SSC GD Constable Previous Year Paper (Held on: 22nd November 2021 Shift 1)

Logic:

Row wise:

(first number ÷ 2) + Third number × 3 = Second number

Row 1 : 34, 38, 7

(34 ÷ 2) + 7 × 3 = 17 + 21 = 38

Row 2 : 46, 38, 5

(46 ÷ 2) + 5 × 3 = 23 + 15 = 38 

Row 3 : 84, ?, 15

(84 ÷ 2) + 15 × 3 = 42 + 45 = 87

Hence, the correct answer is "87".

Alternate Method The logic followed here is :-

Row 1 : 34, 38, 7

Row 2 : 46, 38, 5

Row 3 : 84, ?, 15

Hence, the correct answer is "87".

The number from among the given options that can replace the question mark (?) in the following series is as shown below :-

Hence, the correct answer is "262".

Alternate Method 

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Hence, the correct answer is "262".

The figure from among the given options that can replace the question mark (?) in the following series is as shown below :

• First position line with a symbol rotates 180⁰ and moves to fourth position from figure to figure.
• Second position line moves to first position, Third position line moves to second position, Fourth position lines moves to third position from figure to figure.

Hence, the correct answer is "Option 4".

The logic followed here is :-

Hence, the correct answer is "BYC".

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

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

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

In the given figure, Opposite faces are :

 

∴ Here, the pair of letters which are not opposite are 'O and M'.

Hence, the correct answer is "O and M".

The logic followed here is :-

'RAJU' is written as 'WFOZ'

and

'SITA' is written as 'XNYF'.

Similarly,

'MONU' will be written as :

Hence, the correct answer is "RTSZ".

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

Conclusions:

I. All enzymes are carbohydrates → True (As, All enzymes are vitamins and All vitamins are carbohydrates so, All enzymes are carbohydrates is True)

Il. No enzyme is a carbohydrate → False (As, All enzymes are vitamins and All vitamins are carbohydrates so, No enzyme is a carbohydrate is False)

∴ Here, Only conclusion I follows from given statements and Venn diagram.

Hence, the correct answer is "Only conclusion I follows".

The logic followed here is :-

Five friends, Bhumika, Rashi, Shweta, Vibha and Arunima, are sitting in a row facing east.

Bhumika is sitting between Vibha and Shweta and Rashi is second to the left of Shweta is as shown below :

∴ Here, 'Vibha' is sitting in south end.

Hence, the correct answer is "Vibha".

The logic followed here is :-

DKLH : GPSQ

Similarly,

FRLP : ?

Hence, the correct answer is "IWSY".

After unfolding the paper the figure that formed is as shown below :

Hence, the correct answer is "Option 1".

Confusion Points Option 1 and 2 both are different images.

Option 1: 

Option 2:

The logic followed here is :-

Sound of Bee is called "Buzz".

Similarly,

Sound of Hen is called "Cluck".

Hence, the correct answer is "Cluck".

By using BODMAS RULE :

1) + and ÷

Given equation is : 5 - 24 + 17 × 16 ÷ 4 = 133

After interchanging the signs the equation formed is as follows : 

⇒ 5 - 24 ÷ 17 × 16 + 4 = 133

⇒ 5 - 1.4117 × 16 + 4 = 133

⇒ 5 - 22.588 + 4 = 133

⇒ 9 - 22.588 = 133

⇒ - 13.588 ≠ 133

LHS ≠ RHS

2) × and -

Given equation is : 5 - 24 + 17 × 16 ÷ 4 = 133

After interchanging the signs the equation formed is as follows : 

⇒ 5 × 24 + 17 - 16 ÷ 4 = 133

⇒ 5 × 24 + 17 - 4 = 133

⇒ 120 + 17 - 4 = 133

⇒ 137 - 4 = 133

⇒ 133 = 133

LHS = RHS

3) × and ÷

Given equation is : 5 - 24 + 17 × 16 ÷ 4 = 133

After interchanging the signs the equation formed is as follows : 

⇒ 5 - 24 + 17 ÷ 16 × 4 = 133

⇒ 5 - 24 + 1.0625 × 4 = 133

⇒ 5 - 24 + 4.25 = 133

⇒ 9.25 - 24 = 133

⇒ - 14.75 ≠ 133

LHS ≠ RHS

4) + and ×

Given equation is : 5 - 24 + 17 × 16 ÷ 4 = 133

After interchanging the signs the equation formed is as follows : 

⇒ 5 - 24 × 17 + 16 ÷ 4 = 133

⇒ 5 - 24 × 17 + 4 = 133

⇒ 5 - 408 + 4 = 133

⇒ 9 - 408 = 133

⇒ - 399 ≠ 133

LHS ≠ RHS

Hence, the correct answer is Option 2: "× and -".

Given fruit shop consists of two types of fruits i.e., Oranges and Mangoes

The number of oranges is three times the number of mangoes :

⇒ oranges = 3 × mangoes

⇒ oranges/mangoes = 3/1

Total ration of oranges and mangoes = 3 + 1 = 4

Total number of fruits = oranges + mangoes

Total number of fruits = 3 × mangoes + mangoes

Total number of fruits = 4 × mangoes

1. Consider total number of fruits = 44

⇒ 44 = 4 × mangoes

⇒ mangoes = 11

⇒ oranges = 3 × mangoes = 3 × 11 = 33

2. Consider total number of fruits = 42

⇒ 42 = 4 × mangoes

42 is not divisible by 4 so, 42 cannot the total number of fruits in the shop.

3) Consider total number of fruits = 48

⇒ 48 = 4 × mangoes

⇒ mangoes = 12

⇒ oranges = 3 × mangoes = 3 × 12 = 36

4) Consider total number of fruits = 40

⇒ 40 = 4 × mangoes

⇒ mangoes = 10

⇒ oranges = 3 × mangoes = 3 × 10 = 30

∴ Here, 'Total number of fruits in shop cannot be 42'.

Hence, the correct answer is "42".

The arrangement of the given words in the order in which they appear in an English dictionary is as shown below :

The first two letters "D, U" is common in all words so we can start from third letter.

3. Dubious
4. Durable
5. Dustbin
6. Duster
7. Duty

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

The Venn diagram for the given is representation is as shown below ;

The region which represents tall boys with black eyes but NOT brown hair is letter 'C' has been darken.

∴ Here, tall boys with black eyes but NOT brown hair represents letter 'C' in the region.

Hence, the correct answer is "C".

The logic followed here is :-

1) BEHK

2) HLOR

3) PSVY

4) KNQT

∴ Here, 'HLOR' is different from other three alternatives.

Hence, the correct answer is "HLOR".

The logic followed here is :-

First number = (Second number × 2)²

• 64 : 4 → (4 × 2)² = 8² = 64
• 100 : 5 → (5 × 2)² = 10² = 100

Similarly, 

• ? : 6 → (6 × 2)2 = 122 = 144

Hence, the correct answer is "144".

Eight friends, P, Q, R, S, T, U, V and W, are watching a movie sitting in a line.

1) T is sitting at one of the corners.

Case (i) :

Case (ii) :

2) W is sitting to the immediate right of T.

3) Q is sitting between W and R.

4) R is sitting to the immediate left of P.

5) There are two persons between P and U.

6) V is sitting between S and U.

∴ Here, 'U' is sitting on other corner in line.

Hence, the correct answer is "U".

The logic followed here is :-

Hence, the correct answer is "234".

Given :- N _ K _ T N O K _ T _ _ _ D T

By checking options and substituting accordingly.

1) O D D N O K → N O K D T - N O K D T - N O K D T

   ♦ Here N O K D T is repeated.

2) K D D N O K → N K K D T - N O K D T - N O K D T

3) O D K N O K → N O K D T - N O K K T - N O K D T

4) O N D N O K → N O K N T - N O K D T - N O K D T

   ♦ Option (1) gives a pattern of : N O K D T - N O K D T - N O K D T.

Hence, the correct answer is "O D D N O K".

The mirror image of given combination when the mirror is placed at 'XY' is as shown below :

• The line XY is the mirror.
• The given word "AHKRQP" ends with letter 'P'. So the mirror image will start with "

" ⇒ Option 1 is eliminated.

• The given word "AHKRQP" has third last letter 'R'. So the mirror image should be "

" ⇒ Option 2 and 4 are eliminated.

Hence, the correct answer is "Option 3".

The logic followed here is :-

'LEMON' is written as 'ELMNO'.

Similarly,

'CLUSTER' will be written as :

Hence, the correct answer is "CELRSTU".

Family Chart :

1) P is the sister of R.

2) N is the father of P.

3) N does not have any married daughter.

4) M is the only son of Q and R.

5) S is the paternal grandmother of M.

∴ Here, M is 'grandson' of N.

Hence, the correct answer is "Grandson".

The logic followed here is :-

Number of letters in word × 2

'DICTIONARY' is coded as '20'

Number of letters in word DICTIONARY = 10

Code = 10 × 2 = 20

and

'MOBILITY' is coded as '16'

Number of letters in word MOBILITY = 8

Code = 8 × 2 = 16

Similarly,

'TERMINATION' will be coded as :

Number of letters in word TERMINATION = 11

Code = 11 × 2 = 22

Hence, the correct answer is "22".

The image which is embedded in given figure is as shown below :

Hence, the correct answer is "Option 2".

The correct answer is Italy.

Key Points

• The 16th G20 Summit in October 2021 was hosted by Italy in the city of Rome.
• The summit focussed on three broad, interconnected pillars of action: People, Planet, and Prosperity.
• Prime Minister Narendra Modi took part in the summit.
• ​​At the summit, the leaders committed to the **key Paris Agreement goal of limiting global warming to 1.5 degrees Celsius above pre-industrial levels.**​

Additional Information

• The G20 Summit of 2022 and 2023 will be hosted by Indonesia and India respectively.
• The G20 is a strategic multilateral platform connecting the world's major developed and emerging economies which holds a strategic role in securing future global economic growth and prosperity.
• It consists of 19 countries and European Union.
• It was established in 1999 and headquartered in Mexico.
• Joko Widodo is the current chairman of the G20.
• Argentina, Australia, Brazil, Canada, China, France, Germany, India, Indonesia, Italy, Japan, Republic of Korea, Mexico, Russia, Saudi Arabia, South Africa, Turkey, the United Kingdom, the United States, and the European Union are the members of G20.

Important Points

• 2023
• India hosted the 2023 G20 summit, with the theme "One Earth, One Family, One Future". The summit was chaired by Indian Prime Minister Narendra Modi, and India's presidency began on December 1, 2022. India's priorities included green development, climate finance, and accelerated growth.
• 2024
• Brazil will host the 2024 G20 summit, with the presidency beginning on December 1, 2023 and ending on November 30, 2024. The summit will be held in Rio de Janeiro.

The correct answer is Mudumalai Tiger Reserve.

Key Points

• Mudumalai Tiger Reserve is among the Tiger Reserves which was granted the  'Conservation Assured Tiger Standards' status in July 2021.
• Total of 14 tiger reserves in India had received the 'Conservation Assured Tiger Standards' status.
• The accreditation was given on the occasion of International Tigers day 29 July 2021.
• The Baghrakshaks were recognized for their **remarkable efforts in saving tigers.**​

Additional Information

• Conservation Assured | Tiger Standards (CA|TS) is a global association of Tiger Range countries, which provides entrustment after the assessment of tiger conservation of facilities all over the world.
• It also sets the standards to encourage and guide tiger conservation.
• India has now 53 Tiger Reserves expanded in 18 States.
• The 14 tiger reserves which received Conservation Assured Tiger Standards' status are

1. ​Manas Tiger Reserve,
2. Kaziranga Tiger Reserve
3. Orang Tiger Reserve
4. Satpura Tiger Reserve
5. Kanha Tiger Reserve
6. Panna Tiger Reserve
7. Pench Tiger Reserve
8. Valmiki Tiger Reserve
9. Dudhwa Tiger Reserve
10. Parambikulam Tiger Reserve
11. Mudumalai Tiger Reserve
12. Anamalai Tiger Reserve
13. Bandipur Tiger Reserve
14. Sundarbans Tiger Reserve

The correct answer is May 2020.

Key Points

• The cyclone Amphan hit India on 20 May 2020 in West Bengal.
• The highest speed of wind in the storm was 175 kmph.
• It was the first tropical cyclone of such intensity rose in Bay Bengal.
• The storm adversely affected the coastal districts of Odisha and West Bengal in India and Bangladesh.

Additional Information

• It was estimated that it caused damage of around 13 Billion US dollars.
• Around 85 deaths were reported in eastern India and Bangladesh.
• The name Amphan to the cyclone was given by the country Thailand.

The correct answer is 155.

Key Points

• Under article 155 of the Indian Constitution of India, the Governor of a State shall be appointed by the President by warrant under his hand and seal.

Additional Information

• The below table shows important articles:

The correct answer is 1925.

Key Points

• The Communist Party of India(CPI) was formed in Kanpur on 26 December 1925.
• S. V. Ghate was the first Secretary of CPI.
• The main participants who contributed to the formation of the party were workers, students, peasants and intellectuals.
• CPI is the oldest communist party in India.

Additional Information

• The Communist conference in which CPI was formed was held at Kanpur in the same location at which the congress session was held.
• The Communist Conference was convened by Satya Bhakt.
• CPI worked in close association with Indian National Congress.
• Many small political groups like the Labour Kisan Party of Hindustan (LKPH) merged with CPI.
• On 6 February 1926 at the conference in Krishnanagar the name of the party changed to Workers and Peasants Party of Bengal.

The correct answer is  Kalibangan 

Key Points

• The marks of furrows were discovered in the Kalibangan site of Indus valley currently Rajasthan.
• This shows that the fields were ploughed during Harappan Civilization.
• A wooden furrow was found on that site.
• Harappan seals, unknown scripts, stamps, human skeletons, copper bangles, coins, beads, toys, terracotta and shells were also found at the Harappa site while excavation.

Additional Information

• Lothal is one of the southernmost sites of the ancient Indus valley civilization.
• It was a small Harappan site found in Gujrat near the Gulf Of Khambat.
• It was first excavated in 1957 by S R Rao.
• Dholavira- The site of the Indus valley civilisation is considered to be the second largest Harappan site in India and the fifth largest in the Indian subcontinent.
• Bhansali- It was the Harappan site currently located in Fatehabad district Haryana. Beads of semi-precious stones, terracotta, steatite and bangles of clay, shell, faience and copper are some of the findings on this site.
  

The correct answer is 2005.

Key Points

• The Hindu Succession Act of 1956 was amended to give equal rights to fathers' property to daughters in the year 2005.
• Section 6 of the Hindu Succession Act of 1956 which deals with the participant's right in acquiring the property of a Hindu Undivided family was amended in 2005.
• After this amendment daughters were given equal rights as sons in the distribution of HUF property.
• The amendment was implemented on 9 September 2005.

Additional Information

• The Hindu Succession Act is applicable to Hindus, Jains, Sikhs and Buddhists.
• This act uses the concept of HUF Hindu Undivided Family which means a family which have common ancestors.
• The HUF was further divided into Members and Coparceners(person having right on property)
• Before the amendment,  only sons were considered Coparceners.

The correct answer is Nepal.

Key Points

• South Asian Football Federation(SAFF) Women's championship 2019 was held in the Biratnagar district of  Nepal.
• India became the winner of the event after defeating Nepal by 3-1.
• SAFF Women's championship is played after every 2 years.
• This championship started **in 2010 and India has won all the titles till 2019.**​

Additional Information

• South Asian Football Federation(SAFF) is an association of football-playing countries in South Asia which was founded in 1997.
• Its headquarters are located in Dhaka (Bangladesh).
• Bangladesh, Bhutan, India, Maldives, Nepal, Pakistan and Sri Lanka are member countries of SAFF.
• Kazi Salahuddin is the current president of SAFF.
• The next South Asian Football Federation(SAFF) Women's championship will be held in 2022 in Nepal.
• Loitongbam Ashalata Devi is the captain of the Indian National women's football team.

The correct answer is piece of cork.

Key Points

• The Cell was discovered by Robert Hooke in 1665 by observing a piece of cork under a microscope.
• In his observation, he saw tiny boxlike cavities termed Cells.
• He described his detailed observation in his book Micrographia as an exploration of a tiny unseen world.
• His discovery opened a new dimension of knowledge and exploration to the smallest unit of life The Cell.

Additional Information

• The Cell is the fundamental structural and functional unit of all living organisms.
• After Robert Hooke a dutch scientist Antonie van Leeuwenhoek discoverd other hidden microorganisms Bacteria and Protozoa.
• The classical cell theory was given by Theodor Schwann in 1839 and had three parts.
• ​All living organisms are made up of cells.
• Cells are basic units of life.
• Cells come from pre-existing cells

The correct answer is Bites by stray animals.

Key Points

• Bites by stray animals do not cause food and water contamination,
• Food and water contamination infects them with toxins and harmful chemicals which cause severe diseases such as diarrhoea, dysentery, and food poisoning.
• Food contamination results in the development of bacteria, parasites, and other micro-organisms which enter our body and disturb our metabolism and other functioning.
• Chemical contamination of food and water can even lead to **acute poisoning or long-term diseases, such as cancer.**​

Additional Information

• Chemical runoff from factories ultimately drains out into our water bodies which are the major source of water for man, the waste from factories contaminates our water bodies which affect human as well as animal life.
• Incorrect food storage leads to the spoilage of food at a faster rate.
• Infectious organisms in the atmosphere occur because of different types of pollution like emission of toxic gases, usage of chemical fertilizers etc it directly or indirectly affects our natural resources like contamination of water bodies, fertility of the soil, these adverse effects results in contamination of food and water at different levels.

The correct answer is Chholiya.

Key Points

• Choliya is a sword dance meant to depict the martial art tradition of the Kumaoni tribe in Uttarakhand.
• It is a very old tradition mainly practised in Rajput weddings and other meets.
• Along with swords and shields, the dancers were dressed like Kumaon warriors.
• The dancer carries regional brass instruments like Turi or Ransing.

Additional Information

• Gair- Folk dance of Rajasthan performed by Bhil community.
• Kachchhi Ghodi- Folk dance originated in the Shekhawati region of Rajasthan. A special costume of the horse is worn by the dancers.
• Chari- It is a kind of female group dance of Rajasthan, females perform this dance by putting a water container. This dance describes the art of collecting water.
• This dance is mainly common in Kishangarh and Ajmer regions.

The correct answer is Kesari.

Key Points

• Kesari newspaper published in the Marathi language is one of the strongest critics of British rule.
• Kesari was founded by nationalist leader Lokmanya Bal Gangadhar Tilak on 4 Januray 1881.
• The newspaper was actively used as the voice of the Indian National freedom movement.
• In 1897 Bal Gangadhar Tilak was charged by the British government for **his critical views in the newspaper against the government. **​

Additional Information

• Lokmanya B. G. Tilak started two newspapers Kesari in Marathi language and Maratha in English language.
• Many prominent freedom fighters became editors of these newspapers, like Vishnushastri Chiplunkar, and Gopal Ganesh Agarkar.
• Amrita Bazar Patrika was started by Sisir Ghosh and Moti Lal Ghosh in 1868.
• The Tribune is an Indian English-language daily newspaper founded in 1881 by Sardar Dyal Singh.
• The Hindu is an English daily newspaper founded by G Subramanyam Iyer in 1878.

The correct answer is Mutation.

Key Points

• The process of change in the base pair sequence of an organism is called Mutation.
• Mutation refers to the abnormality in the genetic sequence of an organism.
• The mutation results in an alteration In the composition of DNA.
• It leads to variation in the normal characteristics of an organism, these variations can have negative or positive effects on the organism.
• It is a heritable change and can also affect the offspring.
• Geneticist Hugo de Vries coined the term Mutation in 1901

Additional Information

• Decantation- The process of removing liquid components from a mixture having solid or other immiscible substances.
• Pollination- Process or transfer of pollen grains from anther to stigma.
• Ionisation- Process by which any atom acquires positive or negative charge by gaining or losing of electrons.

The correct answer is The cervical vertebral maturation method.

Key Points

• The cervical vertebral maturation method (CVM) method is used to track the growth of skeletal maturation at a particular point in time.
• Along with evolving technology, various methods of age calculation have been developed using different elements and visualization techniques like ultrasound, x-ray etc.
• Bone age assessment based on hand and wrist radiographs is one of the most preferred techniques of getting information about bone age.
• Various methods have been developed now days to compute bone age scores from radiographs by comparing the maturity of hand & wrist bones.
• Some of them are  Greulich & Pyle (GP) Atlas,  Tanner Whitehouse (TW2) Method,  The Gilsanz & Ratibin (GR) Atlas, Automatic Skeletal Bone Age Assessment etc.​​

Additional Information

• The Greulich-Pyle method- It is an integrated method based on “The Radiographic Atlas of Skeletal Development of the Hand and Wrist”, by Dr William Walter Greulich and Dr Sarah Idell Pyle, which was last published in 1959, but still one of the most commonly used atlas for bone age measurement by radiologists in western countries.
• The Tanner-Whitehouse method- The Tanner-Whitehouse II method is a bone-specific scoring technique in which a numerical score is assigned to selected hand-wrist bones depending on the appearance of certain well-defined maturity indicators.
• The FELS method of assessing the skeletal maturity of the hand wrist involves the provision of a range of shapes to which maturity indicator grades which can be assigned and in the statistical methods used to construct the scale of skeletal maturity.

The correct answer is Subarnarekha

Key Points

• The Hundru falls located in Ranchi are formed by the river Subernrekha.
• It falls from a height of 320 feet and forms one of the highest waterfalls of state Jharkhand.
• It is located at 45km distance from the main city of Ranchi.
• Hundru falls has great tourist significance due to its scenic beauty
• Its base forms a pool which is a famous picnic spot.
• The city of Jamshedpur having the TATA industry is situated on the bank of river Subarnarekha.

Additional Information

• Umngot River- It is also known by the name of Dawki River which flows through Dawki town at the bottom of the West Jaintia Hills district in the Indian state of Meghalaya.
• Tsangpo- The river Brahmaputra is called with the name the Yarlung Tsangpo when it enters Tibet. It originates from the Kailash range of the Himalayas.
• Teesta- Teesta River at rises from Pauhunri Mountain of eastern Himalayas and flows from Sikkim and West Bengal and enters the Bay of Bengal after passing through neighbouring country Bangladesh.

The correct answer is Abdul Rahim Khan-i-Khanan.

Key Points

• Abdul Rahim Khan-i-Khanan court poet of Mughal emperor Akbar was an eminent scholar of Sanskrit, Hindi and Rajasthani alongside Persian, Arabic and Turki.
• He was one of the nine important rank holders of Navratnas from the court of Mughal emperor Akbar.
• He was the son of Bairam Khan mentor and guardian of Akbar.
• He translated Baburnama into Persian and also wrote two astrology books in  Sanskrit named **Khetakautukam, and Dwatrimshadyogavali.**​

Additional Information

• Akbar was the third Mughal ruler of India.
• Birbal was one of the top rank ministers of the court of Mughal emperor Akbar, he was part of Navratna.
• Ras Khan whose previous name was Syed Ibrahim Khan was a Sufi Muslim poet but later became the devotee of Hindu God Lord Krishna.
• Akbar was the third Mughal ruler of India.

The current answer is URL.

Key Points

• URL is NOT a service provided to its clients by banks in India.
• URL stands for Uniform Resource Locator it is a kind of link or unique address which specifies the location of a file or data present on the web.
• In simple language, URL is the address which we enter in our web browser to go to a particular site like www.testbook.com.
• NEFT, RTGS, IMPS, ECS, and Credit Cards are some of the services provided by the banks to the customers.​

Additional Information

• NEFT- Stands for National Electronic Funds Transfer and is a kind of electronic fund transfer service provided by banks to customers to transfer their money all over the country. It was first started in November 2005.
• RTGS-  Real-time gross settlement is a special type of funds transfer system which enables the transfer of money or securities between one bank to any other bank on a real-time and gross basis. Large funds transfers take place under this service. The minimum limit for this service is 2 lakh rupees.
• ECS- which stands for Electronic Clearance Service is a mode of payment which is used in the type of transactions that are repetitive in nature for example salary, pension, premium, and dividend.

The correct answer is Akkitham Achuthan Namboothiri.

Key Points

• Akkitham Achuthan Namboothiri got the Jnanpith award in 2019.
• He got the award for his outstanding contribution to the field of Malayalam literature.
• He was a well-known poet and essayist, known for his plain and crystal clear way of writing.
• Some of his prominent works are **Irupatham Noottandinte Ithihasam, , Balidarshanam, and Nimisha Kshetram.**​

Additional Information

• He received many prestigious awards like Padma Shri, Ezhuthachan Award, Kendra Sahitya Akademi Award, Kerala Sahitya Akademi Award for Poetry, and Odakkuzhal Award, Vallathol Award.
• He was born on 18 March 1926 at Amettikkara, near the Palakkad district of Kerala.
• Jnanpith Award is the highest and oldest honour of India given for outstanding contribution in the field of literature.
• It was first awarded in 1925.
• Assamese poet Nilamani Phookan was conferred the 56th Jnanpith Award 2022.

The correct answer is Sumit Sangwan.

Key Points

• Sumit Sangwan won a bronze medal in the 81 kg category.
• Alexis Valentine International Boxing Tournament was the first sports event to be held after the lockdown.
• Amit Panghal(52 kg), Sanjeet(91 kg) and Ashish Kumar (75 kg) won gold medals at the tournament.

Additional Information

• Amit Panghal is also a  silver medalist at the 2019 AIBA World Boxing Championships.
• Ashish Kumar clinched a gold medal by defeating his opponent from the USA, Joseph Gerome Hiks.
• India has been involved in amateur boxing since the 1920s and made its mark in Asia in the 1950s and 60s.

The correct answer is Option 4.

Key Points

• Human capital is the intangible collective resources possessed by individuals and groups within a given population.
• These resources include all the knowledge(Education), talents, skills, Health (abilities), experience, intelligence, training, judgment, and wisdom possessed individually and collectively, the cumulative total of which represents a form of wealth available to nations and organizations to accomplish their goals. Land is not amongst the components of Human Capital.
• Human capital is available to generate material wealth for an economy or a private firm. In a public organization, human capital is available as a resource to provide for public welfare.
• How human capital is developed and managed may be one of the most important determinants of economic and organizational performance.

The correct answer is 1928.

Key Points

• Motilal Nehru chaired a committee responsible for drafting the constitution in 1928.
• Jawaharlal Nehru was the secretary of the committee.
• The constitution drafted by the committee was termed as Nehru committee report or Nehru Report.
• The Nehru report was submitted on the 28th of August 1928 by Motilal Nehru at an all-party conference held in Lucknow.
• Some other members of the committee were Subhash Chandra Bose, Mangal Singh, Tej Bahadur Sapru, Ali Imam etc.

Additional Information  

• The committee was made in protest against Simon Commission introduced in India by Britishers in 1928.
• The commission was aggressively opposed because there was no Indian member in that.
• Responding to the protest against the Simon Commission the Secretary of State of India at that time Lord BIrkinhead challenged India's political leader to prepare a draft of the constitution.
• Indian leaders accepted the challenge and prepared a draft of the constitution.
• Some of the recommendations of the Nehru report were:
• Dominion Status
• Equal Rights for men and women
• No State Religion
• Supreme Court
• Reservation for minorities

The correct answer is Sivaji Ganeshan.

Key Points

• Sivaji Ganesan as the first Indian actor to be made a Chevalier of the Ordre des Arts et des Lettres in 1995.
• His full name was Villupuram Chinnaiya Manrayar Ganesamoorthy, popularly known as Sivaji Ganesan.
• He was a south Indian actor and acted in Tamil, Telugu, Kannada, Malayalam and Hindi movies.
• He worked for 5 decades in the Indian film industry and acted in 288 films.
• In 1997 he won the highest film honour in Indian cinema Dada Saheb Falke award.

Additional Information

• He received many prestigious awards like  Padam Shri in 1966, the Filmfare award, National Film Award, and NTR National Award.
• The Chevalier of the Ordre des Arts et des Lettres which means Order of the Arts and the Letters is one of the highest French Honours given by the Ministry of Culture.
• It is given for the outstanding contribution to the field of arts and literature.
• Soumitra Chatterjee was also honoured with this award in 1999 for their contribution to Indian Cinema.

The correct answer is 1435.

Key Points

• The Gajpati Kingdom of Odisha was established in 1435 by Emperor Kapilendra Deva.
• It was a medieval Hindu dynasty formed after Ganga rulers.
• It was expanded to Andhra Pradesh, West Bengal, Central parts of Madhya Pradesh and Jharkhand.
• The last ruler of the Gajpati kingdom was Kakharua Deva who was killed by Govinda Vidyadhara, the founder of the Bhoi dynasty.

Additional Information

• The rulers of the Gajpati kingdom were followers of Vaishnavism and worshipped Lord Vishnu.
• The word Gajpati means lord of elephants.
• It is also said that the Gajpati empire was established by Suryavamsi rulers

The correct answer is Mount Kangto.

Key Points

• Mount Kangto also known as Kanggardo Rize is the highest peak in Arunachal Pradesh.
• It is 7090 metres high and lies in the East Kameng district of Arunachal Pradesh.
• It is a part of the Eastern Himalayan range which lies on the border of India and China.
• It occupies 32nd place in the list of mountains of India heightwise.

Additional Information

• K2 is the second-highest mountain on Earth. It lies in the Karakoram range, partially in the Gilgit-Baltistan region of Pakistan-administered Kashmir and partially in a China-administered territory of the Kashmir region
• It lies in the Karakoram range of the Himalayas.
• Its height is 8611metres.
• Mt. Everest is the highest Mountain peak in the world.
• The Aravali Range located in Rajasthan India is one of the oldest mountain range of the world
• Colonel Ranveer Jamwal is  first Indian to summit the seven highest mountains in the world in 2019.

The correct answer is Anil Kumble.

Key Points

• Anil Kumble bowled 14 overs with a bandage around his fractured jaw against the West Indies at Antigua in 2002.
• It was the fourth test match of the series in Antigua Recreation Ground West Indies.
• He was struck on his jaw by a West Indies bowler Mervyn Dillon while batting.
• He took the wicked of Brian Lara while bowling with a broken Jaw.

Additional Information

• The match was drawn.
• Anil Kumble is also known as Jumbo.
• He is also a former coach, captain of the Indian cricket team and commentator.
• He had a carrier of 18 years in international cricket.
• He received a number of awards like the Arjuna award, Wisden Cricketer of the year award in 1996,  Padma Shri, and ICC cricket Hall of fame in the year 2015.

Shortcut Trick

The original quantity of mixture = 3x + 4x  = 7x

According to the question,

⇒ $\frac{3x}{4x + 8} = \frac{5}{8}$

⇒ 24x = 20x + 40

⇒ x = 10

The original quantity of mixture = 7 x 10 = 70 litre

∴ The original quantity of the mixture is 70 litre.

Additional InformationGiven:

In an initial mixture ratio of alcohol and water = 3 : 4.

Calculation:

Let the quantity of alcohol = 3k

Quantity of water = 4k

The original quantity of mixture = 3k + 4k

⇒ 7k

According to the question,

⇒ $\frac{3k}{4k + 8} = \frac{5}{8}$

⇒ 24x = 20x + 40

⇒ x = 10

The original quantity of mixture = 7 x 10 = 70 litre

∴ The original quantity of the mixture is 70 litre.

Calculation:

Smallest number of five digit = 10000

LCM of 18, 21 and 24 = 504

Now,

10000 ÷ 504 

⇒ Quotient = 19 and Remainder = 424

⇒ Divisor = 504 and Dividend = 10000

Required number = Dividend + (Divisor - Remainder)

⇒ 10000 + (504 - 424)

⇒ 10080

∴ Required number is 10080.

Shortcut Trick

Difference for 2 years = PR²/(100)² 

⇒ 5000 x 64/ 10000 = 32

∴ Difference for 2 years is ₹32. 

Alternate MethodGiven:

Principle = ₹5,000

Rate per annum = 8%

Time = 2 years

Formula used:

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

Compound interest = $P[(1 + \frac{r}{100})^t - 1]$ 

Calculation:

SI = 5000 x 8 x 2/100 = 800

CI = $5000[(1 + \frac{8}{100})^2 - 1]$

⇒ CI = Rs. 832

Difference between CI and SI for 2 years = 832 - 800

⇒ 32

∴ Difference for 2 years is ₹32.

Given:

x : 2y = 4 : 9

2 : x = 3 : 4

Calculation:

2/x = 3/4

⇒ x = 8/3

Now,

⇒ x/2y = 4/9

⇒ $\frac{8}{3 \times 2y} = \frac{4}{9}$

⇒ y = 3

Given:

$(\frac{2}{5}of \left.7 \frac{1}{2} \div 2 \frac{1}{4})+(5 \frac{1}{2} \div 3 \frac{2}{3} \text { of } 6\right)-1 \frac{1}{3} \times \frac{5}{8}$

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

$(\frac{2}{5} \times \frac{15}{2} \div \frac{9}{4}) + ( \frac{11}{2} \div \frac{11}{3} \times 6) - \frac{4}{3} \times \frac{5}{8}$

⇒ $(3 \div \frac{9}{4}) + ( \frac{11}{2} \div 22) - \frac{4}{3} \times \frac{5}{8}$

⇒ $(3 \times \frac{4}{9}) + ( \frac{11}{2} \times \frac{1}{22}) - \frac{4}{3} \times \frac{5}{8}$

⇒ $\frac{4}{3} + \frac{1}{4} - \frac{5}{6}$

⇒ $\frac{16 + 3 - 10}{12}$

⇒$\frac{3}{4}$

Shortcut Trick

 The average weight which is increase than the replacement of one man will also increase the weight of the all men.

Then weight of the new person = Weight of the replaced person  + (total men x average weight increase)

50 + (8 x 2.5) = 70 kg

∴ Then weight of the new person is 70 kg.

Alternate MethodGiven:

Weight of the replaced person = 50 kg

Average weight increase of 8 person = 2.5 kg

Concept used:

Average = Sum of observation / Number of observation

Sum of observation = Average x Number of observation

Calculation:

Let average weight of 8 person = a

then total weight = 8a

and New person weight = X

New total weight = 8a - 50 + X

According to question,

⇒ (8a - 50 + X) ÷ 8 = a + 2.5

⇒ 8a - 50 + X = 8a + 20

⇒ X = 70 kg

∴ Then weight of the new person is 70 kg.

Given:

$\frac{\frac{3}{7} \div \frac{3}{7} \times \frac{3}{7}}{\frac{3}{7} \div \frac{3}{7} \circ f \frac{3}{7}}-\frac{9}{49}$

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

$\frac{\frac{3}{7} \div \frac{3}{7} \times \frac{3}{7}}{\frac{3}{7} \div \frac{3}{7} \circ f \frac{3}{7}}-\frac{9}{49}$

⇒ $\frac{\frac{3}{7} \div \frac{3}{7} \times \frac{3}{7}}{\frac{3}{7} \div \frac{3}{7} \times \frac{3}{7}}-\frac{9}{49}$

⇒ $\frac{\frac{3}{7} \div \frac{3}{7} \times \frac{3}{7}}{\frac{3}{7} \div \frac {9}{49}}-\frac{9}{49}$

⇒ $\frac{\frac{3}{7} \times \frac{7}{3} \times \frac{3}{7}}{\frac{3}{7} \times \frac {49}{9}}-\frac{9}{49}$

⇒ $\frac{\frac{3}{7}}{\frac{7}{3}}-\frac{9}{49}$

⇒ $\frac{9}{49} - \frac{9}{49}$

⇒ 0

∴ The required answer is 0.

Shortcut TrickSmallest number = 6 x 2 = 12

Largest number = 6 x 7 = 42 

According to question

⇒ (42)2 + (12)2 = 1908

∴ Sum of the squares of the largest and the smallest number is 1908.

Alternate MethodGiven:

Ratio of four number =  2 : 3 : 5 : 7  

Their HCF = 6

Concept used:

Number = HCF x ratio of number

Calculation:

Smallest number = HCF x smallest ratio

⇒ 6 x 2 = 12

Largest number = HCF x largest ratio

⇒ 6 x 7 = 42 

According to question

⇒ (42)² + (12)²

⇒ 1764 + 144 

⇒ 1908

∴ Sum of the squares of the largest and the smallest number is 1908.

Shortcut Trick

According to question,

P = Q x 220/100

⇒ P/Q = 11/5

Required percentage = $\frac{5 \times 100}{11 +5}$ = 31.25%

∴ Required percentage is 31.25%.

Alternate MethodGiven:

P is 220% of Q

Calculation:

According to question,

P = Q x 220/100

⇒ P/Q = 11/5

Let P = 11

⇒ Q = 5

then P + Q = 11 + 5 = 16

Required percentage = $\frac{5 \times 100}{16}$ 

⇒ 31.25%

∴ Required percentage is 31.25%.

Given:

Marked price = Rs. 16,500

Discount % on marked price = 12%

Profit % = 18%

Formula used:

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

Calculation:

Cost price for retailer after discount = 16500 x 88/100

⇒ Rs. 14,520

Selling price at 18% profit = 14520 x 118/100

⇒ Rs.17,133.60

∴  The selling price is Rs. 17133.60.

Additional Information

• Profit = 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

Let length of the tunnel = L meter

⇒ $\frac{(L + 243) \times 18}{60 \times 5}$ = 42

⇒ L + 243  = 700

⇒ L = 700 - 243 = 457 m

∴ Length of the tunnel is 457 m.

Alternate MethodGiven:

Length of the train = 243 m

Train speed = 60 km/h

Time = 42 second

Formula used:

Distance = Speed x Time 

Time = Distance ÷ Speed

Calculation:

Let length of tunnel = L meter

Speed of train  = 60 km/h x 5/18 

50/3 m/sec

According to question,

⇒ $\frac{(L + 243) \times 18}{60 \times 5}$ = 42

⇒ L + 243  = 7 x 20 x 5

⇒ L = 700 - 243

⇒ L= 457 m

∴ Length of the tunnel is 457 m.

Hint When convert the speed km/h to m/s then = km/h x 5/18

When convert the speed m/s to km/h then = m/s x 18/5

Shortcut Trick 2πr = 506

⇒ 2 x $22 \over 7$ x r = 506 ⇒ r = 161/2

The cost for levelling the ground = πr² x 14 = 

⇒ $\frac{22}{7} \times \frac{161}{2} \times \frac{161}{2} \times 14$ = Rs. 2,85,131

∴ The cost for levelling the ground is Rs. 2,85,131.

Alternate MethodGiven:

Perimeter of circular garden = 506 m

Cost of levelling = 14/m²

Formula used:

Perimeter of circle =  2πr

Area of circle = πr²

Calculation:

Perimeter of circle = 2πr = 506

⇒ 2 x $22 \over 7$ x r = 506 

⇒ r = 161/2 m

The cost for levelling the ground  = Area of circle x 14

⇒ πr² x 14

⇒ $\frac{22}{7} \times \frac{161}{2} \times \frac{161}{2} \times 14$

⇒ Rs. 2,85,131

∴ The cost for levelling the ground is Rs. 2,85,131.

Shortcut Trick

Let Cost Price = 100 

Selling price = 148

New cost price = 120

New Profit % = (148 - 120) x 100/120 = 70/3%

Decrease in profit percentage = $48 - \frac{70}{3}$ = 24.67%

∴ Decrease in profit percentage is 24.67%.

Alternate MethodFormula used:

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

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

Calculation:

Let Cost Price = 100 

Selling price at 48% profit = 100 x 148/100 

⇒ 148

New cost price = 100 x 120/100

⇒ 120

New Profit % = (148 - 120) x 100/120

⇒ 28 x 5/6

⇒ 70/3%

Decrease in profit percentage = $48 - \frac{70}{3}$

⇒ (144 - 70)/3

⇒ 24.67%

∴ Decrease in profit percentage is 24.67%

Additional InformationWhen the percentage (%) or fraction (a/b) or ratio (a : b) is given in the question and the answer is also to come out in the percentage (%) or fraction (a/b) or ratio (a : b), then there is no need to take the real value.

Profit = 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

Speed of train = 45 km/h x 5/18 = 12.5 m/s

Length of train = 12.5 m/s x 12 sec. = 150 m

∴ Length of train is 150 m.

Alternate MethodGiven:

Speed in train = 45 km/h

Time = 12 sec.

Formula used:

Distance = Speed x Time 

Concept used:

1 km = 1000 m

1 hour = 3600 sec

Calculation:

Speed of train = 45 km x 1000 m/3600 sec

⇒ 45 km/h x 5/18

⇒ 12.5 m/s

Now,

Length of train = Train cover the distance in 1 second.

⇒ 12.5 m/s x 12 sec

⇒ 150 m

∴ Length of train is 150 m.

Mistake PointsIf Convert km/h to m/s = km/h x 5/18

and if convert m/s to km/h = m/s x 18/5.

Shortcut TrickIn question compound interest calculate in monthly

Interest for 12 month = 24%

Then for 1 month = 2%

Compound interest = 

 

CI = 150 + 150 + 150 + 3 + 3 + 3 + 0.06 = 459.06 ≈ Rs. 459

∴ Required compound interest is Rs. 459. 

Alternate MethodGiven:

Principle = Rs. 7,500

Rate per annum = 24%

Time = 3 month

Formula used:

Compound interest = $P[(1 + \frac{r}{100})^t - 1]$

Calculation:

Interest for 12 month = 24%

⇒ Then for 1 month = 2%

Compound interest = $7500[(1 + \frac{2}{100})^3 - 1]$

⇒ $7500[(\frac{51}{50})^3 - 1]$

⇒ $7500(\frac{132651 - 125000}{125000})$

⇒ $7500\times \frac{7651}{125000}$

⇒ 459.06 ≈ Rs. 459

∴ Required compound interest is Rs. 459. 

Key PointsCompound interest is the addition of interest to the principle sum of loan or deposit, or in other words, interest on principle plus interest.

or interest on (Principle + interest)

Shortcut TrickSP = $\frac{11}{8}$ x CP

Then SP/CP = 11/8

Profit % = 3 x 100/8 = 37.5%

∴ Profit% is 37.5%.

Alternate MethodGiven:

SP = $\frac{11}{8}$ x CP

Formula used:

Profit = Selling price - Cost price

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

Calculation:

According to question,

SP = $\frac{11}{8}$ x CP

⇒ SP/CP = 11/8

⇒ Let SP = 11k

⇒ CP = 8k

⇒ Profit = 11k - 8k

⇒ Profit = 3k

⇒ Profit % = 3k x 100/8k = 37.5%

∴ Profit% is 37.5%.

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

 

Cost price of A = 600 x 3/5 = Rs. 360

∴ Cost price of A is Rs. 360.

Alternate MethodGiven:

Cost price of (A + B) = Rs. 600

A sell at profit = 20%

B sell at loss = 10%

Whole profit = 8%

Formula used:

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

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

Calculation:

Let Cost price of A = Rs. A

Cost price of B = Rs. (600 - A)

According to the question,

$A \times \frac{120}{100} + (600 - A) \times \frac{90}{100} = 600 \times \frac {108}{100}$

⇒  $\frac{120A + 54000 - 90A}{100} = 648$ 

⇒ 30 A + 54000 = 64800

⇒ 30A = 10800

⇒ A = 360

∴ Cost price of A is Rs. 360.

Additional Information

• Profit = 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

Volume of cylinder = πr²h

⇒ Increase in radius = $20 + 20 + \frac{20 \times 20}{100}$ = 44%

⇒ Total increase/decrease = $44 - \frac{100}{3} - \frac{44 \times 100}{100 \times 3}$

⇒ (132 - 100 - 44)/3

⇒  - 4%                                     [(-) denote decrease ]

∴ Percentage change in volume is decreased by 4%.

Alternate MethodGiven:

Radis of cylinder is increased = 20%

Decrease of height = $33 \frac{1}{3} \%$ 

Formula used:

Volume of cylinder = πr2h         

(where r = radius and h = height)

Equivalent increase or decrease = ± a ± b ± (a × b)/100

Calculation:

Initial volume of cylinder =  πr2h  

Radius after 20% increase = r x 120/100 

⇒ New radius = 6r/5

Height after $33 \frac{1}{3} \%$  = $100 \over 3$%decrease = h x ($100 - \frac{100}{3}$%)

⇒ h x ($\frac{200}{3}$%)

⇒ h x ($\frac{200}{3 \times 100}$)

⇒ New height = $\frac{2h}{3}$

New volume of cylinder = π$({6r \over5})^2$​$2h \over 3$

​⇒ New volume = $\frac{24}{25} πr^2h$​​

Now,

Decrease in volume = πr2h - $\frac{24}{25} πr^2h$

⇒ $πr^2h \over 25$

​​Percentage decrease in volume = $\frac{πr^2h \times 100}{25 \times πr^2h}$ 

⇒ 4%

∴ Percentage change in volume is decreased by 4%.

Additional InformationPercentage increase or decrease  = (New observation - old observation) x 100/ old observation

If successive increase is a% and b% then equivalent increase = a + b + (a x b)/100

If successive decrease is a% and b% then equivalent increase = - a - b + (a x b)/100

If successive increase is a% and decrease is b% then equivalent increase or decrease = a - b - (a x b)/100

**Given:**10% of A = B

Calculation:

A x 10/100 = B

⇒ B = A/10

Now,

⇒ B% of 20 = $\frac{A}{10} \times \frac{1}{100} \times 20$

⇒ B% of 20 = ${A} \times \frac{2}{100}$

∴ B% of 20 = 2% of A.

Shortcut Trick 

Wages is divided in the ratio of efficiency.

Total wage = 24 + 20 + 15 = 2950

⇒ 59 = 2950

Amount of B = 2950 x 20/59 = 1000

∴ Amount of B is Rs. 1,000.

Alternate MethodGiven:

A can alone complete the work = 5 days

B can alone complete the work = 6 days

C can alone complete the work = 8 days

Concept used:

Total work = (Sum of Efficiency) x total days

A person alone can complete the job = Total work / Efficiency of alone person

Calculation:

Total work = LCM of 5 days, 6 days and 8 days

⇒ 120 unit

Efficiency of A = 120/5 = 24

Efficiency of B = 120/6 = 20

Efficiency of C = 120/8 = 15

Now,

Wages is divided in the ratio of efficiency.

⇒ Total wage = 24 + 20 + 15 = 2950

⇒ 59 = 2950

Amount of B = 2950 x 20/59 = 1000

∴ Amount of B is Rs. 1,000.

Shortcut Trick

Average marks in the remaining subjects = $\frac{(5 \times 72) - (3 \times 70)}{2}$

⇒ $\frac{360 - 210}{2}$ = 75

∴ Average marks in the remaining subjects is 75.

Alternate MethodGiven:

Average marks of 5 subject = 72

Average marks of 3 subject = 70

Formula used:

Average = (Sum of observation) ÷ (Number of observation)

Sum of observation = Average x (Number of observation)

Calculation:

Sum of the 5 subjects = 5 x 72 = 360

Sum of the 3 subjects = 3 x 70 = 210

⇒ Remaining subject = 5 - 3 = 2

Sum of the remaining 2 subjects = 360 - 210 

⇒ 150

Average of the remaining 2 subjects = 150/2

⇒ 75

∴ Average marks in the remaining subjects is 75.

Given:

(a + b - c) : (b + c - a) : (a + c - b ) = 4 : 5 : 9

Calculation:

a + b - c = 4        ------(1)

b + c - a = 5        ------(2)

a + c - b = 9        ------(3)

Addition the equation (1) and (2)

⇒ 2b = 9 ⇒ b = 9/2

Addition the equation (2) and (3)

⇒ 2c = 14 ⇒ c = 7

Addition the equation (1) and (3)

⇒ 2a = 13 ⇒ a = 13/2

Now, 

a - b : c - b : c - a = (13/2 - 9/2) : (7 - 9/2) : (7 - 13/2)

⇒ 2 : 5/2 : 1/2

⇒ 4 : 5 : 1             (LCM of 2 and 2 is 2)

∴ (a - b) : (c - b) : (c - a) = 4 : 5 : 1.

Shortcut TrickAccording to question,

CI of half yearly - CI of yearly = Rs. 964

⇒ $P[(1 + \frac{10}{100})^4 - 1]$ - $P[(1 + \frac{20}{100})^2 - 1]$ = 964

⇒ $P[(\frac{11}{10})^4 - 1]$ - $P[(\frac{6}{5})^2 - 1]$ = 964

⇒ $\frac{4641P - 4400P}{10000}$ = 964

⇒ 241P = 964 x 10000

⇒ P = Rs. 40,000

∴ Sum is Rs. 40,000.

Alternate MethodGiven:

Rate per annum = 20%

Time = 2 years

CI of half yearly - CI of yearly = Rs. 964

Formula used:

Compound Interest = $P[(1 + \frac{r}{100})^t - 1]$

Calculation:

Let sum = Rs. P

Rate per annum = 20%

Rate for half yearly = 20/2 = 10%

When rate is calculated half yearly then time for 2 year = 2 x 2 = 4 

According to question,

CI of half yearly - CI of yearly = Rs. 964

⇒ $P[(1 + \frac{10}{100})^4 - 1]$ - $P[(1 + \frac{20}{100})^2 - 1]$ = 964

⇒ $P[(\frac{11}{10})^4 - 1]$ - $P[(\frac{6}{5})^2 - 1]$ = 964

⇒ $P[\frac{14641 - 10000}{10000}]$ - $P[\frac{36 - 25}{25}]$ = 964

⇒ $P\frac{4641}{10000}$ - $P\frac{11}{25}$ = 964

⇒ $\frac{4641P - 4400P}{10000}$ = 964

⇒ 241P = 964 x 10000

⇒ P = Rs. 40,000

∴ Sum is Rs. 40,000.

Shortcut Trick

                       X : Y : Z

Days               6 : 3 : 2

Efficiency     1/6 : 1/3 : 1/2           

(Efficiency is inversely proportional to days)

⇒ Efficiency   1 : 2 : 3    

If they work together then finish it in 2 days ,

so total work = (1 + 2 + 3) x 2 = 12 unit

Y alone can finish the job = 12/2 = 6 days

∴ Y alone can finish the job = 6 days.

Alternate MethodGiven:

X takes twice as compare to Y and thrice as compare to  Z to finish a job.

If working all together, they can finish it in 2 days

Concept used:

Efficiency is inversely proportional to days

Total work = (Sum of Efficiency) x total days

A person alone can complete the job = Total work/ Efficiency of alone person

Calculation:

Let Z alone can complete the job = 2k days

Y alone can complete the job = 3k days

X alone can complete the job = 6k days

Now,

                       X : Y : Z

Days              6k : 3k : 2k

Efficiency       1/6k : 1/3k : 1/2k           

(Efficiency is inversely proportional to days)

⇒ Efficiency   1k : 2k : 3k                     

(LCM of 6, 3 and 2 is 6)

If they work together then finish it in 2 days

⇒ So, total work = (1k + 2k + 3k) x 2

⇒ 12k unit

⇒ Y alone can finish the job = 12k/2k = 6 days

∴ Y alone can finish the job = 6 days.

Shortcut Trick

⇒ $210 \times \frac{190}{100} = MRP \times \frac{95}{100}$

⇒ MRP = Rs. 420 

∴ The MRP is Rs. 420.

Alternate MethodGiven:

CP = Rs. 210

Formula used:

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

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

Calculation:

SP for gain 20% = 210 x 190/100

⇒ Rs. 399

According to question,

MRP x 95/100 = 399

⇒ MRP = Rs. 420 

∴ The MRP is Rs. 420.

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