SSC GD Constable Previous Year Paper (Held on: 18th November 2021 Shift 2)

The table is alphabets place value:

The pattern followed here is:

CREAM : FPJYZ

Similarly,

CHECK : ?

Hence, 'CHECK' is coded as "FFJAV".

According to the sequence in the dictionary:

The correct order of the given words is:

"Ho" is common in all words.

5. Hopeless
6. Hospital
7. Hostel 
8. Hostile
9. House

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

The embedded part of this image is:

Hence, option (1) is the correct answer.

Table show alphabet serial number –

The pattern followed is,

Hence, “CST” is complete the series.

Eight persons facing centre: A, B, C, D, E, F, G and H.

1. D is sitting between F and H.

2. E is sitting second to the left of D.

3. C is sitting third to the right of A.

4. A is not sitting between B and G.

Final sitting arrangement:

Hence, “E” is sitting opposite A.

According to the given information

‘when’ is coded as bel.

Hence, 'bel’ is the correct answer.

The pattern followed here is,

Let (1^st number : 2^nd number)

(2^nd number)² + 6 = 1^st number

Now follow the steps:

70 : 8

=> 8² + 6 = 64 + 6 = 70 = 1^st number

Similarly,

87 : ?

=> 9² + 6 = 81 + 6 = 87 = 1^st number

Hence, "87" is correct answer.

The table is alphabets place value:

The pattern followed here is:

All alphabet opposite place values are coded as numbers.

‘GREW’ is coded as ‘209224’

​Similarly, 

'TYPE' = ?

Hence, the correct answer is "721122".

The image obtained when the paper is unfolded is,

Hence, option 2 is the correct answer.

The opposite surface of the open dice can be found by the below method:-

• Alternate surfaces are opposite to each other.
• No two opposite surfaces are touched by side or by corners

So, by using the above rule we can find the opposite surface of open dice.

Below are the opposite surfaces:-

 

Note:- Two opposite faces are never seen together or adjacent to each other.

Given:

In figure (A): None of the opposite faces are seen together nor they are adjacent to each other. Thus this cube can be made.

In figure (B): ‘4’ and ‘3’ are opposite faces but here they are seen together which is wrong. Thus this cube cannot be made.

In figure (C): None of the opposite faces are seen together nor they are adjacent to each other. Thus this cube can be made.

In figure (D): ‘6’ and ‘1’ are opposite faces but here they are seen together which is wrong. Thus this cube cannot be made.

Hence, ‘A and C’ is the correct answer.

The logic followed here is:

A dictionary means a book that contains a list of the words in a language in the order of the alphabet and that tells you what they mean, in the same or another language.

• 'Dictionary' is a book where we can find any 'Meaning' in another language.

Similarly,

Encyclopaedia Means A book or set of books that give information about very many subjects, arranged in the order of the alphabet.

• 'Encyclopaedia' is a book where we can find any 'Knowledge' about subjects.

Hence, ‘Knowledge’ is the correct answer.

The Venn diagrams best represent the relationship between - 

     ♦   Passengers, Flight, Train figures are shown below:

Some passengers are traveling by flight and some are travel by train.

Hence, ‘option 3’ is the correct answer.

BODMAS rule:-

Decoding the information, 

Given:

6 C (57 B 8) D 7 B 32 A 9

After replacing the signs from left to right and using the BODMAS rule,

= 6 × (57 - 8) ÷ 7 - 32 + 9

= 6 × 49 ÷ 7 - 32 + 9

= 6 × 7 - 32 + 9

= 42 - 32 + 9

= 51 – 32

= 19

Hence, “19” is the correct answer.

The pattern followed here is:

 

Hence, '68' is the correct answer.

The correct mirror image of the given figure when the mirror is held at the right side is:

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

Additional InformationIn Mirror image left side and right side changed vice-versa where the top and bottom remain the same.

The reflection of an object into the water is its water image. It appears by inverting an object vertically i.e. upside down.

The water image of the figure looks like the mirror image of the figure in case the mirror is horizontally at the bottom of the figure.

Water image is just a reflection where top and bottom part of the images changed where left and right side of the image remain same.

Given: Z _ K F _ O K G Z _ K _ Z O _ I

By checking options and substituting accordingly.

1)  OZOHK → Z O K F / Z O K G / Z O K H / Z O K I

     ►  Here the last letter of the word is increased by +1.

            ♦   F + 1 = G, G + 1 = H, H + 1 = I

2)  OZKHK → Z O K F / Z O K G / Z K K H / Z O K I

3)  OZOHZ → Z O K F / Z O K G / Z O K H / Z O Z I

4)  KZOHK → Z K K F / Z O K G / Z O K H / Z O K I

    ♦   Option (1) gives a pattern of Z O K F / Z O K G / Z O K H / Z O K I

Hence, ‘OZOHK’ is the correct answer.

Given:

 

Here the pattern followed in each column is:

(2^nd number + 3^rd number) ÷ 5 = 1^st number

Column 1: 9, 18, 27

(2^nd number + 3^rd number) ÷ 5

= (18 + 27) ÷ 5

= 45 ÷ 5

= 9 = 1^st number

Column 2: 18, 32, 58

(2^nd number + 3^rd number) ÷ 5

= (32 + 58) ÷ 5

= 90 ÷ 5

= 18 = 1^st number

Similarly,

Column 3: ?, 79, 46

(2^nd number + 3^rd number) ÷ 5

= (79 + 46) ÷ 5

= 125 ÷ 5

= 25 = 1^st number

Hence, “25” is correct answer.

The pattern followed here is:

 

Hence, '242' is the correct answer.

Let the number is x

1) A number when added to 4 times to itself.

=> x + 4x = 5x

2) Gets equal to 10 times to its predecessor.

=> 5x = 10(x - 1)

=> 5x = 10x – 10

=> 10x – 5x = 10       

=> 5x = 10

=> x = 2

Hence, “2” is that number.

Total six friends:-  P, Q, R, S, T and U

1. Q is at the right end.

2. U is sitting to the immediate left of T, and T is sitting to the immediate left of Q.

3. R is sitting to the immediate right of S.

4. P is sitting to the immediate left of S.

Hence, 'P' is sitting at the left end.

The figure that will replace the question mark (?) in the following figure series is shown below:

1. The triangle rotates in a clockwise direction in box each corner and the triangle convert into a square shape and square shape converts into a triangle shape.

2. Line rotate in a clockwise direction and one by one line increase.

Final series is

Hence, ‘option 3’ is the correct answer.

The table is alphabets place value:

The pattern followed here is:

• Consonants are increased by +2.
• Vowels are decreased by -2.

‘CHAINED’ is written as ‘EJYGPCF’

Similarly,

'MEADOW' = ?

Hence, 'MEADOW' is coded as "OCYFMY".

Logic: First letter + Second letter = Third letter

Option (1): ODS →

O + D = S

⇒ 15 + 4 = 19

Option (2): AHI →

A + H = I

⇒ 1 + 8 = 9

Option (3): GNU →

G + N = U

⇒  7 + 14 = 21

Option (4): DOU →

D + O = U

⇒ 4 + 15 = 19 ≠ 21

Therefore, option(4) does not follow the logic.

Hence, the correct answer is "DOU".

Preparing the family tree using the following symbols,

Given:

1. Manoj and Darshan are the sons of Kripal and Sona.

2. Sona is the mother-in-law of Charul's mother Swapnil.

3. Ajay and Charul are brother and sister.

4. Neha, Niti and Nakul are the daughters of Manoj and the only cousins of Ajay.

Hence, Darshan have "2" children.

Statements:

All girls are actors.

All actors are singers.

The least possible diagram for the given statements is as follows

Conclusions:

1. Some girls are not singers → False (because all girls are actors and all actors are singers so all girls are singers)
2. No actor is a girl → False (because all girls are actors so definitely some actors are also girls)
3. All girls are singers → True (because all girls are actors and all actors are singers so all girls are also singers)

Hence, “Only conclusion 3 follows".

The correct answer is Maulana Abul Kalam Azad.

Key Points

• ​​Maulana Abul Kalam Azad wrote the book ‘India Wins Freedom’.
• The book India Wins Freedom gives a detailed description and analysis of the meaning of 'Pakistan', the formation of India and the partition of India.
• The book "India Wins Freedom" is one of his books which narrates and narrates the utmost importance of history and events which are still kept hidden and treasured on the safe side of the contemporary relevance of the nation.
• "India Wins Freedom" was written by Azad's personal secretary "Humayun Khan", which was scrutinized closely by Maulana Abdul Kalam Azad before being brought into the domain of the general public.
• Maulana Abul Kalam was one of the most influential freedom fighters during the freedom struggle of independent India.
• He was also a noted writer, poet and journalist.
• He was a prominent political leader of the Indian National Congress and was elected as Congress President in 1923 and 1940.

Additional Information

• Sardar Vallabhbhai Patel
• ​Sardar Vallabhbhai Patel was a senior leader of the Indian National Congress and a prominent figure in the Indian freedom struggle.
• Later became the first Deputy Prime Minister of India and the first Home Minister.​
• Dr BR Ambedkar
• ​Dr BR Ambedkar was popularly known as Babasaheb Ambedkar and everyone knows that he was one of the architects of the Indian Constitution.
• He was also a noted political leader, eminent jurist, Buddhist activist, philosopher, anthropologist, historian, orator, writer, economist, scholar and editor.​
• Jawaharlal Nehru
• ​Pandit Jawaharlal Nehru was the first Prime Minister of India and a key figure in the Indian independence struggle and the process of political development in the country after independence.

The correct answer is Mumbai.

Key Points

• The Corporate Office of Axis Bank is located at Axis House Mumbai.
• Axis Bank is the third largest private sector bank operating in India.
• The bank was established in 1993 and began its operations in 1994.

Additional Information List of Banks and their headquater

The correct answer is Kezang D Thongdok.

Key Points

• Kezang D. Thongdok of Arunachal Pradesh won the Dada Saheb Phalke Award 2020 for his short documentary "Chi Lupo."
• Chi Lupo, documented by Kezang D Thongdok is a short documentary on honey hunting.
• Chi Lupo depicts the honey hunting tradition prevalent in the Shertukpen community in which "chi" means honey while "lipo" means hunter.
• This age-old tradition of honey hunting is slowly dying out with each passing day.
• To keep alive this indigenous practice of honey hunting, Kezang de Thongdok documented the centuries-old tradition of honey hunting.

Additional Information

• Kasinathuni Viswanath
• Kasinathuni Viswanath is a famous south Indian film actor, writer, and director.
• Bommireddy Nagi Reddy
• ​Bommi Nagi Reddy was an Indian film producer and director mainly in Telugu cinema.
• Akkineni Nageswara Rao
• ​Akkineni Nageswara Rao was an Indian actor and producer, known for his work predominantly in Telugu cinema.

The correct answer is Kakori Conspiracy.

Key Points

• The Kakori conspiracy took place before the arrival of the Simon Commission in India.
• The Kakori Train Action was a train robbery, carried out on August 9, 1925, by the revolutionaries of the Indian independence movement against the British Raj in a village called Kakori near Lucknow.
• This robbery was carried out by 10 revolutionaries including Hindustan Republican Association's revolutionary Ram Prasad Bismil, Ashfaq Ullah Khan, Rajendra Lahiri, Keshav Chakraborty, Mukundi Lal and Banwari Lal.
• Significantly, freedom fighters Ram Prasad Bismil, Ashfaq Ullah Khan and Roshan Singh were hanged on 19 December 1927 for their involvement in the Kakori conspiracy.

Additional Information

• The First Round Table Conference
• ​The first Round Table Conference started on 12 November 1930 in London.
• During this time, the independence movement in India was in full swing and there were constant demands for the grant of Dominion status to India.
• Gandhi-Irwin Pact
• ​A political pact was signed by Mahatma Gandhi and the then Viceroy of India, Lord Irwin, before the Second Round Table Conference in London on 5 March 1931.
• Quit India Movement
• ​The Quit India Movement was a civil disobedience movement in India launched in August 1942 in response to Mahatma Gandhi's call for India's immediate independence.

The correct answer is the Human development index.

Key Points

• Human development index
• The first UNDP Human Development Report was published in 1990.
• The Human Development Index is a report published by the United Nations Development Program (UNDP).
• ​The Human Development Index (HDI) is a statistical tool used to measure a country's overall achievement in social and economic dimensions.
• The purpose of the HDI is to rank countries on the Human Development Scale in terms of the abilities of humans within countries to perform tasks.
• The Human Development Index (HDI) is an index that measures key dimensions of human development.
• The three key dimensions are:
• ​A long and healthy life- is measured by life expectancy.
• Access to education-  measured by expected years of schooling of children at school-entry age and mean years of schooling of the adult population.
• And a decent standard of living- measured by Gross National Income per capita adjusted for the price level of the country.

The correct answer is Lord Dalhousie.

Key Points

• The doctrine of lapse, a formula formulated by Lord Dalhousie, Governor-General of India (1848–56), to deal with questions of succession in Hindu Indian states.
• According to this policy, if the king did not have any natural-born heir then the kingdom would lapse to the British or would be administered and occupied by the British.
• Indian states such as Satara, Nagpur and Jhansi were annexed under this policy.

Additional Information

• Lord Dalhousie
• ​On 12 January 1848, he was appointed Governor-General of India and Governor of Bengal.
• Dalhousie considered the consolidation of British power in India as its main objective.
• He was responsible for introducing many modern reforms in India such as railways, telegraph and postal networks and public works.​
• ​​He is best remembered for the Doctrine of Lapse Policy, which many attributes directly to the Indian Rebellion of 1857.
• Lord Dalhousie also started many Anglo-vernacular schools in India.
• Lord Ripon
• ​Viceroy of India from 1880-84.
• The Vernacular Press Act was cancelled in 1882.
• The first Factory Act was implemented in 1881.
• Warren Hastings
• ​First Governor of the Presidency of Fort Williams.
• First Governor-General of Bengal.
• Warren Hastings played an important role in the abolition of dual system.
• To collect the revenue a Board of Revenue was set up at Calcutta.

The correct answer is Swaroop Singh Kuntal.

Key Points

• Indian Army's officer Lt. Col. Swaroop Singh Kuntal became the fastest Indian to complete Ironman Malaysia in a record timing of 12 hours and 14 minutes.
• The Ironman Malaysia was organised on October 26 on Langkawi Island in Malaysia. Athletes from all over the world participated.
• Ironman consists of 3.8 km of sea swimming followed by 180 km of cycling and finally 42.2 km of running.
• All events are required to be done in a cut-off time of 17 hours.
• Ironman Malaysia is one of the toughest competitions because it has an elevation of around 3,000m on the 180 km cycling course.
• During cycling maximum temperature reached 38°C and while running it reached 35°C.

Additional Information

• Swaroop Singh Kuntal
• Kuntal is posted in Jhansi. He is a paratrooper and an IITian.​
• Earlier, he participated in many marathons and ultra-marathons.
• He won a 12-hour stadium run at Chandigarh where he covered 118.7 km.
• Kuntal has represented Uttar Pradesh in the 23^rd National Road Cycling Championship in 2018.
• Earlier in September 2018, he won Ironman at Jaipur International Triathlon.
• Kuntal trained very hard to participate in Ironman Malaysia and his preparation included extensive running, cycling, swimming, and strength training.

The correct answer is Nitin Menon.

Key Points

• Nitin Menon was the youngest umpire to enter the ICC Elite Panel in 2020.
• Indian umpire Nitin Menon has been included in the International Cricket Council's elite panel of umpires.
• He was included in the elite panel for the 2020-21 season.
• He replaced England umpire, Nigel Long.
• Nitin Menon was earlier part of the Emirates ICC International Panel of Umpires.
• He has experience umpiring in three Tests, 24 One Day Internationals and 16 T20 Internationals.
• Nitin Menon is the third Indian after former captain Srinivas Venkataraghavan and Sundaram Ravi to make it to the prestigious panel.
• Nitin Menon has been inducted by a selection panel comprising ICC General Manager (Cricket) Geoff Allardyce (Chairman), Indian commentator Sanjay Manjrekar and matches referees Ranjan Madugalle and David Boon.

Additional Information

• Aleem Dar
• ​Aleem Dar is a Pakistani cricket umpire and former cricketer.
• Sundaram Ravi
• ​Sundaram Ravi is an Indian cricket umpire who was a member of the ICC Elite Panel of Umpires between 2015 and 2019.
• Nigel Llong
• ​Nigel James Long is an English cricket umpire and former first-class cricketer.

The correct answer is Mariyappan Thangavelu.

Key Points

• Mariyappan Thangavelu is a paralympic high jumper.
• He represents India in the 2016 summer paralympic games held in Rio de Janeiro in the men's high jump T-42 category, winning the gold medal in the finals.
• He is India's first Paralympic gold medalist since 2004.

Additional Information

• Rajiv Gandhi Khel Ratna Award
• Rajiv Gandhi Khel Ratna Award is given for​ the spectacular and most exceptional performance in the sphere of sports for four years, at international levels.
• The frist recipient of the award was Chess Grandmaster Viswanath Anand.
• It has a reward of 25 lakhs.
• The 2020 recipients of the award are as follows;
• ​Rohit sharma (Cricket)​
• Mariyappan Thangavelu (Para-Athletics)
• Manika Batra (Table Tennis)
• Vinesh Phogat (Wrestling)
• Rani Rampal (Hockey)

The correct answer is Three.

Key Points

• The election to the Bihar Legislative Assembly was held in three phases from October-November to elect the members of the seventeenth Bihar Legislative Assembly.
• Polling was held in three phases for a total of 243 seats:-
• ​For the first time on 28 October 2020 for 71 seats.
• Second on 3^rd November 2020 for 94 seats.
• Third on 7^th November 2020 for the remaining 78 seats.
• The counting of votes began on 10 November 2020 and the incumbent National Democratic Alliance emerged as the winner with 125 elected MLAs.
• The main opposition alliance of the ( Mahagathbandhan) Grand Alliance won 110 seats.
• Other smaller coalitions and parties won 7 seats while only 1 newly elected MLA was independent.
• Chief Minister Nitish Kumar was elected the leader of the National Democratic Alliance in Bihar and took oath as the Chief Minister.

The correct answer is Greek and Aramaic.

Key Points

• Kandahar bilingual inscription
• The Kandahar bilingual inscription is a famous bilingual inscription in Greek and Aramaic.
• Declared and carved around 260 BC by Ashoka, the ruler of the Indian Maurya Empire.
• ​This is the earliest known inscription of Ashoka, written in the 10^th year of his reign.
• This first inscription was written exclusively in Classical Greek and Aramaic.
• It was discovered in 1958, during some excavation work under a 1-meter-high layer of rubble, and is known as KAI 279.
• It is sometimes considered one of Ashoka's many "Minor Rock Edicts", in contrast to his "Major Rock Edicts", which consist of portions or totality of his Edicts from 1 to 14.
• Two inscriptions have been found in Afghanistan with Greek inscriptions, one of which is a bilingual inscription in Greek and Aramaic, the other being a Kandahar Greek inscription only in Greek.

Additional Information

• Aramaic and Greek
• ​A bilingual Ashokan inscription, inscribed in Greek and Aramaic, is found at Kandhar.
• Persian and Arabic ​
• Arabic & Persian Inscriptions were found in the 14^th-century mosque in Dholka Gujarat, India.

The correct answer is  Firewood.

Key Points

• Sources of Energy
• ​Two major sources of energy are classified as Conventional and Non-Conventional Sources.
• Conventional Sources of Energy
• ​Conventional Sources of Energy are also known as non-renewable sources of energy and are available in limited quantity apart from hydroelectric power.
• They serve both commercial and industrial purposes.
• These can be considered as one of the causes of pollution.
• In addition, it is classified under commercial and non-commercial energy.
• Commercial Energy- Coal, electricity and petroleum.
• Non-commercial Energy- straw, dried dung, firewood.
• Non-Conventional Sources of Energy
• ​Non-conventional sources are also known as renewable sources of energy.
• These are mainly used for domestic purposes.
• They are not responsible for the causes of pollution.
• Examples of non-conventional sources of energy include solar energy, bioenergy, tidal energy and wind power.

The correct answer is the Constitution (Seventy-third Amendment) Act, 1992.

Key Points

• Seventy-third Amendment Act, 1992
• ​In 1992, the 73^rd Constitutional Amendment Act was passed, and it came into effect on April 24, 1993.
• The Act empowered the state governments to formalize village panchayats and adopt necessary procedures to enable them to function as autonomous bodies.
• This act added a new Part-IX to the Indian Constitution.
• This section is titled 'The Panchayats' and it contains provisions from Articles 243 to 243 O.
• In addition, the Act added a new Eleventh Schedule to the Constitution.
• There are 29 Panchayat functional items included in this schedule. It is related to Article 243-G.
• Objective
• ​Democratic decentralization of power and resources from the centre to elected representatives at lower levels to allow individuals to participate more directly in governance.
• The object of the 73^rd amendment pertains to Article 40 of the Constitution which requires the state to organize village panchayats and provide them with the necessary powers and authority to function as units of self-government.

Additional Information

• Sixtieth Amendment Act, 1988
• ​Article 276 of the Constitution relating to taxes on professions, professions, occupations and employment was amended.
• Forty-third Amendment Act, 1977
• ​Restored the jurisdiction of the Supreme Court and the high courts in respect of judicial review and issue of writs.
• Thirty-Seventh Amendment Act, 1975
• ​Parliament passed it on April 26, 1975, to make way for a Legislative Assembly and a Council of Ministers for Arunachal Pradesh, the north-Easternmost Union territory of the country.

The correct answer is 15 minutes.

Key Points

• Football
• Football (soccer) is one of the oldest sports in the world as well; It is also one of the most recognized.
• The objective of football is to score more goals than your opponent in a 90-minute playing period.
• The match is split up into two halves of 45 minutes.
• After the first 45 minutes, players will take a 15-minute rest period called half time.
• There are 11 players in each team. They consist of a goalkeeper and ten outfield players.
• Cups & Trophies- Rovers Cup, Federation Cup, FIFA World Cup, Kalinga Cup, Scissor Cup, Sanjay Gold Cup, Santosh Trophy (National Football) etc.

The correct answer is Osmosis.

Key Points

• Unicellular freshwater organisms and most plant cells tend to gain water through osmosis.
• The absorption of water by plant roots is also an example of osmosis.
• Osmosis can be defined as the spontaneous movement of solvent molecules through a semi-permeable membrane, from a low-concentration solution to a high-concentration solution.
• Osmosis is purely a mechanical process where cells absorb water without spending any amount of energy.

Additional Information

• Morphogenesis
• ​A biological process that causes a tissue or organ to develop its shape by controlling the spatial distribution of cells during embryonic development.
• Hybridisation
• ​A process of mathematically combining two or more atomic orbitals from the same atom to form a completely different orbital from its constituents is therefore called a hybrid orbital.
• Tropism
• ​The growth rate of plant parts in which the direction of stimulus determines the direction of response is called tropism.
• Example: Phototropism, where plant stems grow upward in response to sunlight.

The correct answer is Samudragupta.

Key Points

• Samudragupta (335AD-380 AD)
• ​Chandragupta I, was succeeded by his son Samudragupta.
• Samudragupta was the greatest king of the Gupta dynasty.
• The most detailed and authentic record of his reign is preserved in the Prayaga Prasasti/Allahabad pillar inscription, composed by his court poet Harisena.
• Samudragupta’s military campaigns justify the description of him as the Napoleon of India by V.A. Smith.
• Titles: Kaviraja, Param Bhagavat, Ashvamedha- parikrama, Vikram Sarva-rajochchhetta only Gupta ruler had the title of Sarva-raj-ochchhetta.
• Allahabad pillar inscriptions mention the title Dharma Prachar Bandhu, i.e. he was the upholder of Brahmanical religion.

Additional Information

• Chandragupta II 
• Chandragupta II, also called Vikramaditya, powerful emperor (reigned c. 380–c. 415 ce) of northern India.
• Ghatotkacha 
• Ghatotkacha was the second ruler of the Gupta Dynasty. He was the successor of his father Sri Gupta. He ruled between 280 AD to 319 AD.
• Vikramaditya
• Vikramaditya ruled over parts of India in the 1^st century BCE, and popular culture credits him with starting the Vikrama Samvat era in 57 BCE.

The correct answer is Romila Thapar.

Key Points

• A book titled “Voices of Dissent” authored by Romila Thapar.
• This book is scheduled to be published in October 2020.
• In Voices of Dissent: Thapar looks at the articulation of nonviolent dissent and relates it to various pivotal moments throughout India's history.
• It also focuses on the recent protests in India against the Citizenship Act and the National Register of Citizens.
• Romila Thapar hails from Lucknow, Uttar Pradesh.
• Her works include A History of India (1966), Interpreting Early India (1992), Early India: From the Origin to AD 1300(2003).
• She was awarded the Padma Bhushan in 2005 and received the Kluge Award in December 2008.

Additional Information

The correct answer is Collateral.

Key Points

• Collateral
• An asset that the borrower owns and uses as a guarantee to the lender until the loan is repaid is called collateral.
• Collateral is a type of security that banks take from their clients.
• The collateral can be in the form of fixed deposits, property papers etc.
• The collateral reduces the risk to the lenders.
• If a borrower defaults on the loan, the lender can seize the collateral and sell it to cover his loss.
• Mortgage and car loans are two types of collateralized loans.
• Other personal assets, such as a savings or investment account, can be used to secure a collateralized personal loan.

The correct answer is Osmosis.

Key Points

• Unicellular freshwater organisms and most plant cells tend to gain water through osmosis.
• The absorption of water by plant roots is also an example of osmosis.
• Osmosis can be defined as the spontaneous movement of solvent molecules through a semi-permeable membrane, from a low-concentration solution to a high-concentration solution.
• Osmosis is purely a mechanical process where cells absorb water without spending any amount of energy.

Additional Information

• Morphogenesis
• ​A biological process that causes a tissue or organ to develop its shape by controlling the spatial distribution of cells during embryonic development.
• Hybridisation
• ​A process of mathematically combining two or more atomic orbitals from the same atom to form a completely different orbital from its constituents is therefore called a hybrid orbital.
• Tropism
• ​The growth rate of plant parts in which the direction of stimulus determines the direction of response is called tropism.
• Example: Phototropism, where plant stems grow upward in response to sunlight.

The correct answer is Alaknanda.

Key Points

• Devprayag
• Devprayag is a town and a Nagar panchayat (municipality) in Tehri Garhwal district in the state of Uttarakhand, India.
• It is one of the Panch Prayag (five confluences) of the Alaknanda River where the Alaknanda and Bhagirathi rivers meet and take the name Ganga.
• According to mythology, there is another river related to this confluence named Saraswati, which originates from Mana village of Badrinath.

Additional Information

• Ghaghara
• ​Ghaghara River is a  tributary of Ganga River.
• This river originates in the Tibetan Plateau near Lake Mansarovar.
• Gandak
• Gandak River, also called Narayani River, river in central Nepal and northern India.
• It is formed by the union of the Kali and Trisuli rivers.
• Meghna
• ​The combined flow of the Ganga (the Padma in Bangladesh), the Barak river and the Jamuna river are known as Meghna in Bangladesh.

The correct answer is Purkinje.

Key Points

• The term 'Protoplasm' is given by Purkinje in 1839.
• It is the living Content of a Cell that is Surrounded by a Plasma Membrane.
• It is basically Composed of a Mixture of Small Molecules such as Nucleic Acids, Proteins, and Lipids

The correct answer is Kamaljeet Sandhu.

Key Points

• Kamaljeet Sandhu
• Kamaljeet Sandhu is a female Indian athlete who won a gold medal at the 1970 Bangkok Asian Games in the 400 m race. She ran the distance in 57.3 seconds.
• She was the first Indian woman athlete to win a gold medal at any Asian game.
• She is from Punjab state in India.
• She received the Padma Shri award in 1971.
• In 1971, she was one of the finalists in the World University Games held at Turin, Italy, in 400 meters race.
• She participated in the Women's 400 meters at the 1972 Munich Olympics, bowing out in the heats.
• She was also a national-level basketball and inter-varsity hockey player.
• She went to the 1982 Asian Games as the coach of the Indian women's sprint team.
• She is also an alumna of Scindia Kanya Vidyalaya.

Additional Information

• K. Malleswari
• ​Karnam Malleswari is a retired Indian weightlifter.
• She is the first Indian woman to win a medal at the Olympics.
• Malleswari won the world title in the 54 kg division in 1994 and 1995 and placed third in 1993 and 1996.
• Durba Banarjee
• ​Durba Banerjee was the first Indian woman commercial pilot.
• Durba Banerjee started her aviation career as a DC3 pilot flying a Dakota with the Air Survey of India.
• Arti Saha
• ​Arati Saha was an Indian swimmer who became the first Asian woman to swim across the English Channel on September 29, 1959.
• She was awarded Padma Shri in 1960.

The correct answer is Khizr Khan.

Key Points

• Jamat Khana Mosque
• The Jamat Khana Masjid or Khilji Mosque is the earliest mosque in Delhi.
• Built in 1315-1325 AD by Khizr Khan, son of Sultan Alauddin Khilji (Khilji dynasty).
• The mosque is the largest structure in the Nizamuddin Basti dargah enclosure (Nizam-ud-din Auliya shrine complex).
• Each of the three bays has a vaulted ceiling with the central one being the largest, as is customary.
• The central bay and entrance are decorated with exquisite geometric motifs and bands of Quranic inscriptions.

Additional Information

• Quṭb al-Din Mubarak Shah
• ​Qutb-ud-din Mubarak Shah Khilji was the son of Ala-ud-din Khilji.
• He is also known as Ikhtiyar al-Din
• Jalal-ud-din Firuz Khilji
• ​Jalal-ud-Din Khalji was the founder of the Khalji Dynasty. He came to power after the overthrow of the so-called Slave Dynasty.
• Ala-ud-din Khilji
• Alauddin Khalji was one of the most powerful rulers of the Khalji dynasty and became the Sultan of Delhi.
• Khizr Khan
• Khizr Khan is the former governor of Punjab who also ruled Delhi as a Sultanate and established the Sayyid dynasty as the fourth dynasty that ruled Delhi in 1414.

The correct answer is 395.

• As of January 2019, there were 395 articles in the Indian Constitution.

Key Points

• Currently, the constitution has a Preamble and 470 articles grouped into 25 parts.
• The constitution is the topmost law of India.
• It is a document that provides laws for political structures, powers, and duties of the government.
• It includes fundamental rights, directive principles, and duties of a citizen.
• India's constitution is the largest constitution in the world.
• It was adopted on 26 November 1949 by the Constituent Assembly of India and became effective on 26 January 1950.

The correct answer is The right mix of minerals and organic matter.

Key Points

• Soil fertility
• The right mix of minerals and organic matter makes the soil fertile.
• Soil fertility is the ability of soil to sustain plant growth by providing essential plant nutrients.
• Plant nutrients include the macronutrients nitrogen, phosphorus and potassium, sulfur, calcium and magnesium.
• The impacts of soil fertility are reflected in most of the Sustainable Development Goals, as they contain economic, social and environmental aspects.
• Nutrient sources include chemical and mineral fertilizers, organic fertilizers, such as livestock manures and composts, and sources of recycled nutrients.
• Some bacteria like rhizobium and blue-green algae are able to fix nitrogen gas from the atmosphere to enrich the soil with nitrogen compounds and increase its fertility.
• The nitrogen-fixing bacteria and blue-green algae are called biological nitrogen fixers.

Shortcut Trick

Leakage rate (L) = 1/6 of cistern per hour

Net rate with inlet (L − I) = 1/10 of cistern per hour

Inlet rate per hour = 1/6 − 1/10 = (5 − 3)/30 = 1/15 of cistern

Capacity = Inlet flow per hour × Time to fill = (10 × 60) × 15 = 9000 litres

∴ The correct answer is 9000 litres.

Alternate Method

Given: Leakage empties in 6 hours, Combined empties in 10 hours. Tap admits 10 litres/min.

Formula: Capacity = Inlet Efficiency × Total Units × Flow Rate

⇒ Efficiency of Tap (B) = (A + B) − A = −3 − (−5) = +2 units/hour

⇒ Time taken by Tap B to fill the cistern alone = 30 ÷ 2 = 15 hours

⇒ Inlet rate per hour = 10 litres/min × 60 min = 600 litres/hour

⇒ Capacity of cistern = 15 hours × 600 litres/hour = 9000 litres

∴ The correct answer is 9000 litres.

Additional Information

Pipes and Cisterns Logic

Inlet pipes have positive efficiency while leaks or outlet pipes have negative efficiency.

Capacity Calculation

Total Capacity = Rate of flow × Time taken to fill/empty. Always ensure time units (minutes/hours) are consistent.

Net Work Done

If a cistern is filled in x hours and emptied in y hours, the net work in 1 hour is (1/x − 1/y).

Shortcut TrickLet x = 5 and y = 2

Then, (8 x 5 - 9 x 2) : (14 x 5 - 13 x 2)

⇒ 22 : 44 = 1 : 2

 ∴ Required ratio is 1 : 2.

Alternate MethodGiven:

x : y = 5 : 2

Calculation:

Let x = 5a

and y = 2a

Then,

⇒ (8 x 5a - 9 x 2a) : (14 x 5a - 13 x 2a)

⇒ (40a - 18a) : (70a - 26a)

⇒ 22a : 44a

⇒ 1:2

∴ Required ratio is 1 : 2.

Shortcut Trick

Average speed = 2ab/(a + b)

Where a and b is speed

⇒ $(2 \times 60 \times 40) \over 60 + 40$ = 48 km/h

∴ Average speed is 48 km/h

Alternate MethodGiven:

Certain distance at a speed = 60 km/h 

Returns of same distance at a speed  = 40 km/h

Formula used:

Average speed = Total distance / Total time

Calculation:

Let distance = a km

⇒ Time = a/60 h

⇒ Time taken on return = a/40

⇒ Total distance = a + a = 2a

Total time taken = a/60 + a/40

⇒ (2a + 3a) / 120

⇒ 5a/120

⇒ a/24

Average speed = $2a \times 24\over a$ = 48 km/h

∴ Average speed is 48 km/h

Mistake PointsIf both direction cover same distance then use,

Average speed = 2ab/(a + b)

Where a and b is speed

Otherwise go with alternate solution.

Shortcut Trick

 8 x 110/100 : 7 x 120/100

⇒ 22 : 21

∴ New Ratio is 22 : 21.

Alternate MethodGiven:

Ration of girls and boys = 8 : 7.

Percentage increase of girls and boys respectively = 10% and 20%

Calculation:

Let numbers of girl = 8a

and numbers of boy = 7a

⇒ Numbers of girl after 10% increase = 8a x 110/100

⇒ 88a/10

⇒ Numbers of boy after 20% increase = 7a x 120/100

⇒ 84a/10

New ratio,

⇒ Girl : Boy = 88a/10 : 84a/10

⇒ Girl : Boy = 22 : 21

∴ New Ratio is 22 : 21.

Shortcut Trick

CP of mixture = (60 x 42 + 120 x 52)/ 60 + 120

⇒ 8760/180 = Rs. 48.66 per kg

⇒ SP on 20% profit = 48.66 x 120/100 = 58.40 per kg

∴ Required rate is 58.40 per kg.

Alternate MethodGiven:

A shopkeeper bought 60 kg of rice at ₹42 per kg

and120 kg rice at ₹52 per kg

Formula used:

Selling price at profit = Cost price x (100 + profit%)/100

Calculation:

Price of 60 kg rice = 60 x 42 = Rs. 2520

Price of 120 kg rice = 120 x 52 = Rs. 6240

Now mix the the both rice then

⇒ Price of mixture per kg = (2520 + 6240) / (60 + 120)

⇒ 8760/180 = Rs. 48.66 per kg

Selling price of per kg on 20% profit = 48.66 x (100 + 20)/100

⇒ 48.66 x 120/100

⇒ Rs. 58.40 per kg

∴ Required rate is 58.40 per kg.

Additional InformationProfit = Selling price - Cost price

Profit% = [(Selling price - Cost price) × 100] ÷ Cost price

Selling price at profit = Cost price x (100 + profit%)/100

Loss = Cost price - Selling price

Loss% = [(Cost price - Selling price) × 100] ÷ Cost price

Selling price at loss = Cost price x (100 - loss%)/100

Selling price at discount = Marked Price x (100 - discount%)/100

Shortcut Trick

 5/7 = 8800

⇒ 1 = 12320

CP = Rs. 12,320

SP = Rs. 8,800

⇒ Loss% = (12320 - 8800) x 100/ 12320 = 28$4 \over 7$%

∴ Loss % is 28$4 \over 7$%. 

Alternate MethodGiven:

Selling price = Rs. 8800

Formula used:

Loss = Cost price - Selling price

Loss% = [(Cost price - Selling price) × 100] ÷ Cost price

Calculation:

Let Cp = A

According to question,

A x 5/7 = 8800

⇒ A = 12,320

Now,

Loss = 12320 - 8800

⇒ Loss = 3520

⇒ Loss% = (12320 - 8800) x 100/ 12320 = 28$4 \over 7$%

∴ Loss % is 28$4 \over 7$%. 

Additional InformationProfit = Selling price - Cost price

Profit% = [(Selling price - Cost price) × 100] ÷ Cost price

Selling price at profit = Cost price x (100 + profit%)/100

Loss = Cost price - Selling price

Loss% = [(Cost price - Selling price) × 100] ÷ Cost price

Selling price at loss = Cost price x (100 - loss%)/100

Selling price at discount = Marked Price x (100 - discount%)/100

Shortcut Trick

Difference between CI and SI for 2 years = Principle x r²/(100)²

⇒ 225 = $P \times 15 \times 15 \over 100 \times 100$

⇒ P = Rs. 10000

∴ Sum is Rs. 10000.

Alternate MethodGiven:

Difference between CI and SI for 2 years = Rs. 225

Rate of interest (R) = 15% per annum

Time = 2 years

Formula used:

Simple interest = (P x R x T)/100, and

Compound Interest = [P (1 + R/100)^T- P]

Where P = Principle or Sum

R = Rate of interest per annum

T= Time

Calculation:

Let Sum = P

⇒ SI = P x 15 x 2/100 = 30P/100

⇒ CI = P (1 + 15/100)² - P

⇒  P (23/20)² - P

⇒  529P - 400P/400

⇒  129P/400

According to question,

Difference between CI and SI for 2 years:

⇒ 225 = ​​129P/400 - 30P/100​

⇒ 225 = (129P - 120P)/400

⇒ 225 = 9P/400

⇒ P = Rs. 10000

∴ Sum is Rs. 10000.

Given:

Two rope length = 8 m and 14 m

Calculation:

⇒ 8 = 2 x 2 x 2

⇒ 14 = 2 x 7

⇒ HCF (Highest Common Factor) of 8 and 14 = 2

∴ Maximum possible length of each piece is 2 m.

Given:

Capacity means volume of one hemisphere = 2.7 ltr

Capacity means volume of another hemisphere = 12.5 ltr

Formula used:

Volume of hemisphere = 2πr3/3

Curved surface are of hemisphere = 2πr2

Total surface area = 3πr2

1 liter = 1000 cm3

Calculation:

 $\frac{2}{3}$ x $\frac{22}{7}$ x r₁³ = 2.7 ltr x 1000 cm³ = 2700 

⇒ r₁³ = (675 x 21/11)

⇒ r1 = (675 x 21/11)1/3

Now 

⇒ $\frac{2}{3}$ x $\frac{22}{7}$ x r₂3 = 12.5 ltr x 1000 cm3 = 12500

⇒ r₂³ = (3125 x 21/11)

⇒ r2 = (3125 x 21/11)1/3

Required ratio,

⇒ r₁ : r₂ = (675 x 21/11)^1/3 : (3125 x 21/11)^1/3 = 3 : 5

Ratio of the area of the inner curved surface = 2πr₁2/2πr₂2

⇒ r12/r22

⇒ (3/5)² = 9 ∶ 25

∴ Required ratio is 9 : 25.

Shortcut Trick

Let first cp = 100

⇒ first sp on 12% profit = 112

Now new cp at 5% less = 95

⇒ new sp = 95 x 110/100 = 104.5

Difference between first sp and new sp = Rs. 180

⇒ 112 - 104.5 = 180 ⇒ 7.5 = 180 ⇒ 1 = 24

⇒ cp = 100 x 24 = Rs. 2400

∴ Cost price of the electric heater is Rs. 2400.

Alternate MethodConcept used:

SP on profit =  Cost price x (100 + profit%)/100

Selling price at loss = Cost price x (100 - loss%)/100

Calculation:

Let first cp = Rs. A

first sp on 12% profit = A x 112/100 = 112A/100

⇒ New cp  on 5% less = A x 95/100 = 95A/100

Now 10% profit on new cp , then 

⇒ New sp = $\frac{95A}{100}\times \frac{110}{100}$ = 1045a/1000

Difference between first sp and new sp = Rs. 180

⇒ $\frac{112A}{100} - \frac{1045A}{1000} = 180$

⇒ $\frac{11120A - 1045A}{1000} = 180$

⇒ $\frac{75A}{1000} =180$

⇒ A= Rs. 2400

∴ Cost price of the electric heater is Rs. 2400.

Additional InformationProfit = Selling price - Cost price

Profit% = [(Selling price - Cost price) × 100] ÷ Cost price

Selling price at profit = Cost price x (100 + profit%)/100

Loss = Cost price - Selling price

Loss% = [(Cost price - Selling price) × 100] ÷ Cost price

Selling price at loss = Cost price x (100 - loss%)/100

Selling price at discount = Cost price x (100 - discount%)/100

Shortcut Trick

⇒ (5 + 7 + 9 + 12 + 13 + t + 20)/7 = t

⇒ 66 + t = 7t

⇒ t = 11

∴ t is 11.

Alternate MethodGiven:

The numbers are 5, 7, 9, 12, 13, t, 20

Average of given numbers = t

Formula used:

Average = Sum of observation / No. of observation

Calculation:

Sum of numbers =  5 + 7 + 9 + 12 + 13 + t + 20

⇒ 66 + t

Number of observation = 7

According to question,

(66 + t)/7 = t

⇒ 7t - t = 66

⇒ 6t = 66

⇒ t =11

∴ t is 11.

Given:

$3 \over4$ ÷ $3 \over4$ of $\frac{3}{4}$ × $4 \over 3$ + $5 \over 2$ ÷ $2 \over 5$ of $5 \over 4$ - $2 \over 3$ - $2 \over 3$ of $5 \over 6$

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

$3 \over4$ ÷ $3 \over4$ x $\frac{3}{4}$ × $4 \over 3$ + $5 \over 2$ ÷ $2 \over 5$ x $5 \over 4$ - $2 \over 3$ - $2 \over 3$ x $5 \over 6$

⇒ $3 \over4$ ÷ $9 \over16$ x $4 \over 3$+ $5 \over 2$ ÷ $1 \over 2$ - $2 \over 3$ - $5 \over 9$

⇒ $3 \over4$ x $16 \over9$ x $4 \over 3$ + $5 \over 2$ x $2$ - $2 \over 3$ - $5 \over 9$

⇒ $16 \over 9$ + $5$ - $2 \over 3$ - $5 \over 9$

⇒ $\frac{16 +45 - 6 - 5}{9}$

⇒ $50 \over 9$

∴ Required answer is 50/9.

Shortcut Trick

If 3.5 = 210

⇒ 1 = 60

⇒ 4 = 4 x 60 = 240

Additional interest = 240 - 210 = Rs.30

∴ Additional interest in one year is Rs.30

Alternate MethodGiven:

Initial R = 3.5%

Initial interest = Rs. 210

New R = 4%

Formula used:

Simple Interest = (Principle × Rate per annum ×Time)/100

Calculation:

Let deposit = Rs. a 

⇒ 210 = (a x 3.5 x 1)/100

⇒ a = 6000

Now,

Simple interest on 4% = (6000 x 4 x 1)/100

⇒ 240

Additional interest = 240 - 210 = Rs. 30

∴ Additional interest  in one year is Rs. 30

Important Points Simple interest = (Principle x Rate per annum x Time)/100

Amount = Simple interest + Principle

Given:

Monthly income ratio of Ramu and Somu = 6 : 5

Ration of their expenditure = 7 : 6

Savings of Ramu and Somu = 1500 and 1000

Concept used:

Monthly income - expenditure = Savings 

Calculation:

Let Ramu's monthly income = 6a

⇒ Somu monthly income = 5a

According to question,

$6a - 1500 \over 5a - 1000$ = $7 \over 6$

⇒  $36a - 9000 = 35a - 7000$

⇒ a = 2000

Monthly income of Ramu = 6a

⇒ 6 x 2000 = Rs.12000 

∴ Monthly income of Ramu is Rs.12000.

Shortcut Trick 

$6x - 1500 \over 5x - 1000$ = $7 \over 6$

⇒  $36x - 9000 = 35x - 7000$

⇒ $x = 2000$

Monthly income of Ramu = 6 x 2000 =Rs.12000 

∴ Monthly income of Ramu is Rs.12000.

Shortcut Trick

Let total amount give on 5%, then SI for 1 year = 9300 x 5 x 1 /100 = 465

Again Let total amount give on 8%, then SI for 1 year = 9300 x 8 x 1/100 = 744

Total interest in 4 year = 2400

Interest for 1 year = 2400/4 = 600

Required Ratio = 144 : 135 = 16 : 15

∴ Required Ratio = 16 : 15.

Alternate MethodGiven:

Total principle = Rs. 9300

Interest at 4 years = Rs. 2400

Formula used:

Simple interest = (Principle x Rate per annum x Time)/100

Calculation:

Let money lent on 5% = a

⇒ Then money lent on 8% = 9300 - a

Interest on 4 year = 2400

⇒ then interest on 1 year = 2400/4

⇒ Rs. 600

According to question,

$\frac{a \times 5 \times 1}{100}$ + $\frac{(9300 - a) \times 8 \times 1}{100}$ = 600

⇒ $\frac{5a}{100}$ + $\frac{74400 - 8a}{100}$ = 600

⇒ $\frac{-3a + 74400}{100}$ = 600

⇒ - 3a + 74400 = 60000

⇒ 3a = 14400

⇒ a = 4800

Now money lent on 5% = a = 4800

⇒ Money lent on 8% = 9300 - 4800 = 4500

Required ratio = 4800 : 4500

∴ Required Ratio = 16 : 15.

Given:

$\rm {{{3 \over 4 } \ of \ 1 {3\over 5} -1× 5 + 2 } \over 24 - 6 +2} ÷ 4$

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

⇒ $\frac{\frac{3}{4} \times \frac{8}{5} - 5 + 2}{26 - 6} \div 4$​

⇒ $\frac{\frac{6}{5} - 3}{20} \div 4$

⇒ $\frac{6 - 15}{5\times 20} \div 4$

⇒ $\frac{-9}{100} \times \frac{1}{4}$

⇒ -9/400

Shortcut Trick

Product of numbers = HCF × LCM = 7 × 1729 = 12103.

Use algebraic identity: (Sum)² = (Difference)² + 4 × Product.

(Sum)² = 42² + 4 × 12103 = 1764 + 48412 = 50176.

Sum = √50176 = 224.

∴ The correct answer is 224.

Alternate Method

Given: HCF = 7, LCM = 1729, Difference = 42.

Formula Used: Product of numbers = HCF × LCM | Numbers = HCF × a, HCF × b (where a, b are co-prime).

⇒ Let the two numbers be 7a and 7b.

⇒ LCM = 7 × a × b = 1729

⇒ ab = 1729 ÷ 7 = 247

⇒ 7a − 7b = 42 ⇒ 7(a − b) = 42 ⇒ a − b = 6

⇒ (a + b)² = (a − b)² + 4ab = 6² + 4(247)

⇒ (a + b)² = 36 + 988 = 1024

⇒ a + b = √1024 = 32

⇒ Sum of numbers = 7(a + b) = 7 × 32 = 224

∴ The correct answer is 224.

Additional Information

Product Rule of HCF and LCM

For any two numbers x and y, the product of the numbers is always equal to the product of their HCF and LCM: x × y = HCF(x,y) × LCM(x,y).

HCF Multiplier Property

Any two numbers can be expressed as Ha and Hb, where H is the HCF and a, b are co-prime integers (GCD(a,b) = 1).

LCM Formula

The LCM of two numbers Ha and Hb is given by H × a × b.

Algebraic Identity for Sum

To find the sum given the difference and product: (x + y)² = (x − y)² + 4xy.

Shortcut Trick

2πrh : 4πr²

⇒ rh : 2r²

⇒ 10 x 15 : 2 x 5²

⇒ 3 : 1 

∴ Required ratio is 3 : 1.

Alternate Method

Given:

Radius of cylinder = 10 cm

Height of cylinder = 15 cm

Radius of sphere = 5 cm

Formula used:

Curved surface area of cylinder = 2πrh

Surface area of sphere = 4πr²

Calculation:

According to question,

⇒ 2πrh : 4πr2

⇒ rh : 2r2

⇒ 10 x 15 : 2 x 52

⇒ 3 : 1 

∴ Required ratio is 3 : 1.

Additional Information

Volume of cylinder = πr²h

Curved surface area of cylinder = 2πrh

Total surface are of cylinder = 2πr (h + r)

Volume of sphere = 4/3 πr³

Surface area of sphere = 4πr2

Shortcut Trick

 Trick = (Increase% x 100) ÷ (100 +  Increase%)

⇒ (33 x 100) ÷ (100 + 33)

⇒ $\frac{33 × 100}{133}$ = 24.8%

∴ Required % is 24.8%.

Alternate Method - 1Given:

Price of sugar rises = 33%.

Concept used:

​Selling price at profit = Cost price x (100 + profit%)/100

Calculation:

Let initial price of sugar = 100

⇒ Initial consumption = 100

⇒ Total expenditure = price x consumption

⇒ 100 x 100 = 10000

Now new price of sugar after increase of 33% = 100 + 33 = 133

But new expenditure is remain same = 10000

⇒ New consumption = expenditure ÷  new price

⇒ New consumption = 10000/133

⇒ % Decrease in consumption = 100 - 10000/133 = 3300/133

∴ % Decrease in consumption is 24.8.

Alternate Method - 2 Given:

Price of sugar rises = 33%.

Concept used:

Selling price at profit = Cost price x (100 + profit%)/100

Calculation:

Let initial price of sugar = Rs, A

⇒ Initial consumption = B

⇒ Total expenditure = price x consumption

⇒ Total expenditure = A x B = AB

Now new price of sugar after increase of 33% = A x (100 + 33) /100

⇒ 133A/100

⇒ New expenditure is remain same = AB

⇒ New consumption = expenditure ÷ new price

⇒ New consumption = $\frac{AB × 100}{133A}$ = 100B/133

⇒ Decrease in consumption = B - 100B/133

⇒ 33B/133

⇒ % Decrease in consumption = $\frac{33B \times 100}{133 \times B}$ = 24.8

∴ % Decrease in consumption is 24.8.

Important PointsProfit = Selling price - Cost price

Profit% = [(Selling price - Cost price) × 100] ÷ Cost price

Selling price at profit = Cost price x (100 + profit%)/100

Loss = Cost price - Selling price

Loss% = [(Cost price - Selling price) × 100] ÷ Cost price

Selling price at loss = Cost price x (100 - loss%)/100

Selling price at discount = Cost price x (100 - discount%)/100

Shortcut Trick

First Successive discount = 45%, 3%, 2%

Price after discount = 15000 x 0.55 x 0.97 x 0.98 = 7842.45

Discount = 15000 - 7842.45 = 7157.55

Second Successive discount = 25%, 12%, 13%

Price after discount  = 15000 x 0.75 x 0.88 x 0.87 = 8613

Discount = 15000 - 8613 = 6387

If choose first successive discount then money-saving = 7157.55 - 6387 = Rs. 770.55 

∴ Required saving money is Rs. 770.55 

Alternate MethodGiven:

First Successive discount = 45%, 3%, 2%

Second Successive discount = 25%, 12%, 13%

Price of article = Rs. 15000

Formula used:

Selling price at discount = Marked Price x (100 - discount%)/100

Calculation:

Price after first Successive discount discount = (15000 x 55 x 97 x 98)/ 100 x 100 x 100

⇒ 15000 x 0.55 x 0.97 x 0.98 = 7842.45

Discount = 15000 - 7842.45 = 7157.55

Now,

Price after second Successive discount discount = (15000 x 75 x 88 x 87)/ 100 x 100 x 100

⇒ 15000 x 0.75 x 0.88 x 0.87 = 8613

⇒ Discount = 15000 - 8613 = 6387

If choose first successive discount then money-saving = 7157.55 - 6387 = Rs. 770.55 

∴ Required saving money is Rs. 770.55 

Additional InformationProfit = Selling price - Cost price

Profit% = [(Selling price - Cost price) × 100] ÷ Cost price

Selling price at profit = Cost price x (100 + profit%)/100

Loss = Cost price - Selling price

Loss% = [(Cost price - Selling price) × 100] ÷ Cost price

Selling price at loss = Cost price x (100 - loss%)/100

Shortcut Trick 80% = 4/5

here, 55 representing 20% means 1/5 part.

⇒ 4/5 parts = 4 × 55 = 220

∴ four-fifths of the original number is 220.

Alternate Method

Calculation:

Let original number = a

According to question,

⇒ a - 55 = a x 80/100

⇒ a - 4a/5 = 55

⇒ a = 275

Now, 

275 x 4/5 = 220

∴ four-fifth of the original number is 220.

Shortcut Trick

If successive discount a% and b%

equivalent discount = a + b - ab/100

⇒ 50 + 30 - 50 x 30/100 = 65%

⇒ 65 + 20 - 65 x 20/100 = 72%

∴ Equivalent discount is 72%

Alternate MethodGiven:

Successive discount = 50%, 30% and 20%

Concept used:

If successive discount a% and b%

equivalent discount = a + b - ab/100

Calculation:

Let total value = 100

First discount 50% = 100 x 50/100 = 50

⇒ Remaining = 100 - 50 = 50

Second discount 30% on remaining 50 = 50 x 30/100 = 15

⇒ Remaining = 50 - 15 = 35 

Third discount 20% on remaining 35 = 35 x 20/100 = 7

⇒ Total discount = 50 + 15 + 7 = 72%

∴ Equivalent discount is 72%

Key PointsSuccessive discount means discount on the discount. (just like Compound Interest rate= interest on interest)

If the first discount is a% and 2^nd discount is b% then,

Total discount = (a + b - ab/100) %

Shortcut Trick

For A,

2/3 = 10 ⇒ 1 = 15 days 

A can complete total work = 15 days

For B,

4/5 = 8 ⇒ 1 = 10 days

B can complete total work = 10 days

(A + B) can do work together 5 days = 5 (2 + 3) = 25 

Remaining work = 30 - 25 = 5 

Now For C, 6 days = 5

Efficiency of C ⇒ 1 days = 5/6

C can done 75% of total work = $\frac{30 \times 75}{100} \div \frac{5}{6}$ = $\frac{45}{2} \times \frac{6}{5}$ = 27

∴ C can done 75% of total work in 27 days.

Alternate MethodGiven:

A can complete $2 \over 3$ of a work = 10 days

B can complete $4 \over 5$ of the same work in 8 days

They work together for 5 days

Concept used:

Efficiency of men = Total work / Total days

Calculation:

For A can complete 2/3 work  = 10

⇒ A can complete total work = 15 days

⇒ A can done work in 1 day = 1/15

For B can complete 4/5 work = 8

⇒ B can complete total work = 10 days

⇒ B can done work in 1 day = 1/10

⇒ (A + B) work done in 5 days = 5 x (1/15 + 1/10) 

⇒ 25/30

Here total work is LCM of 15 and 10 = 30

⇒ (A + B) work done in 5 days = 25

⇒ Remaining work = 30 - 25 = 5

Now C can do remaining work 5 = 6 days 

⇒ Efficiency of C = 5/6

⇒ C can done 75% of total work = $\frac{30 \times 75}{100} \div \frac{5}{6}$ = $\frac{45}{2} \times \frac{6}{5}$ = 27

∴ C can done 75% of total work in 27 days.

Shortcut Trick

Difference of wrong measurements = 61 - 46 = 15 cm

⇒ Mean variation = 15 ÷ 15 = 1 cm

⇒ New mean = 50 + 1 = 51 cm

∴ Correct mean is 51 cm.

Alternate MethodGiven:

Total measurements = 15

Initial mean = 50 cm

Formula used:

Average / Mean = Sum of observation / Number of observation

Sum of observation = Average x number of observation 

Mean variation = Difference ÷ Total measurements

Calculation:

Sum of observation 15 x 50 =750 cm

Difference of wrong measurements = 61 - 46 = 15 cm

New sum of observation = 750 + 15 = 765

Correct mean = 765/15

⇒ 51 cm

∴ Correct mean is 51 cm.

Mistake Points

If mistaken observation is less than real observation than mean variation = (real observation - mistaken observation)/ Total number of observation and in this condition correct mean is always higher than incorrect mean.

If mistaken observation is more than real observation than mean variation = (mistaken observation - real observation)/ Total number of observation and in this condition correct mean is always less than incorrect mean.