To solve this problem, we first determine the current ages of A, B, and C using their given ratio and the sum of their ages. Once their current ages are known, we calculate their ages after ten years and then find the ratio of A's age to B's age at that future time.
Correct Option: C) 12 : 19
This problem involves concepts of speed, distance, and time. We are given two scenarios with different speeds and arrival times. We need to find the speed required to reach the destination at a specific intermediate time. We can use the formula \(\text{Distance} = \text{Speed} \times \text{Time}\) to solve this problem. Since the distance is constant, we can set up equations based on the given information to find the actual travel time and then the required speed.
The question asks about the products formed when an acid reacts with a metal carbonate. This is a fundamental chemical reaction type. We need to recall the general equation for such a reaction to identify all the products.
General Reaction: When an acid reacts with a metal carbonate, the typical products are a salt, water, and carbon dioxide gas.
Example Reaction: Let's consider a common example, the reaction of hydrochloric acid (\(\text{HCl}\)) with calcium carbonate (\(\text{CaCO}_3\)).
The balanced chemical equation is:
\[ \text{2HCl(aq)} + \text{CaCO}_3\text{(s)} \rightarrow \text{CaCl}_2\text{(aq)} + \text{H}_2\text{O(l)} + \text{CO}_2\text{(g)} \]Identifying Products:
Conclusion: From the example and the general reaction, it is clear that water, carbon dioxide, and salt are all formed during the reaction between an acid and a metal carbonate.
Correct Option: D) All of the options
When an acid reacts with a metal carbonate, it produces a salt, water, and carbon dioxide gas. This is a standard reaction in chemistry. For example, hydrochloric acid reacting with sodium carbonate produces sodium chloride (salt), water, and carbon dioxide.
The question asks about the reference gas used to calculate Global Warming Potential (GWP). GWP is a measure of how much energy the emissions of 1 ton of a given gas will absorb over a given period of time, relative to the emissions of 1 ton of carbon dioxide (\(\text{CO}_2\)). Understanding this definition is key to identifying the correct reference gas.
C) Carbon dioxide is the universally accepted reference gas for calculating Global Warming Potential (GWP). Its GWP is defined as 1, and the GWP of other gases indicates how many times more warming they cause than an equivalent mass of carbon dioxide over a specified period.
The question asks for the year when the first Commonwealth Games were held. This is a factual recall question related to sports history. We need to identify the correct founding year from the given options.
Correct Option: D) The first Commonwealth Games, then known as the British Empire Games, were held in 1930 in Hamilton, Canada. This event brought together athletes from 11 countries of the British Empire to compete in 6 sports.
The question asks to identify the easternmost state of India. This requires knowledge of India's geography and the relative positions of its states, particularly those in the North-Eastern region.
B) Arunachal Pradesh is India's easternmost state. Its easternmost point, Kibithu, is located at approximately \(97^\circ 23'\) East longitude, making it the first place in India to witness the sunrise.
To find the odd one out, we need to identify a common pattern or rule that applies to three of the given options, and then find the option that does not follow this rule. We will analyze the positional values of the letters in each option.
Correct Option: D) CGKR
The pattern for options A, B, and C is that the difference between consecutive letters increases by 2, starting from +3 (i.e., +3, +5, +7). Option D does not follow this pattern, as its differences are +4, +4, +7.
If Simple Interest is 12.5% more than the principal and number of years (n), rate (r) are numerically in the ratio 2 : 1, then find the values of n, r.
n=20, r=10%
n=14; r=7%
n=12, r=6%
n=15; r=7\( \frac{1}{2} \)%
We are given information about Simple Interest (SI) in relation to the Principal (P) and a ratio between the number of years (n) and the rate (r). We need to find the values of n and r. We will use the formula for Simple Interest and the given conditions to form equations and solve for n and r.
12.5% can be written as a fraction:
\[ 12.5\% = \frac{12.5}{100} = \frac{1}{8} \]So, SI is \(\frac{1}{8}\) of the Principal more than the Principal. This means:
\[ \text{SI} = \text{P} + \frac{1}{8}\text{P} = \frac{9}{8}\text{P} \]Given that \(n:r = 2:1\), we can write:
\[ \frac{n}{r} = \frac{2}{1} \implies n = 2r \]The formula for Simple Interest is:
\[ \text{SI} = \frac{\text{P} \times n \times r}{100} \]Substitute \(\text{SI} = \frac{9}{8}\text{P}\) and \(n = 2r\) into the formula:
\[ \frac{9}{8}\text{P} = \frac{\text{P} \times (2r) \times r}{100} \]Cancel P from both sides (assuming P is not zero):
\[ \frac{9}{8} = \frac{2r^2}{100} \]Multiply both sides by 100:
\[ \frac{9}{8} \times 100 = 2r^2 \]\[ \frac{900}{8} = 2r^2 \]\[ \frac{225}{2} = 2r^2 \]Divide by 2:
\[ r^2 = \frac{225}{4} \]Take the square root:
\[ r = \sqrt{\frac{225}{4}} = \frac{15}{2} = 7.5\% \]Using the relation \(n = 2r\):
\[ n = 2 \times 7.5 = 15 \text{ years} \]The calculated values are \(n=15\) and \(r=7.5\%\). This matches option D.
D) n=15; r=7\( \frac{1}{2} \)%
To find the gain percentage, we need to establish a relationship between the cost price (CP) and the selling price (SP) of a single item. The problem states that the cost price of 25 items is equal to the selling price of 20 items. We can use this information to find the profit or loss and then calculate the gain percentage.
Let the cost price of one item be \(CP\) and the selling price of one item be \(SP\).
According to the problem statement, the cost price of 25 items is equal to the selling price of 20 items. We can write this as an equation:
\[ 25 \times CP = 20 \times SP \]Rearrange the equation to find the ratio of \(SP\) to \(CP\):
\[ \frac{SP}{CP} = \frac{25}{20} \]\[ \frac{SP}{CP} = \frac{5}{4} \]This means that if the cost price of an item is 4 units, its selling price is 5 units. Since \(SP > CP\), there is a gain (profit).
Calculate the gain:
\[ \text{Gain} = SP - CP \]\[ \text{Gain} = 5 - 4 = 1 \text{ unit} \]Calculate the gain percentage using the formula:
\[ \text{Gain percentage} = \frac{\text{Gain}}{\text{CP}} \times 100\% \]\[ \text{Gain percentage} = \frac{1}{4} \times 100\% \]\[ \text{Gain percentage} = 25\% \]D) 25% is the correct gain percentage.
The question asks about the sport associated with the 'Fed Cup'. This requires general knowledge about major international sports tournaments.
Correct Option: B) Women's tennis
The Fed Cup (now known as the Billie Jean King Cup) is the world cup of women's tennis. It is an international team competition contested annually by national teams.