SSC GD Constable Previous Year Paper (Held on: 8th December 2021 Shift 2)

The figure that can replace the question mark is given below:

Hence, "Option - (3)" is the correct answer.

Given :

• Two train tickets from station A to B and three tickets from station A to C cost ₹8,750.
• Three tickets from station A to B and two tickets from station A to C cost ₹9,825.

To find : Fares for stations B and C from station A

Explanation :

Let the fare of train ticket from station A to B be = X

Let the fare of train ticket from station A to C be = Y

So, according to the question  the equation will be :

2X + 3Y = 8750 → (1st equation)

3X + 2Y = 9825 → (2nd equation)

Now, solving both the equations :

→ Making the X variable same, so multiplying 1st equation by 3 and 2nd equation by 2.

(2X + 3Y = 8750) 3 ⇒ 6X + 9Y = 26250

(3X + 2Y = 9825) 2 ⇒ 6X + 4Y = 19650

Now, As '6X' is same in both the equations therefore :

9Y - 26250 = 4Y - 19650

9Y - 4Y = 26250 - 19650

5Y = 6600

Y = 1320

Putting the value 'Y' in 1st equation:

2X + (3 × 1320) = 8750

2X + 3960 = 8750

2X = 8750 - 3960

2X = 4790

X = 2395

Thus, according to the given information fares for stations B and C from station A is ₹2395 and ₹1320 respectively.

Hence, "₹2,395 and ₹1,320" is the correct answer

The pattern followed here is : 

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Hence, "142" is the correct answer.

Given :

• Six friends - P, Q, R, S, T and U.
• They are sitting in a row facing north.

​Explanation : 

1) P is sitting to the immediate left of R and second to the right of S.

There are three possible cases for the position of S.

• Case - (1)

​

• Case - (2)

​

• Case - (3)

​

2) T is sitting to the immediate right of R

3) Q is sitting to the immediate left of S. 

As in case - (1) there is no possible position for Q, therefore this case is eliminated.

As in case - (3) there is no possible position for T, therefore this case is eliminated.

• Case - (2)

4) U is sitting second to the left of R.

• Case - (2)

​

Thus, according to the final arrangement T is sitting at the extreme right end of the row.

Hence, "T" is the correct answer.

Given : 48 × 5 + 9 ÷ 6 − (32 − 7) + 9

According to the question :

• The signs ‘×’ and ‘÷’ are interchanged
• The numbers ‘6’ and ‘5’ are interchanged

​So, After interchanging the signs and numbers:

= 48 ÷ 6 + 9 × 5 − (32 − 7) + 9

= 48 ÷ 6 + 9 × 5 - 32 + 7 + 9

= 8 + 9 × 5 - 32 + 7 + 9

= 8 + 45 + 7 + 9 - 32

= 69 - 32

= 37

Hence, "37" is the correct answer.

Logic : Square of (Second number - 2) = First number

So,

• 144 : 14

$(14 - 2)^2$ = 144

$(12)^2$ = 144

144 = 144 (LHS = RHS)

Similarly,

• 81 : ?

Doing the reverse calculation :

As the required answer is 81, so '81' is the square of '9'

So, it can be said that :-

(? - 2) = 9

? = 11

Hence, "11" is the correct answer.

Logic : The number of letters in a word - 1

So,

• DERMATOLOGY is coded as :

​Number of letters = 11

11 - 1 = 10

• MAXIMUM is coded as :

​​Number of letters = 7

7 - 1 = 6

Similarly,

• NOCTURNAL is coded as :

​​Number of letters = 9

9 - 1 = 8

​Hence, "8" is the correct answer.

The Venn diagram that best represents the relationship between 'Pumpkin, Spinach, Potato' is shown below:

As 'Pumpkin, Spinach, Potato' are three different types of vegetables therefore all of them will be shown separately.

Hence, "Option - (4)" is the correct answer.

According to given figure:

The figure will appear when it is opened as follows:

Hence, the correct answer is "option - (2)".

The correct mirror image of the given combination when mirror is placed at PQ is as shown below:

Detailed Explanation:

• The line PQ is the mirror
• The figure "

" the mirror is placed horizontally instead of vertically ⇒ Option 1 is eliminated.

• The figure "

" the part of the figure is "

". So, the mirror image should be "

" ⇒ Option 2 is eliminated..

• The figure "

" the part of the figure is "

". So, the mirror image should be "

" ⇒ Option 4 is eliminated.

Hence, the correct answer is "Option - (3)".

Logic : (1) is added to and subtracted from each position value alternately starting with the addition.

So,

• PHARMACEUTICAL is written as :

​

​Similarly,

• ELECTRONIC is written as :

​

Hence, "FKFBUQPMJB" is the correct answer.

So, according to the question :

1) K is the son of R

2) K is the brother of M.

3) M is the daughter of J

4) V is the wife of J's son.

5) H is K's son. 

Thus, according to the final family tree H is the paternal grandson of R and J.

Hence, "Paternal grandson" is the correct answer.

Given : _ B I R _ I R B _

By checking options :

1. CBH → C B I R B I R B H → (It doesn't Follows the pattern)
2. RBI → R B I R B I R B I → (It follows the pattern of : RBI - RBI - RBI)
3. HIG → H B I R I I R B G → (It doesn't Follows the pattern)
4. TIC → T B I R I I R B C → (It doesn't Follows the pattern)

⇒Option - (2) gives the pattern of "R B I - R B I - R B I"

Hence, "RBI" is the correct answer.

Logic : The pattern followed here is column wise.

Square (Square root of first number + Square root of second number )² = Third number 

So,

• First column

$({ \sqrt{25}} + { \sqrt{36}})^2$ = 121

$(5 + 6)^2$ = 121

$(11)^2$ = 121

121 = 121 (LHS = RHS)

• Second column

$({ \sqrt{49}} + { \sqrt{64}})^2$ = 225

$(7 + 8)^2$ = 225

$(15)^2$ = 225

225 = 225 (LHS = RHS)

Similarly,

• Third column

$({ \sqrt{144}} + { \sqrt{196}})^2$ = ?

$(12 + 14)^2$ = ?

$(26)^2$ = ?

? = 676

Hence, "676" is the correct answer.

Logic :

• First letter - (1) is added to each position value
• Second letter - (2) is subtracted from each position value
• Third letter - (3) is added to each position value
• Fourth letter- (4) is subtracted from each position value

So,

Hence, "PGOU" is the correct answer.

According to the sequence in the dictionary.

1. School
2. Secure
3. Source
4. Stress
5. Sweet

Hence, the correct answer is "1, 4, 3, 2, 5".

The faces opposite to each other are shown below:

⇒ As the alternate positions becomes opposite to each other and the remaining two faces becomes opposite to each other.

So, opposite pairs are:

• 1 → 2
• 3 → 4
• 6 → 5

Therefore,

(A) →

⇒ Correct (As 1 is opposite to 2, 3 is opposite to 4 and 5 is opposite to 6. So one number of each pair is shown)

(B) →

⇒Correct (As 2 is opposite to 1, 4 is opposite to 3 and 6 is opposite to 5. So one number of each pair is shown)

(C) → 

⇒Incorrect (As 4 is opposite to 3, 3 is opposite to 4 and 5 is opposite to 6. So one full pair cannot be shown)

(D) →

⇒Incorrect (As 1 is opposite to 2, 2 is opposite to 1 and 3 is opposite to 4. So one full pair cannot be shown)

Hence, "Only A and B" is the correct answer.

Logic : Difference between the position value is (5).

So,

• TYDI

​

• AFKP

​

• GKOV

​

• KPUZ

​

Thus, Out of the given options only GKOV doesn't have a common position value difference i.e 5.

Hence, "GKOV" is the correct answer.

The least possible Venn diagram for the given statements is as shown below :

Conclusions:

I. Some canals are wells → Follow (As all canals are rivers. So, it is definitely true)

II. Some rivers are wells → Follow (As all canals are rivers, all wells are canals. So, it is definitely true)

∴ Here, Both conclusions I and II follow.

Hence, the correct answer is "Both conclusions I and II follow".

The number of rectangles are shown below:

Thus, according to the given figure there are 9 rectangles.

Hence, "9" is the correct answer.

The pattern followed here is : Immediate next number is the reverse of the previous number.

Hence, "98" is the correct answer.

The pattern followed here is :

• Study of coins is called numismatics.

​Similarly,

• Study of mountains is called orography.

​Hence, "Mountains" is the correct answer.

Additional Information

1. Mountains - Study of mountains is called orography.
2. Shells - Study of shells is called conchology.
3. Fossils - Study of fossils is called paleontology.
4. Eggs - Study of eggs is called oology.

Logic : Immediate next letter of the first term according to English alphabetic series is written and then reversed = Second term

So,

• SLOWER : SFXPMT

​

​Similarly,

• MEAGRE : ?

​

Hence, "FSHBFN" is the correct answer.

Given : Six children, Anand, Badri, Chaya, Dhruv, Srikar and Umesh are standing in a line, facing north. 

Explanation :

1) Umesh is standing second to the right of Srikar and to the immediate left of Chaya.

There are three possible cases for the position of Umesh.

• Case - (1)

​

• Case - (2)

​

• Case - (3)

​​

2) Badri is between Dhruv and Chaya.

As in case - (2) and case - (3) there is no possible position for Badri and Dhruv, therefore these cases are eliminated.

After positioning Badri and Dhruv only one position is left which will be occupied by the only person left i.e Anand.

• Case - (1)

Thus, according to the final arrangement Anand is standing fourth to the left of Dhruv.

Hence, "Anand" is the correct answer.

Logic :

• Consonants - Immediate next letter according to English alphabetic series is written.
• Vowels - Immediate previous letter according to English alphabetic series is written.

So,

• PLACE is written as :

​

• BEAUTY is written as :

​

Similarly,

• MANSION is written as :

​

Hence, "NZOTHNO" is the correct answer.

The correct answer is Mental Healthcare Act, 2017.

Key Points

• Section 20 of the Mental Healthcare Act, of 2017 gives every person with mental illness a right to live with dignity.
• ​In India, the Mental Health Care Act 2017 was passed on 7 April 2017 and came into force on 29 May 2018.
• The act effectively decriminalized attempted suicide which was punishable under Section 309 of the Indian Penal Code.
• The law was described as;
• "An Act to provide for mental healthcare and services for persons with mental illness and to protect, promote and fulfil the rights of such persons during delivery of mental healthcare and services and for matters connected therewith or incidental thereto."
• This Act superseded the previously existing Mental Health Act, of 1987 which was passed on 22 May 1987.

Additional Information

• The Indian Penal Code (IPC) is the official criminal code of India.
• It is a comprehensive code intended to cover all substantive aspects of criminal law.
• In India, the Mental Health Act was passed on 22 May 1987.
• The law was described in its opening paragraph as "An Act to consolidate and amend the law relating to the treatment and care of mentally ill persons, to make better provision with respect to their property and affairs and for matters connected therewith or incidental thereto.
• The National Medical Commission (NMC) has been constituted by an act of Parliament known as the National Medical Commission Act, 2019 which came into force on 25.9.2020 by gazette notification dated 24.9.2020.
• The Board of Governors in supersession of the Medical Council of India constituted under section 3A of the Indian Medical Council Act, 1956 stands dissolved thereafter.

The correct answer is Idea.

Key Points

• In September 2020, Vodafone and Idea announced their new unified brand identity by renaming all their products under a new name.
• Vodafone-Idea announced a new and unified brand identity by renaming all its products under the brand name 'Vi'.
• Vodafone-Idea on Monday, 7 September, announced a new and unified brand identity by renaming all its products under the brand name 'Vi'.

Additional Information

• Vodafone Idea Limited is an Aditya Birla Group and Vodafone Group partnership.
• It is India's leading telecom service provider.
• The Company provides pan India Voice and Data services across 2G, 3G and 4G platforms.

The correct answer is Project Air Care.

Key Points

• Project Air Care was launched in November 2020 to combat the rising air pollution in Gurugram.
• On November 11, 2020, Haryana Chief Minister (CM), Manohar Lal Khattar virtually unveiled 'Project Air Care' to combat rising Air Pollution in Gurugram, Haryana.

Additional Information

• Air Pollution is the presence of undesirable solid or gaseous particles or particulate matter in the air, in an amount that is harmful to humans.
• Primary pollutants: Emitted directly from the source.
• E.g: CO2, CO, SO2, Ozone, Lead, Methane etc.
• Secondary pollutants: It is produced by the interaction of two or more primary pollutants.
• E.g: Smog, FlyAsh etc.

The correct answer is 1605.

Key Points

• Mughal emperor Akbar die in1605.
• He was only thirteen years old at the time of Humayun’s death.
• When his father died, Akbar was at Kalanaur in Punjab and therefore his coronation took place in Kalanaur itself in 1556.
• It was his tutor and Humayun’s favourite and confidant Bairam Khan, who served as the regent of the Mughal emperor from 1556 to 1560.
• As a conqueror, Akbar triumphed all over North India.
• The first four years of Akbar’s rule saw the expansion of the Mughal empire from Kabul to Jaunpur, including Gwalior and Ajmer, under his regent Bairam Khan.
• One of the major achievements of his regency period was the defeat of Hemu and the Afghan forces in the second battle of Panipat in 1556, who were posing a serious threat to the Mughal Empire.

Additional Information

The correct answer is Assam.

Key Points

• ‘Ankiya Nats’ are one-act plays distinct to the culture of Assam.
• Ankia Naats are a class of one act plays performed in Assam, India.
• The invention of the Ankia Naat is usually attributed to the medieval saint and social reformer Srimanta Sankardeva.

Additional Information

• Assam is the meeting ground of diverse cultures.
• The people of the enchanting state of Assam are an intermixture of various racial stocks such as Mongoloid, Indo-Burmese, Indo-Iranian and Aryan.
• Assam is known for Assam tea and Assam silk.
• The state was the first site for oil drilling in Asia.
• Assam is home to the one-horned Indian rhinoceros, along with the wild water buffalo, pygmy hog, tiger and various species of Asiatic birds, and provides one of the last wild habitats for the Asian elephant.

The correct answer is Rajasthan.

Key Points

• Nahargarh Fort located at Rajasthan.
• The Nahargarh Fort is proudly on a ridge of the Aravalli hills, which forms an impressive northern backdrop for the city of Jaipur.
• It was constructed during the reign of Jai Singh in 1734 and later expanded in 1868.
• Nahargarh, meaning the abode of tigers, was a formidable blocker protecting Jaipur against attacking enemies.
• Jaipur is the capital of Rajasthan is popularly known as the Pink City.

Additional Information

The correct answer is acceleration.

Key Points

• The rate of change in the velocity of an object per unit time is referred as acceleration.
• When the velocity of a moving object changes either in magnitude or in direction or in both, then the body is said to be in acceleration.
• The rate of change in velocity is called acceleration.
• $⇒ a =\frac{Δ v}{Δ t}$
• Where Δv = change in velocity/speed and Δt = time

Additional Information

• The average speed is the total distance traveled by the object in a particular time interval.
• Average velocity is a vector quantity. Average velocity is defined as the change in position or displacement (∆x) divided by the time intervals (∆t) in which the displacement occurs.
• Motion is the action or process of moving or of changing place or position; movement. power of movement, as of a living body.

The correct answer is It includes that the country should uphold a Presidential form of government.

Key Points

• The Constitution of a country provides for the set of rules and powers for the proper governance of the Country and distributes the powers and functions accordingly.
• It is the draft from where the government derives its powers and responsibilities and people derive their rights and freedoms.
• It agrees on certain ideals the country should uphold.
• Constitutions define the various institutions of government; prescribe their composition, powers and functions; and regulate relations between them.
• Almost all constitutions establish legislative, executive and judicial branches of government.

Additional Information

• There are a total of 25 parts in the Constitution of India in which the common articles are grouped together.
• Originally the constitution contained 395 articles divided into 22 parts and 8 schedules.
• At present, there are 448 articles in 25 parts, 12 schedules.

The correct answer is Dil Bechara.

Key Points

• Farah Khan won the Best Choreography award at the Filmfare Awards 2021 for the film Dil Bechara.
• The late actor Irrfan Khan was honored with the Lifetime Achievement Award at the 66th edition of the Filmfare Awards 2021 held in Mumbai.
• Irrfan Khan also won a posthumous award:
• Best Actor - for his work in Angrezi Medium.
• Irrfan Khan died on April 29 in Mumbai at the age of 53 last year after a long battle with cancer.
• Taapsee Pannu won the Best Actress Award for Thappad, which also bagged the Best Film, Best Story, and Best Editing trophies.
• Amitabh Bachchan won the Best Actor (Critics) award for his performance in Gulabo Sitabo.
• Saif Ali Khan picked the Best Actor In A Supporting Role award for his work in Tanhaji: The Unsung Warrior
• Kajol's Devi won the Best Short Film (Popular Choice) award.

Additional Information

• 67th Filmfare Awards 2022
• Best Film: Shershaah (Dharma Productions)
• Best Director: Vishnuvardhan (Shershaah)
• Best Actor: Ranveer Singh (83) as Kapil Dev
• Best Actress: Kriti Sanon, Mimi as Mimi Rathore
• Best Supporting Actor: Pankaj Tripathi (Mimi)
• Best Supporting Actress: Sai Tamhankar (Mimi)

The correct answer is Nij.

Key Points

• Nij was a system of indigo cultivation in British India.
• There were two main systems of indigo cultivation – nij and ryoti.
• Within the system of nij cultivation, the planter produced indigo in lands that he directly controlled.
• He either bought the land or rented it from other zamindars and produced indigo by directly employing hired labourers.

Additional Information

• Indigo could be cultivated on bonded land, which were already densely populated.
• Only small plots scattered over the landscape could be acquired.
• Planters needed large areas in compact blocks to cultivating indigo in plantations.
• They attempted to lease in the land around the indigo factory, and evict the peasants from the area.
• Those living around the indigo factory faced eviction from their land and it always led to conflicts and tension.

The correct answer is He Bing Jiao.

Key Points

• Indian star shuttler PV Sindhu has secured a bronze medal at the Tokyo Olympics, defeating China’s He Bing Jiao in Women’s Singles.
• PV Sindhu also created history by becoming the first Indian woman to win two consecutive individual Olympic medals.
• She had won silver at Rio Olympics in 2016.

Additional Information

• List of winners in Olympics 2020 from India:
• Neeraj Chopra: Javelin Throw (Gold)
• Mirabai Chanu: Weightlifting (Silver)
• PV Sindhu: Badminton (Bronze)
• Lovlina Borgohain: Boxing (Bronze)
• Men's Hockey Team (Bronze)
• Ravi Dahiya: Wrestling (Silver)
• Bajrang Punia: Wrestling (Bronze)

The correct answer is Sri Lanka.

Key Points

• The Mahaweli Ganga River is a 335 km long river, ranking as the longest river in Sri Lanka.
• It has a drainage basin of 10,448 km², the largest in the country, which covers almost one-fifth of the total area of the island.
• It rises on the Hatton Plateau on the western side of the island’s hill country, flows north through the tea and rubber-growing region, and turns east near Kandy; it then turns north across the lowlands and receives its principal tributary.

Additional Information 

• Irrawaddy is the longest river in Myanmar.
• Indus is the longest river in Pakistan.
• The Yangtze is the longest river in Asia.
• The Godavari is the longest river in Peninsular India.
• The longest river in the world is the ​Nile.

The correct answer is presiding deity.

Key Points

• In September 2021, a two-judge bench of the Supreme Court ruled that the presiding deity of the temple is/are the owner/s of the land attached to it.
• Top court upholds circulars issued under the Madhya Pradesh Land Revenue Code, 1959.
• A 2-judge bench of the Supreme Court has ruled that the presiding deity of a temple is the owner of the land attached to the temple, while priests are only required to perform rituals and maintain the properties of the deity.

Additional Information

• The seat of the Supreme Court (Article 130): The Constitution declares Delhi as the seat of the Supreme Court.
• It also authorizes the CJI to appoint other places or places as seats of the Supreme Court.
• He can decide in this regard only with the approval of the President.
• This provision is only optional and not compulsory. This means that no court can give any direction either to the President or to the Chief Justice to appoint any other place as the seat of the Supreme Court.

The correct answer is botany.

Key Points

• The scientific study of different aspects of plants is called botany.
• Botany is the scientific study of plants:
• how plants function,
• what they look like,
• how they are related to each other,
• where they grow,
• how people make use of plants, and
• how plants evolved.

Additional Information

The correct answer is Nita Ambani.

Key Points

• Nita Ambani, Chairperson of the Reliance Foundation, was elected as an individual member of the International Olympic Committee (IOC).
• She is the first Indian to join the international body and is still the only individual member of India.
• Her election to the body of the universe is before she hits the age of 70.
• She was nominated by the IOC Executive Board in June 2016 and voted by the IOC Delegates at the 129th Session in Rio de Janeiro.
• The autonomous screening process follows a revised protocol for the appointment of IOC members based on the recommendations of the Olympic Agenda 2020.
• Individuals are selected on merit and elected by current IOC members.

Additional Information

• Founded on 23 June 1894, the International Olympic Committee is a non-profit independent international organization.
• Based in Lausanne, Switzerland, Olympic Capital is entirely privately funded and distributes 90 percent of its revenues to the wider sporting movement for the development of sports and athletes at all levels.
• The International Olympic Committee is the patron of the Olympic Games and the leader of the Olympic Movement.

The correct answer is courtyard.

Key Points 

• Indus Valley Civilisation generally had rooms built around a courtyard.
• Indus Valley Civilisation, also known as Harappan Civilisation or Bronze Age civilization, is one of the oldest civilizations in the world.
• The nuclear dates of the civilization appear to be about 2500–1750 BC.
• ‘Harappa’ was the first Indus site to be discovered in 1921 by Dayaram Sahni.
• Metals such as copper, lead, gold, bronze, and silver were used by the metallurgists of the Indus Valley.
• Several crucibles of copper slag are discovered here, which marks the beginning of metallurgy.
• Indus Valley Civilisation also got the credit for the development of various alloys in the South-Asian countries.
• They used to make alloys such as bronze, tin, and arsenic bronze by smelting copper with other metals.
• Bronze was extensively used in making sculptures.

Additional Information Name of the major cities are given below:

Mohenjodaro (Sind)-It is located on the right bank of the Indus.

Kalibangan (Rajasthan)-It was on the banks of the river Ghaggar river.

Chanhudaro - It lies on the left bank of the Indus in the south of Mohenjodaro.

Lothal(Gujarat) - It is located at the head of the Gulf of Cambay.

Surkotada (Gujarat) - It is at the head of the Rann of Kutch.

Banawali (Haryana) - It was situated on the banks of the now-extinct Sarasvati.

Dholavira (Gujarat) - It excavated is in the Kutch district.

The correct answer is It is a price lower than the market price.

Key Points

• The issue price is the price at which shares are offered for sale when they first become available to the public.
• It is a price lower than the market price.
• When the issuer at the outset decides the issue price and mentions it in the offer document, it is in the offer document, it is commonly known as a “Fixed price issue”
• When the price of an issue is discovered on the basis of demand raised from prospective investors at various investors at various price levels, it is called a ‘Book built issue’

Additional Information

• An initial public offering (IPO) refers to the process of offering shares of a private corporation to the public in a new stock issuance.
• Fixed Price Issues and Book Built Issues are two major types of IPO.
• All types of investors are required to bring in 100% of the application money as a margin along with the application for securities in Public Issues.
• This has been done to avoid inflated demand in Public Issues and to provide a level playing field to all investors subscribing to securities.

The correct answer is Germany.

Key Points

• India defeated Germany to win the men's hockey bronze medal at the Olympic Games held in Tokyo in 2021.
• Indian hockey team Captian (Male) - Manpreet Singh
• Indian Hockey team Captain (Female) - Rani Rampal
• India won three bronze medals at the Summer Olympic Games in 1972, 1968, and 2020(Tokyo).
• India's team won eight gold medals in 1928, 1932, 1936, 1948, 1952, 1956, 1964, and 1980.
• India won one silver medal in the Rome Olympics in the year 1960 and Pakistan won the Gold medal that year.

Additional Information 

The correct answer is Demography.

Key Points

• Demography is the statistical study of human populations.
• It includes the study of the size, age, gender, occupation, structure, and distributions of different populations.
• Demographic information is used in marketing, governmental research, and surveys and sampling to collect information about people's age, gender, education, income, or body phenotype.
• It also includes the analysis of the relationships between economic, social, cultural, and biological processes influencing a population.

Additional Information

• The study of Algae is known as Phycology.  
• It is also referred to as algology in some spheres, phycology is the study of algae; members of the plant kingdom.
• Pomology is the branch of horticulture that is concerned with the study and cultivation of Fruits.
• The study of human beauty is called Kalology.
• Kalology is the study of beauty and the ways in which beauty influences society.

The correct answer is 68.

Key Points

• According to ‘ADB (Asian Development Bank) Annual Report 2018’ 68 countries are the members of ADB.
• ADB (Asian Development Bank) is an international development finance institution whose mission is to help its developing member countries reduce poverty and improve the quality of life of their people.
• Headquartered in Manila, and established in 1966, ADB is owned and financed by its 68 members, of which 49 are from the region and 19 are from other parts of the globe.
• ADB's main partners are governments, the private sector, non-government organizations, development agencies, community-based organizations, and foundations.
• Under Strategy 2020, a long-term strategic framework adopted in 2008, ADB will follow three complementary strategic agendas: inclusive growth, environmentally sustainable growth, and regional integration.
• Although most lending is in the public sector - and to governments - ADB also provides direct assistance to private enterprises of developing countries through equity investments, guarantees, and loans.

Additional Information

The correct answer is The League did not support the partition of Bengal.

Key Points

• All India Muslim League 
• After the creation of the Indian National Congress and its time as a ‘representative’ party for the people of the Indian sub-continent, there was felt a need to reassess its claims of unbiased representation. ​
• The communal idea was sown into the Indian political ethos that Muslims are a separate nation first by philosopher and Muslim reformist Sir Syed Ahmed Khan.
• All India Muslim League was formed in Dhaka in 1906.
• Hence Statement 2 is correct.
• It was formed by a group of Muslim landlords and nawabs.
• The founders of the Muslim League were: Vikar-ul-Mulk, Khwaja Salimullah, Syed Amir Ali, Syed Nabiullah, Khan Bahadur Ghulam and Mustafa Chowdhury.
• ​Hence Statement 4 is correct.
• He suggested Muslims to get aligning with the British rather than rebel against them.
• The AIML was the first Muslim political party in India.
• The league supported the partition of Bengal.
• ​​Hence Statement 1 is incorrect.
• It desired a separate electorate for Muslims
• Hence Statement 3 is correct.

Additional Information 

• The following are the reasons for the establishment of the Muslim League
• Indifferent attitude of Congress toward Muslims
• Educational and Economic Backwardness
• Urdu-Hindi Controversy
• The Evolution of Minto Marley Reforms
• The Success of Simla Deputation
• ​To Save Muslim Entity

The correct answer is 2030.

Key Points

• Union Budget 2020-21 envisages creating a ‘future-ready’ railway system by the year 2030.
• During the Union budget, 2021- 2022 the Finance Minister announces that Indian Railways have prepared a national rail plan for India 2030.
• The plan is to create a ‘future-ready’ railway system by 2030.
• The main aim of the national rail plan is to bring down the logistics cost:
• It is expected that Western Dedicated Freight Corridor (DFC) and Eastern DFC will be commissioned by June 2022.
• It also announces the 100% electrification of broad gauge rail tracks by December 2023.

Additional Information 

• The Passenger convenience and safety measures proposed in the union budget 2021- 2022 are:
• Introduction of aesthetically designed Vista Dome LHB coach on tourist routes.
• Introduction of an indigenously developed automatic train protection system that eliminates train collision due to human error.
• The budget also provided a record sum of Rs. 1,10,055 crore for Railways of which Rs. 1,07,100 crore is for capital expenditure.

The correct answer is The Padma is a prominent river of the region.

Key Points 

• The Great Indian Desert is called the Thar Desert.
• Hence statement 1 is correct.
• It is one of the hot deserts of the world and largest in India.
• Hence statement 4 is correct.
• Many National Parks and Wildlife Sanctuaries are located in this area.
• The vegetation cover is low, with thorny bushes.
• ​Hence statement 2 is correct.
• ​The Luni is the largest river in the Thar Desert of northwest India.
• Hence statement 3 is incorrect.

 Important Points 

• Great Indian Thar Desert:
• It is the world's 17th-largest desert and the world's 9th-largest subtropical desert.
• About 85% of the Thar Desert is located in India, with the remaining 15% in Pakistan.
• More than 60% of the desert lies in the Indian state of Rajasthan, and it extends into the states of Gujarat, Punjab, Haryana, and the Pakistani province of Sindh.

The correct answer is CSIR.

Key Points

• CSIR institutes topped the National Ranking Index 2020.
• The CSIR of Delhi topped the National Ranking Index 2020 which ranks scientific research institutes.
• CSIR was followed by IISc Bangalore.
• The first rank holder CSIR had a share percentage of 87.74 and 142 counts.
• Followed by CSIR, IISC Bangalore had a share percentage of 83.61 and 211 counts.
• The third rank was won by the Tata Institute of Fundamental Research (TIFR) with a share percentage of 62.18 and 232 counts.

Additional Information

• Council of Scientific & Industrial Research
• It was established by the Government of India in September 1942 as an autonomous body.  
• It comes under the Ministry of Science & Technology.

The correct answer is Akkitham Achuthan Namboothiri.

Key Points

• Akkitham Achuthan Namboothiri won the Jnanpith Award in 2019.
• He is a renowned Malayalam poet.
• He is also the 6th Malayalam Poet to receive the Jnanpith award.
• The Jnanpith Award is the Highest Literary award in India.
• It is awarded to an author to acknowledge his/her excellence in Literature.
• The awardee gets a b
• Akkithamhas authored 55 books till now.
• Amitav Ghosh won the 54th Jnanpith Award.

Additional Information

• The award is given by one of the premier literary organizations of India - Bharatiya Jnanpith.
• Jnanpith Award has achieved the recognition of the highest literary award in the country.
• It has been conferred to literary geniuses of various Indian languages, who have brought many laurels to our nation through their creations.
• Bharatiya Jnanpith has also instituted another award namely the Moortidevi Award.

Shortcut Trick

Rate is compounded half-yearly, so Effective Rate = 10% ÷ 2 = 5%.

Ratio of Amount to Principal = 9261 : 8000.

Expressing as powers: 9261/8000 = (21/20)³.

The power 3 indicates 3 half-yearly periods.

Time = 3 ÷ 2 = 1 1/2 years.

∴ The correct answer is 1 1/2 years.

Alternate Method

Given: Principal (P) = ₹8,000, Amount (A) = ₹9,261, Annual Rate (R) = 10%.

Formula Used: A = P(1 + r/100)ⁿ, where r is the rate per compounding period and n is the number of periods.

⇒ Half-yearly Rate (r) = 10% ÷ 2 = 5%

⇒ 9261 = 8000(1 + 5/100)ⁿ

⇒ 9261 ÷ 8000 = (1 + 1/20)ⁿ

⇒ 9261/8000 = (21/20)ⁿ

⇒ (21)³ ÷ (20)³ = (21/20)ⁿ

⇒ (21/20)³ = (21/20)ⁿ

⇒ n = 3 half-years

⇒ Time period = 3 ÷ 2 = 1 1/2 years

∴ The correct answer is 1 1/2 years.

Additional Information

Half-yearly Compounding

When interest is compounded half-yearly, the annual rate is divided by 2 and the time (years) is multiplied by 2 to find the number of periods.

Quarterly Compounding

For quarterly compounding, the rate is divided by 4 and the time is multiplied by 4. Formula: A = P(1 + R/400)^4T.

Effective Rate of Interest

It is the actual annual interest rate when compounding occurs more than once a year. For 10% p.a. half-yearly, the effective rate is 5 + 5 + (5 × 5)/100 = 10.25%.

Given:

The Average of 25 observations is 50.

Solution:

Sum of 25 Observations = 25 × 50 = 1250

Sum of first 13 observation = 13 × 40 = 520

Sum of last 13 Observation = 13 × 58 = 754

Sum of 26 Observations (First 13 + Last 13)

⇒  520 + 754 = 1274

⇒ 13^th Observation = Sum of 26 Observation - Sum of 25 Observation.

⇒ 1274 - 1250 = 24

∴ 13th Observation = 24

Shortcut Trick

Let MP = 100, Then 

SP = 100 × 0.9 × 0.8 = 72

Here, 100 → 1800, Then 1 → 18

∴ 72 → 72 × 18 = 1296

Alternate Method

Given:

Marked price of a saree is 1800

Successive Discounts 10 % and 20 %

Formula used:

Selling price = Marked price × (100 - D₁) / 100 × (100 - D2) / 100

Calculation:

Selling price = 1800 × (90 / 100) × (80 / 100)

⇒ 18 × 9 × 8 = 1296

Selling price of the saree is 1296

Given:

P/Q = 2/3  (33.33% = 1/3)

Formula used:

Percentage less/more = (A - B)/B × 100

Calculation:

Percentage by which Q earns more than P = (3 - 2)/2 × 100

⇒ 50%

∴ Thus Q earn 50% more than P.

Given:

Speed while going North = 14 km/h

Speed while going South = 24 km/h

Distance apart = 47.5 km

Concept used:

If two objects are in same direction then 

Relative speed = S₂ - S₁

If two objects are in opposite direction then

Relative speed = S₂ + S₁

Time = Distance/Speed

Calculation:

Time = Distance/Speed

Here according to question relative speed will be considered.

Time = 47.5/38 = 1.25 h

∴ The correct answer is 1.25 h or 1$1\over4$h.

Shortcut Trick

Rate =15% per annum

According to question interest is compounded 8-monthly

∴ Rate (r) = 15 × 2/3 = 10% (every 8 month)

Now by applying successive method,

⇒ 1331 = 9982.50 i.e. 1 = 7.5

⇒ Principal = 1000 × 7.5 = 7500

Now the interest is compounded annually

∴ Rate = 15% and Time = 2 years

By applying successive method,

⇒ 400 = 7500 i.e. 1 = 18.75

Amount  = 529 × 18.75 = Rs.9918.75 

Hence, The amount will be ₹ 9919.

Alternate Method

Given:

Amount = Rs.9982.50

Time = 3 years (because interest compounded 8 monthly)

Rate = 15% per annum 

Formula used:

A = P[1 + r/100]^T

Where A = Amount, r = Rate of interest, T = Time

Calculation:

We have interest compounded 8 monthly, then

r = 15 × 2/3 = 10% and year will be 3 years

∴ 9982.50 = P[1 + 10/100]³

⇒ 9982.50 = P × 1.1³ = P × 1.331

⇒ P = 9982.50/1.331 = 7500

Now, if r = 15% and T = 2 years

⇒ A = 7500[1 + 15/100]² = 7500 × 1.15²

⇒ A = 7500 × 1.3225 = 1918.75

Hence, The amount will be ₹ 9919.

Given:

$6{1 \over 4} ÷ \left[ {4{7 \over 8} + {3 \over 4} × \left( {9{1 \over 2} - 7{2 \over 3}} \right)} \right]$

Concept:

Follow the BODMAS rule according to the table given below:

Calculation:

$6{1 \over 4} ÷ \left[ {4{7 \over 8} + {3 \over 4} × \left( {9{1 \over 2} - 7{2 \over 3}} \right)} \right]$

⇒ $25\over4$ ÷ $[{39\over8}+{3\over4}×({{19\over2}-{23\over3}})]$

⇒ $25\over4$ ÷ $[{39\over8}+{3\over4}×({{57-46}\over6})]$ 

⇒ $25\over4$ ÷ $[{39\over8}+{3\over4}×{11\over6}]$

⇒ $25\over4$ ÷ $[{39\over8}+{11\over8}]$

⇒ $25\over4$ ÷ $50\over8$ = $25\over4$ × $8\over50$ = 1

∴ The correct answer is 1.

Shortcut Trick

Use the Cross-Multiplication Method for the Income ratio (5 : 8) and Savings ratio (3 : 4) with given Expenditures.

Difference in cross-products of ratios: |(5 × 4) − (8 × 3)| = |20 − 24| = 4 units.

Difference in cross-products of values: |(3 × 60,000) − (4 × 36,000)| = |180,000 − 144,000| = 36,000.

4 units = ₹36,000 ⇒ 1 unit = ₹9,000.

Income of B = 8 units × 9,000 = ₹72,000.

Savings of B = Income − Expenditure = 72,000 − 60,000 = ₹12,000.

∴ The correct answer is ₹12,000.

Alternate Method

Given:

Ratio of Incomes of A and B = 5 : 8

Expenditure of A = ₹36,000 | Expenditure of B = ₹60,000

Ratio of Savings of A and B = 3 : 4

Formula Used:

Income − Expenditure = Savings

Calculations:

Let the Incomes of A and B be 5x and 8x respectively.

⇒ Savings of A = 5x − 36,000

⇒ Savings of B = 8x − 60,000

⇒ (5x − 36,000) / (8x − 60,000) = 3 / 4

⇒ 4 × (5x − 36,000) = 3 × (8x − 60,000)

⇒ 20x − 144,000 = 24x − 180,000

⇒ 24x − 20x = 180,000 − 144,000

⇒ 4x = 36,000

⇒ x = 9,000

⇒ Savings of B = 8 × 9,000 − 60,000

⇒ Savings of B = 72,000 − 60,000 = 12,000

∴ The correct answer is ₹12,000.

Additional Information

Income-Expenditure Relationship

The fundamental equation for financial problems is Income = Expenditure + Savings. If any two ratios are given along with absolute values of the third component, the variables can be solved linearly.

Cross-Multiplication Method

For equations of the form (ax − c)/(bx − d) = m/n, the shortcut is |an − bm| units = |nd − mc|. This directly helps in finding the common multiplier 'x'.

Ratio Scaling

Ratios can be scaled by a constant factor without changing the relationship. In income problems, ensure the multiplier is applied to the base income ratio before calculating individual savings or expenditures.

Given:

Train covers a distance in 12 hr at a speed of 75 km/h

Formula used:

Speed = Distance/Time

Calculation:

Speed = Distance/Time

⇒ 75 = Distance/12

⇒ Distance = 900 km

If its speed decreases by 3 hr

then speed = 12 - 3 = 9 km/h

Now, Speed = Distance/Time

⇒ Speed = 900/9 = 100 km/h

So, the speed is 100 km/h

Given:

Average age of three members (5 years ago) = 24 years

Average age of wife and child (6 years ago) = 18 years

Formula used:

Average = Sum of observations/number of observations

Calculation:

Let H, W and C be present age of husband, wife and Son.

5 years ago the average = 24 years

∴ (H - 5) + (W - 5) + (C - 5) = 24 × 3

⇒ H + W + C = 72 + 15 = 87     -----(1)

Now, from the second condition

⇒ (W - 6) + (C - 6) = 18 × 2

⇒ W + C = 36 + 12 = 48

Put W + C = 48 in eq(1)

⇒ H + 48 = 87

⇒ H = 87 - 48 = 39

Hence, the age of husband is 39 years.

Calculation:

Let x be the number

According to the question,

⇒ 40% of x + 165 = x

⇒ 40x/100 + 165 = x

⇒ 2x/5 + 165 = x

⇒ x - 2x/5 = 165

⇒ 3x/5 = 165

⇒ x = 275

∴ The correct answer is 275.

Shortcut Trick Calculation:

165 is added to 40% of a number then it becomes number itself

⇒ 60% of the number = 165

⇒ 10% of the number = 27.5

⇒ 100% of the number = 275

Hence the required number is 275.

Given:

 72 ÷ 180 × 5 - [96 of 64 × 5 - 25 ÷ 16 × (23 - 29) - 11] ÷ 7$5 \over 6$ 

Concept used:

Calculation:

⇒  72 ÷ 180 × 5 + [96 ÷ 64 × 5 - 25 ÷ 16 × (23 - 29) - 11] ÷ 7$5 \over 6$

⇒ 72/180 × 5 + [96/64 × 5 - 25 ÷ 16 × (23 - 29) - 11] ÷ 7$5 \over 6$

⇒ 2 + [3/2 × 5 - 25/16 × (-6) - 11] ÷ 47/6

⇒ 2 + [15/2 - (25/8 × -3) - 11] ÷ 47/6  

⇒ 2 + (15/2 + 75/8 - 11) ÷ 47/6

⇒ 2 + (60 + 75 - 88)/8 ÷ 47/6

⇒ 2 + 47/8 ÷ 47/6

⇒ 2 + 47/8 × 6/47

⇒ 2 + 3/4

⇒  $2 {3 \over4}$

Shortcut Trick

Gain = 20% of CP = ₹10.50

⇒ CP = (10.50 ÷ 20) × 100 = ₹52.50

SP = CP + Gain = 52.50 + 10.50 = ₹63

Discount = 28% on MP ⇒ SP = 72% of MP

⇒ MP = (63 ÷ 72) × 100 = ₹87.50

∴ The correct answer is ₹87.50.

Alternate Method

Given: Discount% = 28%, Gain% = 20%, Gain Value = ₹10.50. Formulas: Gain = SP − CP | Gain% = (Gain ÷ CP) × 100 | SP = MP × (100 − D%) ÷ 100.

⇒ Gain = 20% of CP = 10.50 ⇒ CP = (10.50 × 100) ÷ 20 = ₹52.50 ⇒ SP = CP + Gain = 52.50 + 10.50 = ₹63 ⇒ SP = MP × (100 − 28) ÷ 100 ⇒ 63 = MP × 72 ÷ 100 ⇒ MP = (63 × 100) ÷ 72 = ₹87.50

∴ The correct answer is ₹87.50.

Additional Information

Relation between CP and MP

The ratio of CP to MP can be directly found using: CP : MP = (100 − D%) : (100 + G%).

Marked Price & Discount

Discount is always calculated on the Marked Price (MP) to arrive at the Selling Price (SP).

Shortcut Trick

Let the four numbers be 9a, 9b, 9c, and 9d (where a, b, c, d are pairwise coprime).

LCM = 9 × a × b × c × d = 270

⇒ a × b × c × d = 30

Product of the numbers = (9a) × (9b) × (9c) × (9d) = 9⁴ × (abcd)

⇒ Product = 6561 × 30 = 196830

∴ The correct answer is 196830.

Alternate Method

Given:

⇒ LCM of four distinct numbers = 270

⇒ HCF of each pair = 9

Four Distinct Numbers (HCF = 9)

9 × 1 9

9 × 2 18

9 × 3 27

9 × 5 45

LCM = 9 × (1 × 2 × 3 × 5) = 270 Product = 9 × 18 × 27 × 45 = 196830

Calculation:

⇒ Since the HCF of each pair is 9, all four distinct numbers must be multiples of 9.

⇒ Let the four numbers be 9a, 9b, 9c, and 9d, where a, b, c, and d are pairwise coprime integers.

⇒ The LCM of these four numbers is evaluated as = 9 × a × b × c × d

⇒ 9abcd = 270

⇒ abcd = 30

⇒ The only four distinct positive pairwise coprime integers whose product evaluates to 30 are 1, 2, 3, and 5.

⇒ Thus, the four numbers are: 9 × 1 = 9, 9 × 2 = 18, 9 × 3 = 27, and 9 × 5 = 45.

⇒ Product of the four numbers = 9 × 18 × 27 × 45

⇒ Product = 196830

∴ The correct answer is 196830.

Additional Information

LCM & HCF of Two Numbers

For any two numbers, the product of the numbers is strictly equal to the product of their HCF and LCM (i.e., a × b = HCF × LCM). However, this direct rule is generally not applicable to three or more numbers.

Pairwise Coprime Numbers

A set of numbers is pairwise coprime if any given pair chosen from the set has an HCF of exactly 1. The LCM of a set of pairwise coprime numbers is always equal to their product.

Multiples of HCF

If the HCF of a set of numbers is H, every number in the set can be factorized as H × k, where k represents distinct integers that do not possess any mutual common factors across the overall group.

Shortcut Trick

Let the Cost Price (CP) be 100%.

At 8% loss, Selling Price (SP₁) = 100% − 8% = 92%.

Since 92% corresponds to ₹460, then 1% = 460 ÷ 92 = ₹5.

New Selling Price (SP₂) = ₹590 corresponds to 590 ÷ 5 = 118%.

Profit percentage = 118% − 100% = 18%.

∴ The correct answer is 18%.

Alternate Method

Given: Selling Price (SP₁) = ₹460, Loss = 8%, New Selling Price (SP₂) = ₹590.

Formula Used: CP = [SP × 100] ÷ [100 − Loss%] | Profit % = [(SP − CP) ÷ CP] × 100

⇒ Cost Price (CP) = (460 × 100) ÷ (100 − 8)

⇒ CP = (460 × 100) ÷ 92

⇒ CP = 5 × 100 = ₹500

⇒ New Profit = New SP − CP = 590 − 500 = ₹90

⇒ Profit Percentage = (90 ÷ 500) × 100

⇒ Profit Percentage = 90 ÷ 5 = 18%

∴ The correct answer is 18%.

Additional Information

Profit and Loss Percentage

Profit % = (Profit ÷ CP) × 100 and Loss % = (Loss ÷ CP) × 100. Both are always calculated on the Cost Price unless stated otherwise.

Successive Percentage Formula

If there are two successive changes of x% and y%, the effective change is [x + y + (xy ÷ 100)]%.

Marked Price and Discount

Selling Price = Marked Price − Discount. Discount percentage is always calculated on the Marked Price (MP).

Shortcut Trick

 

A + B's 6-day work = (30 + 22.5) × 6 = 315

Remaining work = 675 - 315 = 360

∴ A + C's 3-day work = 360

So, (A + C) × 3 = 360

⇒ 30 + C = 360/3 = 120

⇒ C = 90

Time taken by C to complete the work alone

⇒ T_c = 675/90 = 7.5 = 7$\frac{1}{2}$

∴ C alone can complete the work in 7$1\over2$ days.

Alternate Method

Given:

A complete a work in 22$1 \over 2$ days

B complete a work in 30 days

They worked together but after 6 days B had to leave

Calculation:

1-day work of A = 2/45, and 1-day work of B = 1/30

A + B's 1-day work = 2/45 + 1/30 = 7/90

A + B's 6-day work = $7\over90$ × 6 = 7/15

Remaining work when B left = 1 - 7/15 = 8/15

Let C complete the work in x days

∴ C's 1-day work = 1/x

A + C's 1-day work = 2/45 + 1/x 

Remaining work done by A and C in 3 days = (2/45 + 1/x)3 = 8/15

⇒ 2/45 + 1/x = 8/45

⇒ 1/x = 8/45 - 2/45

⇒ 1/x = 6/45

⇒ x = 15/2 = 7$1\over2$

∴ C alone can complete the work in 7$1\over2$ days.

Given:

SP₂ = 9/11 of the actual SP and Loss = 10%

Formula used:

CP = SP × 100/(100 - L%)

P% = P × 100/CP

Where CP = cost price, SP = selling price

And P = profit

Calculation:

Let the actual SP be 11x then SP₂ = 9x

Now loss is 10%, therefore

⇒ CP = 9x × 100 /(100 - 10)

⇒ CP = 9x × 100/90 = 10x

Let SP₃ be 95% of the actual SP

⇒ SP₃ = 95% of 11x = 10.45x

Now profit = 10.45x - 10x = 0.45x

⇒ Profit% = 0.45x × 100/10x = 4.5

Hence, the required profit is 4.5%.

**Given:**​

$4 \over25$, $8 \over35$ and $22\over40$ 

Formula used:

H.C.F of fractions = (H.C.F of numerator) / (L.C.M of denominator)

Calculation:

$4 \over25$, $8 \over35$ and $22\over40$

Factors of 25 = 5 × 5

Factors of 35 = 5 × 7

Factors of 40 = 2 × 2 × 2 × 5

L.C.M of denominator = 5 ×5 × 2³ × 7 = 1400

Factors of 4 = 1 × 2 × 2

Factors of 8 = 1 × 2 × 2 × 2

Factors of 22 = 2 × 11

H.C.F of numerator = 2

H.C.F of fractions = $2\over1400$ 

∴ The H.C.F of fractions is $1\over700$.

Given:

Radius of cone = 18 cm

Height of cone = 35 cm

Formula used: 

Volume of cone = $\frac{1}{3}$πr²h

Calculation:

Volume of cone = $\frac{1}{3}$πr2h

⇒ Volume = $\frac{1}{3}×\frac{22}{7} × 18^2 × 35$

⇒ Volume = 11880 cm³

So, the volume of the cone is 11880 cm³

Given:

Cost price (CP) of Cooker = 9/10 × Selling price (SP)

Formula used:

Profit  = SP - CP 

%Profit  = Profit × 100/CP

Calculation:

According to question, CP = 9/10 × SP

Let CP and SP is 9x and 10x

If it sold at 5% more than, then new SP

SP = 10x + 10x × 5/100 = 21x/2

Now, Profit  = SP - CP

⇒ Profit  = 21x/2 - 9x = 3x/2

∴ Profit % = $\frac{3x}{2×9x}×100$ = $16\frac{2}{3}$

Hence, her gain percentage is $16\frac{2}{3}$%

Given:

Time taken by X and Y together = 6 days

If X = 3x and Y = Y/4, time taken = 4 days

The work would have been completed in 4 days.

Concept used:

Total Work = Time × Efficiency

Calculation:

According to Question

X + Y = 1/6 ------- (1)

3 X + Y/4 = 1/4 -------(2)

Solving two equations we get 

Y = 1/11, X = 5/66

So X alone finish the work in 66/5 days.

∴ The Required Answer is $13 \frac{1}{5}$ days.

Given:

Proportions are 4, 8 and 15.

Formula used:

a : b :: c : d

Fourth Proportion = b × c/a

Calculation:

⇒ 4 : 8 :: 15 : d

⇒ d = 15 × 8/4

⇒ d = 30

∴ The fourth proportional is 30.

Given:

Principal = Rs. 8400, Time Period = 3 years

Compound Interest = Rs. 6115.20

Formula used:

Compound Interest = P × [1 + (R/100)]ⁿ - P

Simple Interest = [P × R × T]/100

Where P = Principal, R = Rate of interest, n = Time in years

Calculation:

According to the Question,

Compound Interest = P × [1 + (R/100)]n - P

⇒ 6115.20 = 8400 × (1 + R/100)³ - 8400

⇒ 6115.20 + 8400 = 8400[((100 + R)/100)³]

⇒ 14515.20/8400 = [(100 + R)/100]³

⇒ 1728/1000 =  [(100 + R)/100]3  

⇒ [(100 + R)/100] = (1728/1000)^1/3

⇒ [(100 + R)/100] = 12/10

⇒ R = 20%

Compound interest for $1{1 \over 2}$ years, when compounded half-yearly

∴ R = 20/2 = 10%, and T = 3 years

Compound Interest = P × [1 + (R/100)]n - P

⇒ 8400 × [(100 + 10%)/100]³ - 8400

⇒ 8400[(110/100)³ - 1]

⇒ 8400 × 331/1000 = 2780.4

Simple Interest on the same sum for the same rate and time,

⇒ Simple Interest = [P × R × T]/100

⇒ [8400 × 20 × (3/2)]/100 = 2520

The required difference = 2780.4 - 2520 = 260.4

∴ Hence the required difference is ₹ 260.4

Given:

The radius (r) = 10.5 cm and Height (h) = 30 cm

The cylindrical vessel is $4 \over5$ full of water

Length of the rectangular tube, l = 44 cm

The breadth of the rectangular tube, b = 36 cm

Formula used: 

The volume of the cylindrical vessel = π r²h

The volume of the rectangular tube = l × b × h

Calculation:

The volume of the cylindrical vessel = π r2h

⇒ $22\over7$ × 10.5 × 10.5 × 30 = 10395 cm³

The cylindrical vessel is $4 \over5$ full of water, therefore

⇒ Volume =  $4 \over5$ × 10395 = 8316

The volume of the rectangular tube = 8316

⇒ l × b × h = 8316

⇒ 44 × 36 × h = 8316

⇒ h = ${8316}\over{44\times36}$ = $5 {1 \over 4}$ cm

∴ The height to the water level rises in the tub is $5 {1 \over 4}$ cm.

Given:

W : X = X : Y = Y : Z = 5 : 6

Calculation:

⇒ W : X : Y : Z = 125 : 150 : 180 : 216

According to the question,

⇒ 125 + 150 + 180 + 216 = 8,052

⇒ 671 = 8,052

⇒ 1 unit = 8,052/671 = 12 

Now, X +  Y = 150 + 180 = 330

⇒ 330 × 12 =  3960

∴ The sum of shares of X & Y is 3,960.

The correct answer is Neat and tidy. 

Key Points

• The most appropriate meaning of the given idiom "spick and span" is neat and tidy.
• Spick and span: something which is spotlessly clean. 
• Example: She keeps her room spick and span.

 Additional Information

• The idiom "spick and span" was adopted in the English language in the 1300s.
• It is taken from the Dutch expression "spiksplinternieuw" which means fresh timbers of a newly built shop.
• This Dutch expression was converted into the English language that we use now. ​