The problem involves calculating the age of a fourth friend given the mean ages of different groups of friends. We will use the formula for the mean (average) to find the total sum of ages for each group and then determine the age of the new friend.
Understand the concept of Mean:
The mean (average) of a set of numbers is calculated by dividing the sum of all numbers by the count of the numbers.
\[ \text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} \]From this, we can derive:
\[ \text{Sum of all values} = \text{Mean} \times \text{Number of values} \]Calculate the sum of ages for the first three friends:
Given that the mean age of three friends is 22.
Number of friends = 3
Mean age = 22
Sum of ages of 3 friends \( = \text{Mean} \times \text{Number of friends} \)
\[ \text{Sum}_3 = 22 \times 3 = 66 \]Calculate the sum of ages for the four friends:
Given that the mean age of four friends is 24.
Number of friends = 4
Mean age = 24
Sum of ages of 4 friends \( = \text{Mean} \times \text{Number of friends} \)
\[ \text{Sum}_4 = 24 \times 4 = 96 \]Find the age of the fourth friend:
The sum of ages of four friends includes the sum of ages of the first three friends plus the age of the fourth friend.
Let the age of the fourth friend be \(x\).
\[ \text{Sum}_4 = \text{Sum}_3 + x \]Substitute the values we calculated:
\[ 96 = 66 + x \]Now, solve for \(x\):
\[ x = 96 - 66 \]\[ x = 30 \]
So, the age of the fourth friend is 30.
Correct Option: B) 30
This is a syllogism-based logical reasoning question. We need to evaluate each conclusion based solely on the given statements, assuming they are true, even if they contradict common knowledge. We should not introduce outside information.
A) Only conclusion I follows.
The question asks about the origin of the quasi-federal form of government in India. This requires knowledge of the sources of the Indian Constitution, specifically which country's constitution influenced the federal structure.
C) Canada — India adopted the concept of a quasi-federal government, characterized by a strong central government and the distribution of powers, from the Canadian Constitution. This includes features like the appointment of state governors by the Centre and residuary powers vesting in the Centre.
This problem involves finding the day of the week after a certain number of days. The key concept here is that the days of the week repeat in a cycle of 7. Therefore, we need to find the remainder when the number of days is divided by 7.
Therefore, if today (Thursday) is the starting day, after 91 days, it will still be Thursday.
Correct Option: A) Thursday
To find the total journey distance, we can use the relationship between distance, speed, and time. The journey is divided into two equal halves in terms of distance. We are given the speeds for each half and the total time taken. We can express the time taken for each half in terms of the distance of one half and then sum them up to equal the total time.
Let the total journey be \(D\) km. Since the journey is divided into two equal halves, the distance of the first half is \(\frac{D}{2}\) km and the distance of the second half is also \(\frac{D}{2}\) km.
The speed for the first half is \(S_1 = 18 \text{ km/h}\). The time taken for the first half, \(T_1\), can be calculated as:
\[ T_1 = \frac{\text{Distance}}{\text{Speed}_1} = \frac{D/2}{18} = \frac{D}{36} \text{ hours} \]The speed for the second half is \(S_2 = 30 \text{ km/h}\). The time taken for the second half, \(T_2\), can be calculated as:
\[ T_2 = \frac{\text{Distance}}{\text{Speed}_2} = \frac{D/2}{30} = \frac{D}{60} \text{ hours} \]The total time taken for the journey is given as 12 hours. So, the sum of the times for the two halves must be equal to 12 hours:
\[ T_1 + T_2 = 12 \]\[ \frac{D}{36} + \frac{D}{60} = 12 \]To solve for \(D\), find a common denominator for 36 and 60. The least common multiple (LCM) of 36 and 60 is 180.
\[ \frac{5D}{180} + \frac{3D}{180} = 12 \]\[ \frac{5D + 3D}{180} = 12 \]\[ \frac{8D}{180} = 12 \]Now, solve for \(D\):
\[ 8D = 12 \times 180 \]\[ 8D = 2160 \]\[ D = \frac{2160}{8} \]\[ D = 270 \text{ km} \]Thus, the total journey is 270 km.
B) 270
The question asks to identify the Vice Chairman of NITI Aayog as of December 2020. This requires knowledge of key appointments in Indian government bodies during that specific period.
Correct Option: A) Rajiv Kumar
This question tests knowledge about the physical characteristics of Indian currency notes, specifically the ₹2,000 banknote. To answer correctly, one needs to recall or know the standard dimensions (length and width) of this particular denomination as issued by the Reserve Bank of India.
Correct Option: C) The ₹2,000 bank note has dimensions of 66 mm × 166 mm. This is the officially stated size by the Reserve Bank of India.
The question asks about the primary themes portrayed in the Indian classical dance form 'Manipuri'. To answer this, one needs to recall the characteristic themes and mythological associations of Manipuri dance.
A) Krishna-Gopis — Manipuri dance is predominantly characterized by themes centered around the love story of Radha and Krishna, and the 'Ras Leela' which depicts Krishna's playful interactions with the Gopis. This makes option A the correct answer.
To find the simple interest rate, we first need to calculate the simple interest earned. This is done by subtracting the principal amount from the total amount. Once the simple interest is known, we can use the simple interest formula \(SI = \frac{P \times R \times T}{100}\) to solve for the rate of interest (R).
Simple Interest is the difference between the Amount and the Principal.
\[ \text{SI} = \text{A} - \text{P} \]\[ \text{SI} = \text{₹}14,632 - \text{₹}12,400 \]\[ \text{SI} = \text{₹}2,232 \]The formula for simple interest is:
\[ \text{SI} = \frac{\text{P} \times \text{R} \times \text{T}}{100} \]The rate of interest is 6% per annum.
Correct Option: A) 6%
We need to find a number based on a given condition and then calculate two-fifth of that number. We can set up an algebraic equation to represent the problem statement and solve for the unknown number.
Let the unknown number be \(x\).
According to the problem, when 42 is subtracted from the number, it reduces to its 70%. We can write this as an equation:
\[ x - 42 = 70\% \text{ of } x \]Convert the percentage to a decimal or fraction:
\[ x - 42 = \frac{70}{100} \times x \]\[ x - 42 = 0.7x \]Now, solve for \(x\). Subtract \(0.7x\) from both sides:
\[ x - 0.7x - 42 = 0 \]\[ 0.3x - 42 = 0 \]Add 42 to both sides:
\[ 0.3x = 42 \]Divide by 0.3 to find \(x\):
\[ x = \frac{42}{0.3} \]\[ x = \frac{42}{\frac{3}{10}} \]\[ x = 42 \times \frac{10}{3} \]\[ x = 14 \times 10 \]\[ x = 140 \]The question asks for two-fifth of that number. Calculate \(\frac{2}{5}\) of \(x\):
\[ \frac{2}{5} \times 140 \]\[ = 2 \times \frac{140}{5} \]\[ = 2 \times 28 \]\[ = 56 \]Correct Option: C) 56