}{8} \]Convert the improper fraction to a mixed number. Divide \(45\) by \(8\):
\[ 45 \div 8 = 5 \text{ with a remainder of } 5 \]\[ x = 5 \frac{5}{8} \]B) The calculated value of \(x\) is \(5 \frac{5}{8}\), which matches option B.
The question asks to identify the incorrect pair of a UN organ/specialized agency and its headquarters. We need to check the headquarters location for each organization listed in the options.
Correct Option: C) World Health Organization (WHO) – New York. This pair is incorrect because the WHO's headquarters is in Geneva, Switzerland, not New York.