Amar Jeet Singh can complete a piece of work in 5 days. With the help of his son he can complete it in 3 days. In how many days can the son independently complete the work?
6 \( \frac{1}{2} \)
7 \( \frac{1}{2} \)
5 \( \frac{1}{2} \)
4 \( \frac{1}{2} \)
This problem can be solved using the concept of work rate. We will calculate the individual work rate of Amar Jeet Singh and the combined work rate of Amar Jeet Singh and his son. Then, we can find the son's individual work rate by subtracting Amar Jeet Singh's rate from the combined rate. Finally, the time taken by the son alone to complete the work is the reciprocal of his work rate.
Amar Jeet Singh can complete the work in 5 days. So, his one-day work (work rate) is:
\[ \text{Amar Jeet Singh's 1-day work} = \frac{1}{5} \text{ of the work} \]With the help of his son, they can complete the work in 3 days. So, their combined one-day work is:
\[ \text{Combined 1-day work} = \frac{1}{3} \text{ of the work} \]The son's one-day work can be found by subtracting Amar Jeet Singh's one-day work from their combined one-day work:
\[ \text{Son's 1-day work} = \text{Combined 1-day work} - \text{Amar Jeet Singh's 1-day work} \] \[ \text{Son's 1-day work} = \frac{1}{3} - \frac{1}{5} \]To subtract these fractions, find a common denominator, which is 15:
\[ \text{Son's 1-day work} = \frac{5}{15} - \frac{3}{15} = \frac{5-3}{15} = \frac{2}{15} \text{ of the work} \]If the son completes \(\frac{2}{15}\) of the work in one day, then the total time taken by him to complete the entire work is the reciprocal of his one-day work:
\[ \text{Time taken by son} = \frac{1}{\text{Son's 1-day work}} = \frac{1}{\frac{2}{15}} = \frac{15}{2} \text{ days} \]Convert this improper fraction to a mixed fraction:
\[ \frac{15}{2} = 7 \frac{1}{2} \text{ days} \]Correct Option: B) 7 \( \frac{1}{2} \)
The question asks to identify the state with the highest per capita income for the Financial Year (FY) 2018-19, based on a report from the Ministry of Statistics and Programme Implementation released in January 2020. This requires knowledge of economic statistics related to Indian states and Union Territories.
Correct Option: D) Goa
To access the Internet, a device needs a unique identifier that allows it to communicate and be located on the network. This identifier is crucial for routing data to and from the device.
Correct Option: A) Unique IP Address is essential because it serves as the primary identifier for any device on the Internet, enabling communication and data exchange.
The question asks for the underlying assumption behind the idiom "A camel is called the ship of the desert." This idiom compares a camel to a ship, implying a functional similarity rather than a physical one. We need to identify which option best explains this functional comparison.
B) Camels are used for transportation in deserts. This option directly addresses the functional similarity implied by the idiom. Camels serve as the primary means of transport across the vast, challenging terrain of deserts, fulfilling a role analogous to that of ships on the sea.
The question asks to identify the South Indian state with the highest number of Archaeological Survey of India (ASI) declared Monuments of National Importance. This requires knowledge of the distribution of such monuments across the southern states.
Correct Option: B) Karnataka has the highest number of Monuments of National Importance declared by the Archaeological Survey of India (ASI) among the South Indian states. It boasts a rich historical and cultural heritage, including sites like Hampi, Pattadakal, and Badami, which contribute significantly to its high count of protected monuments.
Find the value of 0.4 + \( \frac{404}{1000} \)
To solve this problem, we need to convert the fraction into a decimal and then add the two decimal numbers. The key is to align the decimal points correctly before performing the addition.
The given fraction is \( \frac{404}{1000} \). To convert this to a decimal, we divide the numerator by the denominator. Dividing by 1000 means moving the decimal point three places to the left.
\[ \frac{404}{1000} = 0.404 \]Now we need to add the first number, \(0.4\), to the decimal we just obtained, \(0.404\).
\[ 0.4 + 0.404 \]To add decimals, we align the decimal points and add corresponding place values. We can write \(0.4\) as \(0.400\) for easier alignment.
\[ \begin{array}{r} 0.400 \\ + 0.404 \\ \hline 0.804 \end{array} \]Thus, the sum is \(0.804\).
C) 0.804 — As calculated in the step-by-step explanation, the sum of \(0.4\) and \(0.404\) is \(0.804\).
The question asks to identify the leader of the significant railway strike that occurred in India in 1974. This requires knowledge of major historical events and prominent figures in Indian labor movements and politics.
Correct Option: C) George Fernandes was a prominent trade unionist and socialist leader who led the All India Railwaymen's Federation (AIRF) during the nationwide railway strike in May 1974. This strike was a significant event in Indian labor history.
This problem involves the concept of work and time, specifically how the number of workers affects the time taken to complete a task. We will calculate the total work units, the work completed, and then determine the remaining work and the number of workers needed to finish it within the new deadline.
Correct Option: B) 28
To solve this problem, we need to assign a numerical value to each letter in the given word based on its position in the English alphabet (A=1, B=2, ..., Z=26). Then, we will sum up these values for all the letters in the word "EXAGGERATION" to find the total.
Add all the assigned numerical values together:
\[ 5 + 24 + 1 + 7 + 7 + 5 + 18 + 1 + 20 + 9 + 15 + 14 \]Summing these numbers:
\[ 5 + 24 = 29 \]\[ 29 + 1 = 30 \]\[ 30 + 7 = 37 \]\[ 37 + 7 = 44 \]\[ 44 + 5 = 49 \]\[ 49 + 18 = 67 \]\[ 67 + 1 = 68 \]\[ 68 + 20 = 88 \]\[ 88 + 9 = 97 \]\[ 97 + 15 = 112 \]\[ 112 + 14 = 126 \]The total sum of the values of all the letters in the word EXAGGERATION is 126.
D) 126 is the correct total sum of the positional values of the letters in the word EXAGGERATION.
The question asks to identify the freedom fighter known as 'Frontier Gandhi'. This is a direct factual recall question from Indian history, specifically related to the Indian independence movement and its prominent leaders.
Correct Option: B) Khan Abdul Ghaffar Khan is widely known as 'Frontier Gandhi' (Sarhadi Gandhi in Pashto) due to his unwavering commitment to non-violent resistance against British rule in the North-West Frontier Province, mirroring Mahatma Gandhi's philosophy and methods. He founded the Khudai Khidmatgar movement, also known as the "Red Shirts", which advocated for a free and secular India.