Assistant & UDC • Paper-II
Who is known as the Father of Computer?
A)
Steve Jobs
B)
German Konrad Zuse
C)
John Mauchly
D)
Charles Babbage
Charles Babbage is widely recognized as the 'Father of Computer' because he originated the concept of a programmable computer. In the 19th century, he designed the 'Difference Engine' and later the 'Analytical Engine.' The Analytical Engine was particularly significant as it contained the basic logical structure of a modern computer, including an arithmetic logic unit (ALU), control flow in the form of conditional branching and loops, and integrated memory.
Why other options are incorrect:
- Steve Jobs: A co-founder of Apple Inc. and a pioneer of the personal computer revolution, but not the inventor of the computer concept.
- Konrad Zuse: A German engineer who created the Z3, the first working programmable, fully automatic digital computer, but he built upon the foundational concepts established by Babbage.
- John Mauchly: Co-inventor of the ENIAC (Electronic Numerical Integrator and Computer), which was the first general-purpose electronic digital computer, but he is not credited as the 'Father of Computer'.
Assistant & UDC • Paper-II
The basic units of an excel spreadsheet where we enter data is called:
A)
Cell
B)
Room
C)
Table
D)
Margin
In Microsoft Excel and other spreadsheet software, a spreadsheet is organized as a grid of columns (labeled with letters) and rows (labeled with numbers). The intersection of a single row and a single column forms a rectangular box known as a 'Cell'. This cell is the fundamental unit where a user enters data, such as text, numbers, or formulas. Each cell is uniquely identified by its cell address (e.g., A1, B10).
Why other options are incorrect:
- b. Room: This is not a technical term used in spreadsheet software.
- c. Table: A table is a collection of related data organized in rows and columns; it is composed of many cells, rather than being the basic unit itself.
- d. Margin: A margin refers to the blank space around the edges of a page when printing a document, not a data entry unit.
Assistant & UDC • Paper-II
Which one is a “text editor” for Microsoft Windows?
A)
Notepad
B)
Wordpad
C)
Notebook
D)
Excel
A 'text editor' is a program used for editing plain text files (files that contain no formatting like bold, italics, or images).
1. **Notepad (Option a):** This is the default basic text editor included with Microsoft Windows. It handles plain text (.txt files) and is used for simple notes or editing configuration files and code. Therefore, it is the correct answer.
2. **Wordpad (Option b):** This is a 'word processor,' not a simple text editor. It supports Rich Text Format (RTF), allowing for basic formatting like bolding, font changes, and alignment, which distinguishes it from a plain text editor.
3. **Notebook (Option c):** This is not a standard built-in system application for Microsoft Windows. While there are third-party apps with this name, it is not the recognized Windows text editor.
4. **Excel (Option d):** This is a 'spreadsheet application' used for data analysis, calculations, and creating tables, not for text editing.
Assistant & UDC • Paper-II
Machine Intelligence, an intelligence demonstrated by machines, in contrast to the natural intelligence displayed by humans is known as
A)
Robot Functioning
B)
Robotic Intelligence
C)
Artificial Intelligence
D)
Artificial Functioning
The question asks for the term used to describe intelligence demonstrated by machines as opposed to natural human intelligence.
1. **Artificial Intelligence (AI)** is the formal branch of computer science dedicated to creating systems capable of performing tasks that typically require human intelligence, such as visual perception, speech recognition, decision-making, and translation between languages. The term 'Artificial' explicitly contrasts with 'Natural' intelligence.
2. **Robot Functioning** (Option a) refers to the mechanical operation or the execution of programmed tasks by a robot, not the intelligence itself.
3. **Robotic Intelligence** (Option b) is a subset or an application of AI specifically applied to robotics, but it is not the general term for machine intelligence.
4. **Artificial Functioning** (Option d) is not a standard technical term in computer science.
Therefore, 'Artificial Intelligence' is the correct and most comprehensive term.
Assistant & UDC • Paper-II
Which one is the first word processor application?
A)
MS Word
B)
MS Office
C)
Wordstar
D)
Google
To determine the first word processor among the given options, we must look at the chronological release of the software:
1. **WordStar (Option c):** Released in 1978, WordStar was one of the first commercially successful word processing programs for microcomputers (specifically the CP/M operating system). It dominated the market in the late 70s and early 80s.
2. **MS Word (Option a):** Microsoft Word was first released in 1983. While it eventually became the industry standard, it arrived several years after WordStar.
3. **MS Office (Option b):** Microsoft Office is not a single word processor, but a 'suite' of applications (which includes Word, Excel, and PowerPoint). The first version of the Office suite was released in 1989/1990.
4. **Google (Option d):** Google is a company/search engine. While Google Docs is a word processor, it was released in 2006, making it the most recent of the options.
Therefore, among the choices provided, WordStar is the earliest word processor application.
Assistant & UDC • Paper-II
The present governor of Mizoram is
A)
Kummanam Rajasekharan
B)
Jagdish Mukhi
C)
Nibhay Sharma
D)
M.M.Lakhera
Step 1: Identify the current Governor of Mizoram. As of the most recent appointments, Shri Kummanam Rajasekharan was appointed as the Governor of Mizoram (taking office in 2024).
Step 2: Evaluate the options.
- Option (a) Kummanam Rajasekharan is the current incumbent.
- Option (b) Jagdish Mukhi is the former Governor of Mizoram (served from 2018 to 2023).
- Option (c) Nibhay Sharma and Option (d) M.M. Lakhera are not the Governors of Mizoram; they are typically associated with administrative or civil service roles (IAS).
Step 3: Conclusion. Based on current official government records, Kummanam Rajasekharan is the correct answer.
Assistant & UDC • Paper-II
The longest river of Mizoram is
A)
Mat Lui
B)
Ser Lui
C)
Tlawng Lui
D)
Tuirini
The Tlawng River (Tlawng Lui) is the longest and most significant river in the state of Mizoram. It flows through the central part of the state and eventually joins the Kolai River to form the larger river systems that drain into the plains of Bangladesh.
Analysis of other options:
- Mat Lui: A smaller river system in Mizoram.
- Ser Lui: A river in the region, but significantly shorter than the Tlawng.
- Tuirini: One of the major rivers of Mizoram, known for its beauty and importance, but it is not the longest.
Assistant & UDC • Paper-II
Who is the creator and owner of facebook?
A)
Mukseh Ambani
B)
Mark Zuckerberg
C)
Daniel Springteen
D)
Bill Gates
Step-by-step reasoning:
1. Analysis of the question: The question asks for the creator and owner (founder/CEO) of the social media platform Facebook.
2. Evaluating the options:
- Option (a) Mukesh Ambani: He is the chairman and managing director of Reliance Industries, an Indian conglomerate.
- Option (b) Mark Zuckerberg: He co-founded Facebook (now Meta Platforms, Inc.) in 2004 while studying at Harvard University and serves as its CEO.
- Option (c) Daniel Springteen: This name does not correspond to any well-known creator of a major global tech platform.
- Option (d) Bill Gates: He is the co-founder of Microsoft Corporation.
3. Conclusion: Based on historical and corporate facts, Mark Zuckerberg is the correct answer.
Assistant & UDC • Paper-II
Which Company has launched the “Share the Load” Campaign and achieved Guinness World Records Certificate for ‘Largest Laundry Lesson’?
A)
Surf Excel
B)
Tide
C)
Rin
D)
Ariel
The 'Share the Load' campaign was launched by Ariel (a brand owned by Procter & Gamble). The campaign aims to challenge the gender stereotype that laundry and household chores are solely the responsibility of women, encouraging men to share the load of housework. In 2019, Ariel achieved a Guinness World Record for the 'Largest Laundry Lesson' by conducting a massive educational event to promote gender equality in domestic chores.
Why other options are incorrect:
- Surf Excel (Hindustan Unilever) is known for campaigns like 'Daag Acche Hain'.
- Tide (Procter & Gamble) focuses primarily on brightness and cleaning power.
- Rin (Hindustan Unilever) focuses on brightness and whitening.
Assistant & UDC • Paper-II
A cistern can be filled by two taps A and B in 12 hours and 16 hours respectively. The full cistern can be emptied by a third tap C in 8 hours. If all the taps are turned on at the same time, in how much time will the empty cistern be filled up completely?
A)
48 hours
B)
45 hours
C)
42 hours
D)
38 hours
Step-by-step solution:
1. **Determine the rates of each tap per hour**:
- Tap A fills the cistern in 12 hours, so its rate is +1/12 of the cistern per hour.
- Tap B fills the cistern in 16 hours, so its rate is +1/16 of the cistern per hour.
- Tap C empties the cistern in 8 hours, so its rate is -1/8 of the cistern per hour (negative because it is removing water).
2. **Calculate the combined rate when all three taps are open**:
Combined Rate = (Rate of A) + (Rate of B) - (Rate of C)
Combined Rate = 1/12 + 1/16 - 1/8
3. **Find a common denominator**:
The Least Common Multiple (LCM) of 12, 16, and 8 is 48.
- 1/12 = 4/48
- 1/16 = 3/48
- 1/8 = 6/48
4. **Perform the calculation**:
Combined Rate = (4/48) + (3/48) - (6/48)
Combined Rate = (4 + 3 - 6) / 48
Combined Rate = 1/48 of the cistern per hour.
5. **Find the total time to fill the cistern**:
Time = 1 / (Combined Rate) = 1 / (1/48) = 48 hours.
Therefore, the empty cistern will be filled up completely in 48 hours. Options b, c, and d are incorrect as they do not match the calculated result of 48 hours.
Assistant & UDC • Paper-II
Which city is known as city of Skyscrapers?
A)
Los Angeles
B)
New York
C)
Mumbai
D)
Michigan
New York City is globally recognized as the 'City of Skyscrapers' due to its iconic skyline and the high concentration of tall buildings, many of which were pioneers in skyscraper architecture (such as the Empire State Building and the Chrysler Building).
Analysis of other options:
- Los Angeles: While it has tall buildings, it is more known as the center of the entertainment industry (Hollywood) and is characterized by urban sprawl rather than a dense skyscraper core.
- Mumbai: Known as the financial capital of India and having many skyscrapers, it is not the primary global city associated with this specific nickname.
- Michigan: This is a U.S. state, not a city, making it an incorrect option for a 'city' designation.
Assistant & UDC • Paper-II
Green Revolution is also known as
A)
Second Agricultural Revolution
B)
Anti-Red Revolution
C)
Third Agricultural Revolution
D)
Agricultural and Healthy Revolution
The Green Revolution, which began in the mid-20th century (roughly 1940s-1960s), is widely referred to as the 'Second Agricultural Revolution'. It was characterized by the introduction of High-Yielding Varieties (HYV) of seeds (especially wheat and rice), the expansion of irrigation infrastructure, and the increased use of chemical fertilizers and pesticides to drastically increase food production.
Why other options are incorrect:
- Option b (Anti-Red Revolution): This is not a recognized term in agricultural history. 'Red Revolution' usually refers to communism or specific political upheavals.
- Option c (Third Agricultural Revolution): The Third Agricultural Revolution is generally associated with the 'Gene Revolution' or the current era of biotechnology, GMOs, and precision farming.
- Option d (Agricultural and Healthy Revolution): This is a descriptive phrase and not a formal historical or academic term used to identify the Green Revolution.
Assistant & UDC • Paper-II
The full form of an internet language ASAP is:
A)
Assam State Army Personnel
B)
American School of Advance Psychology
C)
As soon as possible
D)
Amsterdam Science and Arts Programme
The term 'ASAP' is a widely used acronym in internet slang, business communication, and general English. It stands for 'As Soon As Possible,' indicating that a task or response is urgent and should be completed at the earliest opportunity. Options a, b, and d are fabricated phrases that do not correspond to the standard meaning of the acronym ASAP in the context of language or internet communication.
Assistant & UDC • Paper-II
By what number should (-3/2 - 3) be divided so that the quotient may be (-2/27)?
A)
4/21
B)
-2/27
C)
-3/17
D)
5/16
Step 1: Simplify the expression inside the parentheses.
Expression = (-3/2 - 3)
To subtract, find a common denominator: -3/2 - 6/2 = -9/2.
Step 2: Set up the division equation.
Let the number we are looking for be 'x'.
According to the problem: (-9/2) ÷ x = -2/27.
Step 3: Solve for x.
(-9/2) / x = -2/27
Multiply both sides by x: -9/2 = (-2/27) * x
To isolate x, multiply both sides by the reciprocal of -2/27, which is -27/2:
x = (-9/2) * (-27/2)
Step 4: Calculate the final value.
x = (-9 * -27) / (2 * 2)
x = 243 / 4
Wait, let's re-evaluate the options provided. The options are small fractions (4/21, -2/27, etc.), while the calculation 243/4 is very large. Let's re-read the expression (-3/2 - 3). If the expression was meant to be (-3/2) / 3 or something else, it would change. However, if we check the options against the logic:
If x = 4/21, then (-9/2) / (4/21) = (-9/2) * (21/4) = -189/8, which is not -2/27.
Let's re-examine the expression (-3/2 - 3). If the expression was actually (-3/2) - (3/something) or if there is a typo in the question's numbers. Let's test the options to see if any fit a common typo.
If the quotient is -2/27 and the divisor is 4/21, the dividend would be (-2/27) * (4/21) = -8/567.
If the dividend was (-3/2 - 3) = -4.5, and the quotient is -2/27, the divisor must be (-4.5) / (-2/27) = (-9/2) * (-27/2) = 243/4 = 60.75.
However, looking at the options provided in typical competitive exams for this specific question, there is often a typo in the transcription of the problem. If the expression was (-3/2) * (something) or if the dividend was actually (-3/2) / 3 = -1/2, then (-1/2) / x = -2/27 => x = (-1/2) / (-2/27) = (-1/2) * (-27/2) = 27/4.
Let's try another interpretation: If the expression was (-3/2) - (3/something). No.
Let's try: (-3/2) / x = -2/27 => x = (-3/2) / (-2/27) = (-3/2) * (-27/2) = 81/4.
Let's re-read the expression as (-3/2) - 3. If the result is -9/2 and the quotient is -2/27, the answer is 243/4. Since 243/4 is not in the options, let's check if the expression was (-3/2) / (-3) = 1/2. Then (1/2) / x = -2/27 => x = (1/2) / (-2/27) = -27/4.
Wait, let's check if the expression was (-3/2) - (3/something) or if the quotient was different. If the dividend was (-3/2) - 3 = -9/2 and the divisor was 243/4, the quotient is -2/27.
Given the options provided (a. 4/21, b. -2/27, c. -3/17, d. 5/16), there is a high probability of a typo in the question's numbers as presented. However, in many official keys for this specific problem (which appears in various UDC banks), the intended expression is often different. If we assume the question meant 'By what number should (-3/2) be divided so that the quotient is (-2/27)', x = 81/4.
Let's test the options backwards:
If x = 4/21 and quotient = -2/27, dividend = (4/21) * (-2/27) = -8/567.
If x = -2/27 and quotient = -2/27, dividend = 4/729.
Actually, looking at the structure of the question from similar sources, the expression is often (-3/2) - (3/4) or similar. If the dividend was (-3/2) - (3/4) = -6/4 - 3/4 = -9/4. Then (-9/4) / x = -2/27 => x = (-9/4) / (-2/27) = (-9/4) * (-27/2) = 243/8.
If the dividend was (-3/2) / 3 = -1/2. Then (-1/2) / x = -2/27 => x = 27/4.
Given the options provided, there is no mathematical way to reach them with the numbers provided. However, if this is a multiple-choice question from a specific exam paper where 'a' is marked correct, the question likely contained a typo. Based on the provided options and the standard format of these exams, the most likely intended dividend was -8/567, which is unlikely.
Re-calculating: (-3/2 - 3) = -4.5.
-4.5 / x = -2/27
-4.5 * 27 / -2 = x
-121.5 / -2 = 60.75 = 243/4.
Since the options are completely different, and I must provide a JSON response, I will provide the mathematical derivation. But if I must choose an option, there is a discrepancy. Let's check if the expression was (-3/2) / (-3) = 1/2. Then 1/2 / x = -2/27 => x = -27/4.
If the dividend was (-3/2) * (-3) = 9/2. Then 9/2 / x = -2/27 => x = (9/2) / (-2/27) = -243/4.
Conclusion: The question as written is mathematically inconsistent with the options. However, following the prompt to solve it: the result is 243/4. If the options are mandatory, there is a typo in the source. I will provide the calculation for the text provided.
Assistant & UDC • Paper-II
The median of the following data : 17, 2, 7, 27, 25, 5, 14, 18, 10, 24, 48, 10, 8, 7, 10, 28 is
A)
10
B)
12
C)
28
D)
48
To find the median of a data set, follow these steps:
1. **Arrange the data in ascending order:**
Original data: 17, 2, 7, 27, 25, 5, 14, 18, 10, 24, 48, 10, 8, 7, 10, 28
Sorted data: 2, 5, 7, 7, 8, 10, 10, 10, 14, 17, 18, 24, 25, 27, 28, 48
2. **Count the number of observations (n):**
There are n = 16 observations.
3. **Determine the median position:**
Since n is even (16), the median is the average of the two middle terms. The middle terms are the (n/2)th and the (n/2 + 1)th terms.
- 8th term = 10
- 9th term = 14
4. **Calculate the average of the middle terms:**
Median = (8th term + 9th term) / 2
Median = (10 + 14) / 2 = 24 / 2 = 12.
Therefore, the median is 12. Option (b) is correct. Options (a), (c), and (d) are incorrect as they do not represent the average of the middle values of the sorted data set.
Assistant & UDC • Paper-II
What is the name of the world’s fastest bullet train that is tested by Japan recently?
A)
ALMA-K
B)
ALTO-I
C)
ALFA-X
D)
ALGO-R
The ALFA-X (a portmanteau of 'ALpha-X') is the experimental next-generation Shinkansen (bullet train) developed by East Japan Railway Company (JR East). It was designed to test new technologies to reduce noise and increase speed. During its testing phase, the ALFA-X reached speeds of 400 km/h (approximately 248 mph), aiming for a commercial operating speed of 360 km/h. Options a (ALMA-K), b (ALTO-I), and d (ALGO-R) are fabricated terms and do not correspond to any known Japanese high-speed rail projects.
Assistant & UDC • Paper-II
The sum of five numbers is 555. The average of the first two numbers is 75 and the third number is 115. The average of the last two numbers is –
A)
130
B)
145
C)
147
D)
152
Step-by-step solution:
1. **Total Sum**: The sum of all five numbers is given as 555.
2. **Sum of the first two numbers**: The average of the first two numbers is 75. Therefore, their sum = $2 \times 75 = 150$.
3. **The third number**: The third number is explicitly given as 115.
4. **Sum of the first three numbers**: Sum = $150 + 115 = 265$.
5. **Sum of the last two numbers**: To find the sum of the remaining two numbers, subtract the sum of the first three from the total sum: $555 - 265 = 290$.
6. **Average of the last two numbers**: The average is the sum divided by the count of numbers. Average = $290 / 2 = 145$.
Comparing this result to the options:
- a. 130 (Incorrect)
- b. 145 (Correct)
- c. 147 (Incorrect)
- d. 152 (Incorrect)
Assistant & UDC • Paper-II
UNESCO stands for
A)
United Nations Education, Scientific and Cultural Organisation
B)
United Nations Education, Scientific and Culture Organisation
C)
United Nations Educational, Scientific and Cultural Organisation
D)
United Nations Educational, Scientific and Culture Organisation
UNESCO is a specialized agency of the United Nations. The correct full form is 'United Nations Educational, Scientific and Cultural Organisation'.
Analysis of options:
- Option (a) uses 'Education' (noun) instead of 'Educational' (adjective).
- Option (b) uses 'Education' and 'Culture' (noun) instead of 'Cultural' (adjective).
- Option (c) correctly uses the adjectives 'Educational', 'Scientific', and 'Cultural' to describe the 'Organisation'.
- Option (d) uses 'Culture' (noun) instead of 'Cultural' (adjective).
In English grammar, when describing an organization's focus, adjectives are used to modify the noun 'Organisation'. Therefore, 'Educational', 'Scientific', and 'Cultural' are the grammatically and officially correct terms.
Assistant & UDC • Paper-II
The name of Femina Miss India World 2019 is
A)
Meenakshi Choudhuri
B)
Suman Rao
C)
Anukreeti Vas
D)
Manushi Chillar
The Femina Miss India 2019 pageant was held on March 19, 2019. Meenakshi Choudhuri was crowned Femina Miss India World 2019.
Analysis of other options:
- Suman Rao: She was Femina Miss India World 2016.
- Anukreeti Vas: She was Femina Miss India World 2018.
- Manushi Chhillar: She was Femina Miss India World 2017 and went on to win the Miss World 2017 title.
Assistant & UDC • Paper-II
Which city is known as the pink city?
A)
Lucknow
B)
Indore
C)
Chennai
D)
Jaipur
Jaipur, the capital of Rajasthan, is globally renowned as the 'Pink City'. This nickname originated in 1876 when Maharaja Sawai Ram Singh II ordered the city to be painted pink to welcome Prince Albert and Queen Victoria of the United Kingdom, as pink was traditionally the color of hospitality.
Analysis of other options:
- Lucknow: Known as the 'City of Nawabs'.
- Indore: Known as the 'Mini Mumbai' of Madhya Pradesh.
- Chennai: Known as the 'Gateway to South India'.
Assistant & UDC • Paper-II
Ministry of Ayush, Government of India was set up in the year
A)
2012
B)
2013
C)
2014
D)
2015
The Ministry of AYUSH (Ayurveda, Yoga & Naturopathy, Unani, Siddha and Homoeopathy) was established as a separate ministry by the Government of India on November 9, 2014. Prior to this, the Department of AYUSH existed as a department under the Ministry of Health and Family Welfare. The elevation to a full-fledged ministry was intended to provide better focus, administration, and development of traditional systems of medicine. Therefore, option (c) 2014 is correct, while 2012, 2013, and 2015 are incorrect as they do not correspond to the date of the ministry's formation.
Assistant & UDC • Paper-II
The movie which bagged the largest number of Academy Awards in 2019 was
A)
The Favorite
B)
Green Book
C)
Bohemian Rhapsody
D)
Roma
The question refers to the 91st Academy Awards (Oscars) held in 2019. To determine the movie with the largest number of awards, we look at the win counts for the provided options:
1. **Roma**: Won 3 Academy Awards (Best Director, Best Foreign Language Film, and Best Cinematography).
2. **Green Book**: Won 2 Academy Awards (Best Picture and Best Original Screenplay).
3. **Bohemian Rhapsody**: Won 2 Academy Awards (Best Actor and Best Sound Mixing).
4. **The Favourite**: Won 1 Academy Award (Best Supporting Actress).
Comparing these totals, 'Roma' bagged the highest number of awards among the listed options. While 'Roma' did not win the most awards of the entire ceremony (that distinction often goes to the Best Picture winner or a dominant technical film), among the specific choices provided in this multiple-choice question, 'Roma' is the correct answer.
Assistant & UDC • Paper-II
The full form of MSACS is
A)
Mizoram State Aid Control Society
B)
Mizoram State Aids Control Society
C)
Mizoram State Aids Counter System
D)
Mizoram State Aids Control System
MSACS stands for the Mizoram State Aids Control Society. It is the nodal agency in the state of Mizoram responsible for implementing the National AIDS Control Programme (NACP) and coordinating activities related to the prevention and control of HIV/AIDS.
Analysis of options:
- Option (a) 'Aid' is singular; the official terminology used in health programs is 'Aids' (referring to Acquired Immunodeficiency Syndrome).
- Option (b) 'Mizoram State Aids Control Society' is the correct official nomenclature.
- Option (c) 'Counter System' is incorrect as it is a Society (an administrative body), not a system.
- Option (d) 'Control System' is incorrect for the same reason; it is a registered Society.
Assistant & UDC • Paper-II
The sum of all two digit odd positive numbers is –
A)
2475
B)
2540
C)
2590
D)
3100
To find the sum of all two-digit odd positive numbers, we identify the sequence: 11, 13, 15, ..., 99.
1. **Identify the sequence**: This is an Arithmetic Progression (AP) where:
- First term (a) = 11
- Last term (l) = 99
- Common difference (d) = 2
2. **Find the number of terms (n)**:
The formula for the n-th term is: l = a + (n - 1)d
99 = 11 + (n - 1)2
99 - 11 = (n - 1)2
88 = (n - 1)2
44 = n - 1
n = 45
3. **Calculate the sum (Sₙ)**:
The formula for the sum of an AP is: Sₙ = (n/2) * (a + l)
S₄₅ = (45 / 2) * (11 + 99)
S₄₅ = (45 / 2) * 110
S₄₅ = 45 * 55
S₄₅ = 2475
Therefore, the sum of all two-digit odd positive numbers is 2475. Option (a) is correct, while options (b), (c), and (d) are incorrect as they do not match the calculated sum.
Assistant & UDC • Paper-II
‘A’ can do a piece of work in 25 days and ‘B’ can finish it in 20 days. They work together for 5 days and then ‘A’ leaves. In how many days will ‘B’ finish the remaining work?
A)
9 days
B)
10 days
C)
11 days
D)
12 days
Step-by-step solution:
1. **Determine the work rates**:
- A can complete the work in 25 days, so A's 1-day work = 1/25.
- B can complete the work in 20 days, so B's 1-day work = 1/20.
2. **Calculate combined work rate**:
- Combined 1-day work of (A + B) = (1/25) + (1/20).
- Finding the LCM of 25 and 20, which is 100.
- (4/100) + (5/100) = 9/100.
3. **Calculate work done in 5 days**:
- Work done by A and B together in 5 days = 5 * (9/100) = 45/100 = 9/20.
4. **Calculate remaining work**:
- Remaining work = 1 - (9/20) = 11/20.
5. **Calculate time taken by B to finish remaining work**:
- Time = (Remaining Work) / (B's 1-day work)
- Time = (11/20) / (1/20) = (11/20) * 20 = 11 days.
Therefore, B will finish the remaining work in 11 days. Option (c) is correct, while options (a), (b), and (d) are incorrect based on the calculation.