This problem involves work and time, specifically comparing the work rates of men and women. We will first determine the individual work rates of one man and one woman. Then, we calculate the work done by the initial group and the remaining work. Finally, we determine how many additional men are needed to complete the remaining work in the specified time.
Calculate the work rate of one man:
16 men can complete a work in 24 days.
Total work units = \(\text{Number of men} \times \text{Days}\)
Let 1 man's 1-day work be \(M\).
\[ 16 \times M \times 24 = \text{Total Work} \]\[ 384M = \text{Total Work} \]Calculate the work rate of one woman:
24 women can complete the same work in 32 days.
Let 1 woman's 1-day work be \(W\).
\[ 24 \times W \times 32 = \text{Total Work} \]\[ 768W = \text{Total Work} \]Establish the relationship between men's and women's work rates:
Since the total work is the same:
\[ 384M = 768W \]\[ M = \frac{768}{384}W \]\[ M = 2W \]This means 1 man's work rate is equal to 2 women's work rate. Or, 1 woman's work rate is half of 1 man's work rate (\(W = \frac{1}{2}M\)). Let's assume the total work is 768 units (LCM of 384 and 768, or simply 768W). Then, 1 man's 1-day work is 2 units, and 1 woman's 1-day work is 1 unit.Calculate work done in the first 12 days:
16 men and 16 women worked for 12 days.
Work done by 16 men in 1 day = \(16 \times M = 16 \times 2 = 32\) units.
Work done by 16 women in 1 day = \(16 \times W = 16 \times 1 = 16\) units.
Total work done per day by the group = \(32 + 16 = 48\) units.
Work done in 12 days = \(48 \times 12 = 576\) units.
Calculate the remaining work:
Total work = 768 units.
Remaining work = \(\text{Total Work} - \text{Work done in 12 days}\)
\[ \text{Remaining work} = 768 - 576 = 192 \text{ units} \]Determine men needed to complete remaining work:
The remaining work (192 units) must be completed by men in 2 days.
Let \(X\) be the total number of men required.
Work done by \(X\) men in 2 days = \(X \times M \times 2\)
Since \(M=2\) units/day:
\[ X \times 2 \times 2 = 192 \]\[ 4X = 192 \]\[ X = \frac{192}{4} \]\[ X = 48 \text{ men} \]This is the total number of men required to finish the remaining work in 2 days.Calculate additional men needed:
Initially, there were 16 men working. The total men required are 48.
Additional men needed = \(\text{Total men required} - \text{Initial men}\)
\[ \text{Additional men} = 48 - 16 = 32 \text{ men} \]A) 32 — As calculated, 32 more men are needed to complete the remaining work in 2 days.
The question asks about the Sikh Guru who invited Sufi saint Hazrat Mian Mir to lay the foundation stone of the Golden Temple (Harmandir Sahib). This is a factual question related to Sikh history and the construction of one of its most sacred sites.
Correct Option: D) Shri Guru Arjan Dev ji
The question asks to identify the major river flowing through the Union Territory of Dadra and Nagar Haveli. This requires knowledge of the geography of Indian Union Territories and their prominent rivers.
The Damanganga River, also known as Daman Ganga, is the major river that flows through the Union Territory of Dadra and Nagar Haveli. It originates in the Western Ghats and flows westwards into the Arabian Sea. The river is crucial for the region's water supply and ecology.
This is a coding-decoding problem where numbers are assigned to words. To find the code for a specific word, we need to identify common words and their corresponding numbers across different statements.
We are looking for the code for the word 'be'.
The common word in Statement 3 and Statement 4 is 'be'.
The numbers associated with Statement 3 are {7, 8, 9}.
The numbers associated with Statement 4 are {7, 0}.
The common number in both sets is '7'.
Since 'be' is the only common word and '7' is the only common number between these two statements, '7' must stand for 'be'.
Correct Option: C) 7 — By comparing the statements where the word 'be' appears, we found that the common number associated with it is 7.
The problem provides a coding scheme where letters are assigned numerical values. We need to identify the pattern of this assignment and then apply it to spell the word 'MASSAGE'.
Correct Option: A) 1311919175 is the correct representation of 'MASSAGE' based on the alphabetical position of each letter.
The question asks to identify the name of the joint proposal drafted by prominent Indian industrialists in 1944 for a planned economy in independent India. This is a direct factual recall question related to the economic history of India.
Correct Option: B) The Bombay Plan
The Bombay Plan was a set of proposals for the post-independence economic development of India. It was published in 1944 by eight prominent Indian industrialists, including J.R.D. Tata, G.D. Birla, Ardeshir Dalal, Sir Purshottamdas Thakurdas, Lala Shri Ram, Kasturbhai Lalbhai, A.D. Shroff, and John Mathai. The plan advocated for a significant role of the state in economic planning and development, aiming for a substantial increase in national income and per capita income over a 15-year period.
The question asks to identify which of the given countries is NOT a member of OPEC (Organization of the Petroleum Exporting Countries). To answer this, one needs to know the current member states of OPEC.
Correct Option: A) Kenya is not a member of OPEC.
The question asks for the number of bones in an adult human body. This is a fundamental fact in human anatomy. We need to recall the standard number of bones present in a healthy adult human skeleton.
Correct Option: C) 206
An adult human body typically has 206 bones. This number is a standard anatomical fact and includes all bones from the skull to the toes, including the vertebral column, ribs, and limb bones.
The question asks for the location of the Bhadra Wildlife Sanctuary. This requires knowledge of the geographical distribution of important wildlife sanctuaries and national parks in India.
Correct Option: B) Karnataka
The Bhadra Wildlife Sanctuary is indeed located in the state of Karnataka. It is known for its diverse flora and fauna, including tigers, elephants, and various bird species. It was declared a Project Tiger Reserve in 1998.
This question tests fundamental knowledge of computer memory units. Understanding the relationship between Bytes and Kilobytes is crucial for anyone working with computers or preparing for competitive exams that cover basic computer concepts.
Correct Option: C) 1024