DSSSB Jail Warder : (1 Dec 2025) Memory-Based Paper (Previous Year Paper)

According to the English alphabet series and its positional value:

The pattern followed here is:

Similarly;

Hence, "BWBXHI" is the correct answer.

Given :

• Eight people - R, S, T, U, V, W, X and Y are living in a building having eight floors.
• Bottommost floor is numbered as 1 to the topmost floor numbered as 8.

​Explanation :

1) W lives four floor below Y and immediate above S.

2. S lives on a prime numbered floor.

3) There are odd number of floors between X and V.

4. V is two floor above U.

5) X neither lives at a prime numbered floor nor at the topmost floor.

6) R lives below T but not adjacent to X.

As is case - (2) there is no possible position for R, therefore this case is eliminated.

Thus, according to the final arrangement R is five floors below U.

Hence, "Five floors below" is the correct answer.

The pattern followed here is:

Numerator is getting added by denominator of previous term and denominator is getting multiply by 2 in every next term.

Hence, the correct answer is 63/64.

Here both the arguments are providing a valid reason but on two different grounds. One is on the grounds of health, while the other is on the ground of employment.

Hence, Either argument I or II is strong.

LOGIC: Arrange according to alphabetical order

And,

Similarly,

Hence, the correct answer is "GHM".

The logic followed is:

Face, Veneer, and Surface is used in reference to the outermost or outer part of something.

But,

A cave is a naturally formed underground chamber in hills.

Hence, the correct answer is "Cave".

Important PointsSurface: The outside part of anything.

Face: It is a surface that is presented to the view or the outer part of anything that can be shown.

Veneer: A decorative covering of fine wood.

The logic is:

bbcbba/bbcbba/bbcbba

After dividing the series in three equal parts, we see that a similar pattern is repeated.

So, the letters that will complete the series is ‘c b b b a’.

Hence, ‘c b b b a’ is the correct answer.

The logic followed here is:

Hence, ‘CQI’ is the correct answer.

The pattern followed is,

2³ × 2 = 16

3³ × 4 = 108

4³ × 6 = 384

5³ × 8 = 1000

Similarly

6³ × 10 = 2160

Hence, ‘2160’ is the correct answer.

According to the English alphabet series and its positional value:

The pattern followed here is:

And;

Similarly;

Hence, "FLGCS" is the correct answer.

Number of students who like history = 110

Number of students who like civics = 160

Number of students who like English = 170

Number of students who like civics and English = 10

Number of students who like English and history = 20

Number of students who like civics and history = 30

Number of students who likes all three subject = 40

Number of student who only likes English = 170 – 10 – 20 – 40 = 100

Hence, ‘100’ is the correct answer.

The least possible Venn diagram for the given statements is as follow

I. Some copies are papers → True

As from statement “1. Some paper are copies”. So, some copies are definitely papers.

II. Some papers are kind → False

It’s possible but not definite. In this case, alternate diagram can be drawn as follows:

In the first diagram this conclusion is false. But from the alternate diagram, conclusion II follows.

III. No paper is kind → False

It’s possible but not definite. From the first diagram this conclusion satisfies. But from the alternate diagram conclusion III fails.

Conclusion II and III forms a complimentary pair of “Some-No”. From this we conclude that either conclusion II or III follow.

Therefore, Only conclusion I and either conclusion II or III follow.

Conditions for “Either-Or” case between two conclusions:

1. Two entities in both the conclusion should be same.
2. Both the conclusions should form complementary pair of “All-Some Not” or “No-Some”.

Note that sequence of entities in both the statements should be same in case of “All-Some Not” pair.

3. Both the conclusions should be possible in some possible Venn diagrams.
4. Both conclusion should NOT be simultaneously true (or false) in a single possible Venn diagram.

Concept:

• A map is a representation or a drawing of the earth’s surface or a part of it drawn on a flat surface according to a scale.
• There are three components of Maps – distance, direction and symbol.

Explanation:

• There are four major directions, North, South, East and West. They are called cardinal points.
• The other four intermediate directions are north-east (NE), southeast(SE), south-west (SW) and north-west (NW).

• We can locate any place more accurately with the help of these intermediate directions.
• We can find out the direction of a place with the help of a compass.

Given: 

• The Doctor is located at X.
• He first goes to A which is 800 m due east of X.
• Then, he goes to B which is 300 m due north of A.
• Then, again he goes to C which is 150 m due west of B.
• And, then finally he goes to Y which is 100 m due north of C.

Hence, from the above diagram, it becomes clear that with respect to the doctor's house the correct direction of the hospital is north-east.

The correct answer is Option 4

We cannot tell from the statement that all students in the said college are genius because only 1 got selected for an internship in NASA.

Since the statement says that the student got selected, it means that NASA follows a process of selection and it cannot be said that NASA hires from the said college only.

Hence both the conclusions are incorrect.

i) Among six boxes in a rack, E is placed two boxes above the box D.

ii) Box A is placed immediately above box C.

iii) Box B is placed adjacent to box F and box E.

This eliminates case 2 and 3.1.

iv)  Box E is not placed at the top of the stack.

This eliminates case 3.2.

1. Box B is placed above box E. → possible but not definite.

2. Box F is placed above box A. → possible but not definite.

3) More than one box is placed between box C and F.  → Definitely True

4. Box D is placed three boxes below box C. → possible but not definite.

Hence, correct answer is option 3.

Below diagram represent mirror image of question figure.

The logic followed here is:

Given 

A # B' means 'A is the son of B',

'A % B' means 'A is the daughter of B',

'A & B' means 'A is the father of B',

'A @ B' means 'A is the brother of B'.

Here, M # N % P & Q @ T

Now, draw the family tree

Therefore, M is the Nephew of T.

Hence, "Option (1)" is the correct answer.

The positions of the letters according to the English alphabet series:

The pattern for this code is as follows;

Similarly;

hence, "PGFSBDUT" is the correct answer.

1. F is second to the right of D.

2) L is to the immediate right of H.

3. H and J are facing towards each other.

So, this case is possible only when H is sitting second left of D.

Hence, there are 3 people between J and N from the left of J.

Emergency helpline numbers is as follows;

102 is the emergency number of Ambulance not for the woman helpline.

Hence, "102 - Women Helpline" is the odd one out and hence it is considered as the correct answer.

Confusion Points

• "112" is the Single Emergency number which provide you all services like fire brigade, and ambulance or the police.

The logic followed here is:

Option 1: 74-88

88 -74 = 14, which is not divisible by 6.

Option 2: 14-20

20 - 14 =  6, which is divisible by 6.

Option 3: 26-38

38 - 26 = 12, which is divisible by 6.

Option 4: 58-70

70 - 58 = 12, which is divisible by 6.

So, Option 1 is different from others.

Hence, "option 1" is the correct answer.

The logic followed is:

i) Point B is 5 m North of point A.

ii) Point C is 5 m West of point B.

iii) Point D is 10 m South of point C.

iv) Point E is 7m East of point D.

Drawing the Diagram as per the given information.

Thus we can see the direction of E is South-East with reference to point B.

Hence, the correct answer is "South-East".

On close observation, we find that the problem figure is embedded in figure (4) as shown below.

Hence, the correct answer is figure 4.

From the given information we draw a tree using the symbols:

P and T are daughters of U and Q is P's daughter.

 Out of 6 people half of them are female i.e. 3 so R, S and U are males.

There is no information given about R but we have S is the father of one male and female and we are left with only R so R is the son of S.

Since there is at least one married couple all the conditions fit when we place S and P as a couple.

Hence the correct answer is option 1)

The Correct answer is Option 2. 

Key Points​

Breaking down the expression based on the defined operations:

20 + 5 becomes 20 × 5 = 100.

5 - 10 becomes 5 + 10 = 15.

10 × 2 becomes 10 - 2 = 8.

2 ÷ 4 remains 2 ÷ 4 = 0.5.

 20 + 5 - 10 × 2 ÷ 4

after replacing the operations

Final expression: 20 × 5 + 10 - 2 ÷ 4 =

100 + 10 - 0.5 = 109.5.

Hence Correct answer is  Option 2 (109.5)

The pattern followed is,

6 × 11 = 66

7 × 13 = 91

8 × 15 = 120

9 × 17 = 153

10 × 19 = 190

Similarly

11 × 21 = 231

Hence, ‘231’ is the correct answer.

In the first and second statements, the common code digit is '2' and the common word is 'carpet'.

So, '2' means 'carpet'.

In the second and third statements, the common code digit is '6' and the common word is 'one'.

So, '6' means 'one'.

Therefore, in the second statement, '5' means 'dust'.

We substitute the values in the given equation and solve it using the BODMAS rule:

Option 1.  +, -, +, ÷, =, ×

(\sqrt(330+6)) - 4 + 13 ÷ 10 = 2 × 7

(\sqrt336)- 4 + 13 ÷ 10 = 2 × 7

18.33 - 4 + 1.3 = 2 × 7

18.33 - 5.3 = 2 × 7

18.33 - 5.3 = 14

13.03 ≠ 14

LHS ≠ RHS

Option 2. ×, +, -, +, ÷ , =

√(330 × 6) + 4 - 13 + 10 ÷ 2 = 7

(\sqrt1980) + 4 - 13 + 10 ÷ 2 = 7

44.49 + 4 - 13 + 5 = 7

48.49 - 18 = 7

30.49 ≠ 7

LHS ≠ RHS

Option 3. +, -, ÷, =, -, ×

√(330 + 6) - 4 ÷ 13 = 10 - 2 × 7

√336 - 4 ÷ 13 = 10 - 2 × 7

(\sqrt336)- 0.30 = 10 - 2 × 7

18.33 - 0.30 = 10 - 14

18.03 ≠ - 4

LHS ≠ RHS

Option 4: -, ×, =, ×, ÷, +

√(330 - 6) × 4 = 13 × 10 ÷ 2 + 7

(\sqrt324) × 4 = 13 × 10 ÷ 2 + 7

18 × 4 = 13 × 5 + 7

72 = 65 + 7

72 = 72

LHS = RHS.

Hence, the correct answer is '-, ×, =, ×, ÷, +'.

The given figure when unfolded is as follows:

Hence, the correct answer is Option 4.

1. Eight friends –P, Q, R, S, T, U, V, and W are sitting in a linear row and all are north direction
2. ‘V’ has three peoples in the left and four peoples on right.

3. ‘V’ has ‘U’ in right but not immediate right.
4. The neighbours of ‘U’ are ‘Q’ and ‘S’ and one of the neighbours of ‘U’ is in ends.
5. ‘R’ sits second to left of ‘U’.

6. ‘W’ does not sit in ends.
7. The position of ‘T’ is second left from ‘R’ and third left from Q. (Implies case 2 is wrong)

Hence, ‘P’ is sitting in the extreme left end.

Option 3.A is true but R is false.

The human skeleton is the internal framework of the human body. It is composed of around 270 bones at birth this number decreases to around 206 bones by adulthood after some bones get fused together. So, babies have more bones than adults.

The smallest bone in the human body is Y Y-shaped bone in-ear called stapes. So, the external human ear is made up of cartilage and is not a bone structure while the internal human ear is a canal made by the fusion of three bones mallus, incus, and stapes. They are popularly called the ear ossicles and were given their Latin names for their distinctive shapes; they are also referred to as the hammer, anvil, and stirrup, respectively. So, A is true and R is false.

 Hence, option 3 is correct.

The least possible Venn diagram is:

I. All charger are mobile → false (It is possible but not definite)

II. Some mobile are house → false (It is possible but not definite)

III. All house are mobile → false (It is possible but not definite)

IV. Some house are charger → true (because All mobile are charger and some charger are house)

Hence, Only conclusion IV follows.

Preparing the family tree by using the following symbol:

The family tree as per the given information:

Here, Gunjan is the sister of Prateek.

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

The logic followed here is:

Hence, ‘JXL’ is the correct answer.

The logic followed here is :-

(First number ÷ 3) + sum of digits of first number = Second number

• 498 : 187 → (498 ÷ 3) + (4 + 9 + 8) = 166 + 21 = 187
• 348 : ? → (348 ÷ 3) + (3 + 4 + 8) = 116 + 15 = 131
• 762 : 269 → (762 ÷ 3) + (7 + 6 + 2) = 254 + 15 = 269

Hence, the correct answer is "131".

The pattern followed in the given series is:

Aerophobia: Flying - Phobia name: Phobia caused by

Cibophobia: Food - Phobia name: Phobia caused by

Similarly,

? : Rooms - ? will be the phobia name.

We consider the given options:

1) Lockiophobia: Fear of childbirth.

2. Somniphobia: Fear of sleep.
   

3) Koinoniphobia: Fear of rooms.

4. Zoophobia: Fear of animals.

Hence the correct answer is option 3.

All mosquitos are insects but rats are not related to insects.

The correct Venn diagram representation is,

Hence, option 4 is the correct answer.

The least possible Venn diagram is:

Conclusions:

I. some roads are stores → false (All roads are houses and some houses are stores but there is no direct relation given between roads and stores.)

II. All houses are roads → false (it is possible but not definite because all roads are houses and some houses are stores.)

III. All stores are roads → false (because All roads are houses and some houses are stores.)

IV. some houses are roads → true (because All roads are houses and some houses are stores.)

Hence, Only conclusion IV follows.

The logic follows here is : 

Light rays falling on a mirror undergo reflection.

Similarly,

light rays falling on water undergo ‘refraction.’

Hence, the correct answer is “Option (4).”

Additional Information

• Conduction: Process by which heat energy is transmitted through collisions between neighboring atoms or molecules
• Dispersion: The separation of light into colors by refraction or diffraction with formation of a spectrum
• Immersion: The act of dipping something in a substance, completely covering it.

Member: I, J, K, L, M and N.

Month: January, February, April, July, August and December.

1. The birthday of N is either in January or August.
2. Two people have birthday between N and J’s birthday.
3. M’s birthday is not in the second half of the year.

4. K’s birthday falls in month having minimum number of days.

(So, K’s birthday falls in February.)

5. At the most three people have birthdays between N and I’s birthday.

(Case II will be eliminated as it doesn’t satisfy point 5.)

(I’s birthday falls in August refer to point 5 and only one month left for L’s birthday i.e. December.)

1. I’s birthday is in January → false.

2. K’s birthday is preceded by N → false.

3. L’s birthday is in December → true.

4. N’s birthday is in February → false.

Hence, ‘L’s birthday is in December’ is the correct statement.

Lavani is a folk dance of Maharashtra. It is a combination of traditional song and dance, which is particularly performed to the beats of Dholki which is a percussion instrument. Lavani is noted for its powerful rhythm and has contributed substantially to the development of Marathi folk theatre.

The correct answer is Cash reserve ratio.

Key Points

The correct answer is Ethane.

Key Points

• Ethane is a saturated hydrocarbon among given options.
• Saturated hydrocarbons are molecules with only single bonds.

 - Ethane

 - Ethene

• Propene

• Acetylene
• Only ethane has all single bond while others have a double and triple bond.
• Methane, Ethane, Propane, Butane, etc are examples of saturated hydrocarbons.
• Alkanes are saturated hydrocarbons and classified as a type of aliphatic hydrocarbon.
• Bonding between every single bond in a saturated hydrocarbon is covalent in nature**.**

Additional Information

• Unsaturated hydrocarbons contain multiple bonding and contain less than the maximum number of hydrogens per carbon.
• Unsaturated hydrocarbons have double or triple covalent between adjacent carbon atoms.
• Aromatic hydrocarbons are a special case of unsaturated hydrocarbons.

The correct answer is Gobind Behari Lal.

• Pulitzer Prize- The Pulitzer Prize is an award for achievements in newspaper, magazine, and online journalism, literature, and musical composition within the United States.

Key Points

• In 1937, Gobind Behari Lal had won the Pulitzer Prize for journalism, along with four others, for his coverage in the field of science.
• Gobind Behari Lal was an Indian-American journalist and independence activist.

Additional Information

• Geeta Anand was awarded the Pulitzer Prize for Explanatory Reporting in the year 2003.
• Jhumpa Lahiri was awarded the Pulitzer Prize for Fiction in the year 2000.
• Sanghamitra Kalita was awarded the Pulitzer Prize for Breaking News Reporting in the year 2016.

The Correct Answer is Option 1 i.e Southern Africa.

The correct answer is the option 2 i.e. Tropical Rainforests.

Key Points

• Tropical evergreen forests are dense, multi-layered, and found in the areas receiving heavy rainfall.
• This type of forest is rich in numerous species of trees.
• It is very dense even the sunlight does not reach the ground.
• Tropical rainforests found in areas of tropical rainforest climate.
• It receives an average rainfall of at least 60 mm and known as also "lowland equatorial evergreen rainforest".
• Thus, these forests always see "Green" and are known as "Evergreen Forests".

• The power of a lens is given by (P = \frac{1}{f})
• Where f is the focal length of the lens.
• In the case of a concave lens, the power will always be negative as the focal length is negative.
• So, (P = \frac{1}{-5} = -0.2D)

The correct answer is 7.55 MTPA.

In News

• Union Minister HD Kumaraswamy unveiled a Rs 20,000 crore expansion plan for SAIL’s Bokaro Steel Plant, increasing production capacity from 5.25 MTPA to 7.55 MTPA.

Key Points

• The expansion plan includes a new 4,500 cubic meter blast furnace, thin slab casting, direct rolling facility, and sinter plant expansion.
• The investment will create 2,500 permanent jobs and 10,000 indirect jobs.
• The project aligns with the Aatmanirbhar Bharat vision and aims to develop a 300 MTPA steel industry by 2030.
• SAIL is also focusing on decarbonisation and renewable energy initiatives, including 150 MW solar power projects.

Additional Information

• Decarbonisation Initiatives
• Reduction of carbon emissions from 2.67 tonnes per tonne of crude steel to less than 2.2 tonnes by 2030.
• Renewable energy push: 30 MW floating solar, 20 MW land-based solar, and 100 MW procurement from Solar Energy Corporation of India.
• Raw Material Security
• Development of Tasra coal mine, expected to produce 3.5 MTPA of domestic coking coal by September 2025, reducing India’s import dependence.
• Upgradation of Chasnala Washery to lower ash content in coal from 28% to 17% for efficient steel production.
• India’s Steel Industry Goals
• India targets a 300 MTPA steel industry by 2030 to meet domestic and export demands.
• The expansion of Bokaro Steel Plant is a step towards achieving self-reliance in steel production under the Developed India 2047 vision.

The correct answer is the Money market.

Key Points

• The money market is the market for short-term funds.
• It provides means for raising funds for meeting short-term needs of cash on one hand and deployment of surplus funds for short period on the other.
• Instruments in the money market are :
• Call money:
• It is a method used by commercial banks to borrow funds from each other to be able to maintain the Cash Reserve Ratio (CRR).
• It is a short-term finance repayable on demand, with a maturity period of 1 day to 15 days.
• The interest paid-on-call money loan is known as the call rate.
• It is a highly fluctuating rate that changes from day to day and sometimes even from hour to hour.
• Commercial bill:
• It is a bill of exchange used to finance the working capital requirement of a business firm.
• It is a short-term, unsecured promissory note, negotiable and transferable by endorsement and delivery with a fixed maturity period.
• When the seller makes credit sales, it draws a bill of exchange on the buyer, to pay the amount on a certain date.
• On acceptance by the buyer, it becomes a trade bill.
• This trade bill, when presented to the bank for discounting, and the bank accepts, is called a commercial bill.
• Thus the money market is appropriate answer.

The correct answer is Nepal.

Key Points

• In 2015, Nepal experienced a devastating earthquake, known as the Gorkha Earthquake, with a magnitude of 7.8.
• The National Disaster Response Force (NDRF) of India was deployed to Nepal to assist in rescue and relief operations.
• India launched Operation Maitri, a comprehensive relief and rescue operation to support Nepal during this disaster.
• The NDRF teams played a key role in rescuing people trapped in debris, providing medical assistance, and distributing essential supplies.
• This humanitarian assistance strengthened the bilateral relations between India and Nepal, showcasing India’s commitment to regional cooperation.

Additional Information

• National Disaster Response Force (NDRF):
• Established in 2006, the NDRF is a specialized force created for disaster response in India.
• It functions under the Ministry of Home Affairs and is composed of 12 battalions equipped to handle natural and man-made disasters.
• The NDRF has been deployed in various national and international disaster operations.
• Operation Maitri:
• It was India’s relief and rescue operation for Nepal after the 2015 earthquake.
• The operation included deploying the Indian Army, Air Force, and the NDRF for rescue, medical aid, and supply distribution.
• India provided monetary aid, essential supplies, and technical assistance to support Nepal’s recovery.
• Gorkha Earthquake (2015):
• The earthquake struck Nepal on April 25, 2015, causing over 9,000 fatalities and affecting millions of people.
• It caused widespread destruction in Kathmandu Valley, including heritage sites like the Dharahara Tower and Durbar Square.
• The disaster triggered avalanches in the Himalayas, including a deadly avalanche at Mount Everest.
• India-Nepal Relations:
• India and Nepal share close historical, cultural, and economic ties, and India is one of Nepal’s largest trading partners.
• India has consistently supported Nepal in times of need, including disaster relief, infrastructure development, and economic aid.
• The 2015 earthquake relief efforts underscored India’s role as a key regional partner in humanitarian assistance.

The correct answer is SIDBI. 

Key Points

• SIDBI does not accept deposits and hence it is a financial institution, not a commercial bank.
• Small Industries Development Bank of India is the apex regulatory body for the overall licensing and regulation of micro, small and medium enterprise finance companies in India.
• SIDBI was incorporated on 02nd April 1990 by the Government of India as a wholly owned subsidiary of IDBI Bank.

Additional Information

• A commercial bank is a financial institution that accepts deposits from the public and gives loans for consumption and investment purposes to earn profit.
• It can also refer to a bank, or a division of a larger bank, that deals with corporations or a large/medium-sized business to differentiate it from a retail bank and an investment bank.
• Commercial banks include private sector banks and public sector banks.

The correct answer is 6.5%.

In News

• The International Monetary Fund (IMF) has revised India’s growth forecast for FY25 to 6.5%, down from the earlier estimate of 7%.

Key Points

• The downgrade is attributed to a sharper-than-expected slowdown in industrial activities in India.
• Despite the FY25 downgrade, the IMF has maintained India’s growth projections for FY26 and FY27 at 6.5%.
• The Reserve Bank of India (RBI) also lowered its growth forecast for FY25 to 6.6%.
• The falling rupee has been identified as a concern for growth, inflation, and exports.

Additional Information

• IMF (International Monetary Fund)
• An international organization that works to ensure global financial stability and promote economic growth.
• Publishes the World Economic Outlook, which provides projections for global and regional economies.
• Falling Rupee Impact
• Depreciation of the rupee can lead to higher inflation, as imports become costlier.
• Exports may become more competitive globally, but weak global demand could limit gains.
• Global Growth Projections
• IMF projects global growth at 3.3% for 2025 and 2026, below the historical average of 3.7%.
• Advanced economies are expected to see inflation converge to targets faster than emerging economies.

The correct answer is INCOIS.

In News

• Indian National Centre for Ocean Information Services (INCOIS) has been honored with the Subhash Chandra Bose Aapda Prabandhan Puraskar for 2025.
• INCOIS runs the Indian Tsunami Early Warning Centre, recognized by UNESCO for its excellence in tsunami monitoring and alert dissemination.
• Its advisories significantly aided in disaster response during Cyclone Phailin (2013) and Cyclone Hudhud (2014).
• Technologies like SARAT support the Indian Coast Guard in search and rescue missions, and SynOPS integrates real-time oceanic data to bolster disaster management.

Key Points

• Subhash Chandra Bose Aapda Prabandhan Puraskar: India’s prestigious award honoring outstanding contributions in the field of disaster management.
• INCOIS: Functions under the Ministry of Earth Sciences, providing essential ocean-based information, early warnings, and advisories for natural disasters.
• Indian Tsunami Early Warning Centre: A UNESCO-certified system offering real-time monitoring to protect coastal populations from tsunamis.
• SARAT and SynOPS: Advanced tools enhancing search and rescue operations, as well as real-time data integration for robust disaster response.

Additional Information

• INCOIS Achievements
• Developed early warning solutions to safeguard lives and property in coastal regions.
• Internationally recognized for tsunami warning capabilities, particularly after the 2004 Indian Ocean tsunami.
• Significance of the Award
• Named after Netaji Subhash Chandra Bose, reflecting courage and dedication to public service.
• Awards individuals and organizations demonstrating exemplary work in disaster risk reduction and management.

The correct answer is 1872.

Key Points

• A population census is the method by which demographic, social, cultural and economic data relating to each and every person in that country are compiled, collected, analysed and disseminated at a specific time over 10 years.
• The first census was conducted in India in 1872, but regular census started in 1881.
• The first census in all India was conducted by the British Raj authorities.

Additional Information

• The 15th Census of India and the 7th Census of Independent India-2011 was started on 1st April 2010 with President being the first citizen to be enumerated, followed by the Vice President of India.
• The slogan of census 2011 was ‘Our Census, Our future’.
• C. Chandramouli was the Census Commissioner of India 2011.
• The population of the nation as per the provisional figures of Census 2011 is 1210.19 million of which 623.7 million (51.54%) are males and 586.46 million (48.46%) are females.
• Uttar Pradesh is the most populous state in India its population is more than the population of Brazil.

Thus, first census started in 1872.

The correct answer is: Similar, Similar

Key Points

• A group of similar cells performing similar functions is known as tissue.
• A tissue is an ensemble of similar cells and their extracellular matrix from the same origin that together carry out a specific function.
• Organs are then formed by the functional grouping together of multiple tissues.

Additional Information

• Types of tissues:
• Classification of tissues can be done in two parts, first is animal tissues, and the second one is plant tissues.
• Animal tissues: The function of animal tissues differs from organism to organism. There are four types of animal tissues-
• Connective Tissues:
• Help in maintaining the form of the organism’s body as well as its organs.
• These tissues also provide internal support to the body.
• They help in holding the organs together.
• They also resist the entering of pathogens in the body.
• There are various forms of connective tissues, such as bone ligaments, tendons, cartilage, etc.
• Connective tissues can be further divided into fibrous, fluid, and skeletal connective tissue
• Muscles Tissues:
• Muscle tissues, as the name suggests, helps in the movement of the body.
• They produce force and generate motion for the movement of the body as well as movement inside organs.
• There are three types of muscle tissues; mainly, they are skeletal, cardiac, and visceral or smooth muscle tissue.
• Nervous Tissues:
• The tissues that are mainly associated with the central nervous system are known as nervous tissue.
• They are mainly found in the brain and spinal cord.
• This tissue is responsible for the communication network inside the body.
• Epithelial Tissues:
• These are the tissues that cover outer parts of the body organs such as the skin, the digestive tract’s inner lining, etc.
• They perform various functions such as act as a sensory reception, helps in filtration and certain other metabolic activities as well.
• It also helps in various processes like diffusion and secretion. Epithelial tissues protect internal organs from pathogens as well.

The correct answer is Tropical Deciduous Forests.

Important Points

• Tropical deciduous forests are also called monsoon forests because the trees in these forests shed their leaves during the dry season and re-grow during the monsoon.

Key Points

• Tropical Evergreen Forests:
• These types of forests are found in the equatorial and tropical regions with more than 200 cms annual rainfall.
• The leaves of trees in such forests are very wide.
• Example: Mahogany, Redwood, Palm, etc.
• Tropical Deciduous Forests:
• These are popularly known as monsoon forests.
• The trees in these types of forests shed their leaves during the dry season and re-grow during the monsoon.
• These types of forests receive rainfall in the range of 70-200 cms.
• These types of forests are further classified as Moist Deciduous Forests and Dry Deciduous Forests.
• Montane Forests:
• In these types of forests, vegetation varies according to altitude.
• Mangrove forests:
• These are formed along the banks of river estuaries.
• These are also called Tidal Forests.
• Mangrove forests of Sundarbans are the largest mangrove forests in the world.

The correct answer is Ecuador.

In News

• President Daniel Noboa of Ecuador declared a 60-day state of emergency in seven provinces, including Guayas and Manabí.
• The decision was made to address rising crime and combat organized armed groups.

Key Points

• The emergency measures include the suspension of home and correspondence inviolability.
• Night curfews have been implemented in 20 cantons to maintain public safety.
• Ecuador is fighting internal armed conflict against criminal groups labeled as terrorists.
• Guayas and Manabí are among the seven provinces under the state of emergency.

Additional Information

• State of Emergency
• A legal declaration used by governments to address crises requiring extraordinary measures.
• Involves temporary suspension of normal laws and enforcement of special rules to ensure public safety.
• Ecuador
• A country located in northwestern South America, bordered by Colombia, Peru, and the Pacific Ocean.
• Known for its biodiversity, the Galápagos Islands, and challenges with organized crime in recent years.
• Ecuador capital: Quito.

The correct answer is Igneous.

Important Points

• The igneous rocks (Ignis – in Latin means ‘Fire’) are formed when magma cools and solidifies.
• As igneous rocks form out of magma and lava from the interior of the earth, they are known as primary rocks.
• When magma in its upward movement cools and turns into a solid form it is called igneous rock. Hence, option 3 is the correct answer.
• The process of cooling and solidification can happen in the earth’s crust or on the surface of the earth.

Additional Information 

• Igneous rocks are classified based on texture.
• The texture depends upon the size and arrangement of grains or other physical conditions of the materials.
• If molten material is cooled slowly at great depths, mineral grains may be very large.
• Sudden cooling (at the surface) results in small and smooth grains.
• Intermediate conditions of cooling would result in intermediate sizes of grains making up igneous rocks.
• Granite, gabbro, pegmatite, basalt, volcanic breccia, and tuff are some examples of igneous rocks.

The correct answer is Karnam Malleshwari.

Key Points

Karnam Malleswari:

• At the Sydney 2000 Olympic Games, weightlifter Karnam Malleswari marked her place in Olympic and Indian sports history.
• As she lifted 110 kg in the “snatch” and 130 kg in the “clean and jerk” for a total of 240 kg, she took the bronze medal and became India’s first woman to win an Olympic medal.

Important PointsPV Sindhu:

• PV Sindhu became the first Indian woman athlete to win two individual Olympic medals as she won the bronze medal at the Tokyo Olympics.
• She had won the silver medal at the 2016 Rio Olympics.

The Correct Answer is Wheat.

Key Points

• Kharif Season:
• Kharif crops also are known as monsoon crops as they are cultivated in the monsoon season.
• These crops are sown at the beginning of the rainy season.
• Rice, maize, bajra, ragi, paddy, sorghum, soybean, groundnut, cotton, etc are all Kharif types of crops.
• Zaid Season:
• It is a short season between Kharif and Rabi seasons.
• The crops grown during this season are known as Zaid crops.
• Pumpkin, cucumber, watermelon, bitter gourd etc are all zaid types of crops.
• Rabi Season:
• These are the crops that are sown at the end of the monsoon season or at the beginning of the winter season.
• These crops also are known as winter crops.
• Wheat, Mustard, Pulses, Barley, etc. are all Rabi types of crops.

The correct answer is The Palas, The Pratiharas and The Rashtrakutas.

Key Points

• The Tripartite Struggle for Kanauj had happened between
• The Palas of Bengal.
• The Pratiharas of Central India.
• The Rashtrakutas of Deccan.
• ​​The struggle lasted for 200 years and weakened all of them which enabled the Turks to overthrow them.
• Medieval History of India: 
• The period of Medieval History of India lies between the 8th and the 18th century A.D.
• The medieval period is a crucial period in the history of India because of the developments in the field of languages, art, religion & culture.
• The period has proved the effect of other religions on the Indian culture.
• Rise of the Rajput clans is the beginning of the Medieval period.
• Division of Medieval history: 
• The medieval period is generally divided into two stages:
• Early medieval period(8th – 12th century A.D): 
• The early medieval period was a major characterized by regional political & social development.
• The regional kingdoms had softened boundaries.
• They were less defined political by administration and coalition than communal affiliation, temple, language.
• Later Medieval period(12th-18th century A.D): 
• The late medieval age began around 1200 AD.
• The period was characterized in part by Islamic conquests.
• It was made possible by the sheer multiplicity of states in the subcontinent.

The correct answer is the Northern Malabar region.

Key Points

• The major industrial region in India
• Mumbai-Pune Industrial Region​
• The Hugli Industrial Region
• Bengaluru-Tamil Nadu Industrial Region
• Gujarat Industrial Region
• Chotanagpur Industrial Region
• Vishakhapatnam-Guntur Industrial Region
• Gurgaon-Delhi-Meerut Industrial Region
• Kollam-Thiruvananthapuram Industrial Region

Additional Information 

• Mumbai-Pune industrial region:  There are more than 8000 registered factories only in greater Mumbai, out of which 350 belong to cotton textiles.
• ​The other industries of the region are engineering goods, chemical industries, food processing industries, leather goods, pharmaceuticals, and film industries.
• Chotanagpur in Jharkhand; This industrial region cover Jharkhand, Odisha, Southern Bihar, and western parts of West Bengal. Having a large concentration of iron and steel industry, it is often called as the ‘Ruhr of India’.
• Vishakhapatnam-Guntur Industrial Region; Agriculture and rich mineral resources in the hinterlands of these ports provide a solid base to industrial growth in this region. Coal fields of the Godavari basin are the main source of energy.
• ​The petroleum refinery at Visakhapatnam facilitated the growth of several petrochemical industries.
• Vishakhapatnam has the most modern iron and steel plant.

The correct answer is Maihar

Key Points 

• In Ustad Allauddin Khan honor, a Sangeet Samaroh is organized annually in Maihar, Satna
• It is organized by the Ustad Allauddin Khan Sangeet Academy in collaboration with the Madhya Pradesh Sanskriti Parishad.
• Allauddin Khan Sangeet Samaroh of Maihar is a three-day festival.
• Allauddin Khan totally reshaped Indian classical music's Maihar Gharana.
• Allauddin Khan was also known as Baba Allauddin Khan.
• He was an Indian sarod player.

• The correct answer is option 4, i.e., Decreases 1000 times.
• When its pH changes to 6, then H+ ion concentration, decreases 1000 times.
• pH tells the concentration of hydrogen ions, lower the pH, higher is the hydrogen ion concentration.
• Acids have pH ranging from 1-6, pH 7 denotes neutral solution, and pH in the range of 8-14 denotes bases.
• The formula for calculating pH is: pH = - log [H +]
• pH of 3 = 10 -3 H +
• pH of 6 = 10 -6 H +
• From the above values, we can clearly see that H + ion concentration decreases by 1000 times.

The correct answer is option 4 i.e., Qutub-ud-din Aibak

• Qutub-ud-din Aibak was the founder of the Slave dynasty in India, who ruled from 1206 to 1210.
• Qutub-ud-din Aibak was also known as Lakh Baksha Sultan because of his generosity.
• He laid the foundation of Qutub Minar which was later completed by Iltutmish.
• The Quwwat-al-Islam mosque was also commissioned by him.
• He built the famous 'Adhai Din Ka Jhonpra' mosque in the city of Ajmer, Rajasthan.
• In 1210, while playing Chaugan, he fell from the horse and died. His tomb is located in Anarkali Bazaar at Lahore.

The correct answer is Bull type.

Key Points

• Five types of gold coins issued by Skandagupta are Archer type, Horseman type, King and queen type, Lion-slayer type and Chhatra type.
• Also, Skandagupta issued 4 types of silver coins Altar type, Garuda type, Madhyadesha type and Bull type.

Bull type is a type of silver coin issued by Skandagupta.

It is not a type of Gold coin.

So bull type will be the correct answer.

Additional Information

• Skandagupta
• He was a ruler of the Gupta dynasty.
• His period was from 455 AD to 467 AD.
• He defeated Hunas.
• He restored the Gupta empire from his enemies.
• He composed the Bhitari Inscription which was written in 19 lines that describe the ancestors of Skandagupta, about himself and his achievements.
• The Bhitakari Inscription also mentions the Skandagupta's conflict with Pushyamitra.

The correct answer is option 4.

Key Points

• B.R. Ambedkar is known as the sculptor of the Indian constitution.
• He was the chairman of the drafting committee.

Additional Information

• V.V. Giri
• He served as the 4th president of India.
• He is the only person to be elected as president as an independent candidate.
• Received Bharat Ratna in 1975.
• Rajendra Prasad
• He was the first president of the Republic of India.
• He was the President of the constituent assembly.
• Dr. S. Radhakrishnan
• He was the 2nd president of India.
• He was the 1st Vice president of India.

The correct answer is Democracy.

Key Points

Indian political system:

• India is a parliamentary democratic secular republic in which the president of India is the head of state & first citizen of India.
• The preamble declares India to be a sovereign, socialist, secular and democratic republic.
• The term Democratic implies that the Constitution of India has an established form of Constitution which gets its authority from the will of the people expressed in an election.

​Democracy:

• Democracy is a form of government in which rulers are elected by the people in a free and fair election, on a universal adult franchise and governed on the basis of certain fundamental rules like a constitution.
• Democracy is more accountable than other governments to its people, responding to their needs, and sensitivities.
• According to Dr Bhimrao Ambedkar, one of the founders of the Indian Constitution, 'Democracy means a way of life which consists of the basic principles of freedom, equality, and fraternity.'
• "Government of the people, by the people and for the people" were the words used by Abraham Lincoln in the year 1863 while talking about democracy.

The Correct answer is Hydrogen.

Key Points

• When an acid reacts with a metal, a displacement reaction takes place in which the metal displaces the hydrogen from the acid to form a salt, and the hydrogen (H2) gas is released**.**
• Acid + Metal → Salt + Hydrogen
• Example: Mg + HCl = MgCl₂ + H₂
• The salt that is produced depends upon which acid and which metal reacts.

Additional Information

• Metals readily react with acid and produce hydrogen gas which burns with a pop sound.
• Metals are placed above hydrogen in reactivity series and displace during a reaction with an acid.
• As acids have the property of giving H+ ions.
• A resultant is formed with the release of hydrogen gas.
• It doesn't matter which metal or which acid is used if there is a reaction we always get hydrogen gas as well as salt.
• However, how quickly the reaction goes depends on the metal used and how high up in the reactivity series it is.

The correct answer is Australia, France, USA, U.K., India, Indonesia, Malaysia, Singapore, and Canada.

In News

• INS Mumbai, an indigenously built destroyer, is participating in the 4th edition of Exercise La Perouse.

Key Points

• Countries participating include India, Australia, France, USA, U.K., Indonesia, Malaysia, Singapore, and Canada.
• Exercise focuses on maritime surveillance, air defense, and tactical interoperability.
• Includes complex multi-domain exercises for enhanced operational synergy.
• Aligns with India’s SAGAR vision for a secure Indo-Pacific region.

Additional Information

• SAGAR Vision
• Security and Growth for All in the Region, India’s strategic initiative for maritime cooperation.
• Exercise La Perouse
• Multinational naval exercise aimed at enhancing tactical interoperability and maritime cooperation.
• INS Mumbai
• An indigenously built guided missile destroyer of the Indian Navy.

The correct answer is salvation.

Key Points

• Ramakrishna Mission (RKM) is a Hindu religious and spiritual organization that forms the core of a worldwide spiritual movement known as the Ramakrishna Movement or the Vedant
• The mission is named after and inspired by the Indian saint Ramakrishna Paramahamsa and founded by Ramakrishna's chief disciple Swami Vivekananda on 1st May 1897.
• The mission bases its work on the principles of karma yoga, the principle of selfless work done with a dedication to God.
• The Ramakrishna Mission has centered around the world and publishes many important Hindu texts.
• It is affiliated with the monastic organization. Vivekananda was greatly influenced by his guru (teacher) Ramakrishna.
• The motto of the mission is - Atmano mokshartham Jagat hitaya cha (For one’s own salvation and for the welfare of the world).

Additional Information

• Swami Vivekananda
• His original name was Narendranath Dutt.
• He attended the Parliament of Religions held at Chicago in 1893 AD and published two papers, Prabhudhha Bharat in English and Udbodhana in Bengali.
• He urged people to inculcate the spirit of liberty, equality and free-thinking.
• He worked for the emancipation of women.
• He emerged as a preacher of Neo-Hinduism.
• He advocated the Doctrine of Service–the service of all human beings.
• He was considered the spiritual father of the modern nationalist movement.

The correct answer is All of these. ​

Key Points

• The Green Revolution was a period that began in the 1960s, during which agriculture in India was transformed into a modern industrial system, such as high-yielding variety (HYV) seeds, mechanized farming equipment, irrigation facilities, use of pesticides. and fertilizers.

Important Points

• The term green revolution was first used by William Gaud and Norman Borlaug is the Father of the Green Revolution.
• In the year 1965, the government of India launched the Green Revolution with the help of a geneticist, now known as the father of the Green revolution (India) M.S. Swaminathan.

The correct answer is Tamil Nadu.

Key Points

• The Gulf of Mannar Marine Biosphere Reserve is located along the southeastern coast of India in the state of Tamil Nadu.
• It was established in 1986 and is the first marine biosphere reserve in Southeast Asia.
• The reserve spans over an area of approximately 10,500 square kilometers and includes 21 islands and adjacent coral reefs.
• It is part of the larger Gulf of Mannar, which is known for its rich marine biodiversity, including various species of fish, coral, and other marine organisms.
• The reserve is managed by the Tamil Nadu Forest Department and is also recognized under the Man and Biosphere Programme by UNESCO.

Additional Information

• Coral Reefs: The Gulf of Mannar is home to one of the richest coral reef ecosystems in the world, with over 100 species of coral.
• Marine Biodiversity: The reserve supports a diverse range of marine life, including endangered species such as the dugong (sea cow) and several species of sea turtles.
• Conservation Efforts: The area is protected under the Wildlife Protection Act of 1972, and various conservation programs are in place to preserve its biodiversity.
• Economic Importance: The Gulf of Mannar is crucial for the local economy, providing livelihoods through fishing, seaweed collection, and tourism.
• Research and Education: The reserve serves as a site for scientific research and environmental education, promoting sustainable use of marine resources.

The correct answer is Dhamma-mahamatta.

• Dhamma-mahamatta was a group of officers instituted to implement and publicize the various aspects of Dhamma.
• Ashoka made them responsible for carrying his message to various sections of society.
• Later they became very powerful and started interfering with state politics.

Additional Information

• Ashoka also is known as "Devanampiya".
• Piyadasi was the son of Mauryan Emperor Bindusara and was born in 304 BC.
• His reign lasted from 268 BC to 232 BC.
• Once he became King, he started expanding his empires by conquest, in the 8th year of his reign he waged a war with Kalinga (present-day Odisha).
• Ashoka's 13th Rock edicts describe the Kalinga war.
• Source of Information about Ashoka:
• There are two main source - 
• Buddhist sources
• Ashoka's edicts
• Ashoka's inscription can be classified into three - 
• Pillar edicts
• Major rock edicts
• Minor rock edicts
• Ashoka uses his name only in four of these places namely 
• Maski
• Brahma Giri (Karnataka)
• Gujjara (MP)
• Nettur (AP)

The correct answer is Sundarban Tiger Reserve

In News

• 154 species of birds were spotted during the third Sundarban Bird Festival held from January 22-26, 2025.

Key Points

• The birding event, aimed at promoting avifauna, included 51 migratory species and 103 resident species.
• Key findings:
• 45 species of waders, mudflat, and shore birds
• 8 species of raptors
• 91 species of forest birds
• 3 species of waterfowl
• 7 species of other birds
• Notably, 12 threatened species were recorded, such as the Eurasian Curlew and Brown-winged Kingfisher.
• The Sundarban Tiger Reserve played a central role, with significant numbers recorded in core and buffer zones.
• The Sundarban region, spanning 4,000 sq. km, is home to about 100 tigers.
• The exercise showed a rise in species diversity compared to previous years (145 species in 2023 and 135 in 2024).

The correct answer is The Vice-President.

Key Points

• The legislature or the Parliament is made of 3 components -
• The President
• The Lok Sabha
• The Rajya Sabha
• The Vice-President is not a member of Parliament unlike the Speaker of Lok Sabha who is a member of the Parliament by the virtue of being an MP.
• Thus, option 2 is the correct answer.

Additional Information 

• As per article 79 of the Constitution, the Parliament of India consists of the President, the Lok Sabha and the Rajya Sabha.
• The President is a part of the legislature, even though he or she does not sit in Parliament.
• The main functions of Parliament are - 
• Control of the Cabinet.
• Criticism of the Cabinet and of individual Minister.
• Parliament secures the information authoritatively.
• Legislation i.e. making laws.
• Financial control.
• Bill passed by the House of Parliament cannot become law without the President's assent.

The correct answer is Karnataka

In News

• Karnataka's forest department has introduced the Garudakshi portal for online FIR registration related to wildlife and forest offenses.

Key Points

• Pilot implementation: The system is being rolled out in Bengaluru Urban, Bhadravathi, Sirsi, and Male Mahadeshwara Wildlife Sanctuary divisions initially.
• Phase-wise expansion: Based on feedback, the portal will be extended to other divisions across the state.
• Software features: Garudakshi includes a Legacy Case Registration Module, Online Forest Offense Registration, Investigation Module, and Reporting and Analytics Module to streamline the process.
• Public involvement: The portal will also enable the public to file complaints about forest offenses via mobile phones or email.

The correct answer is Buddhism.

Key Points

• Jataka tales are works of literature that are about Gautam Buddha's previous births.
• Buddhism: Buddhism is a faith that was founded by Siddhartha Gautama ("the Buddha") in 5th Century B.C.
• The Buddhism religion is based upon the teachings, life experience of its founder Siddhartha Gautam, born in circa 563 BCE.

Additional Information

• Lingayat: Lingayat also called Virashaiva, a member of a Hindu sect with a wide following in southern India that worships Shiva as the only deity.
• Shaivism: Shaivism is the branch of Hinduism that worships Shiva as the supreme deity. It is one of the major branches of Hinduism.
• Jainism: Jainism is a religion that emphasizes complete non - violence, and asceticism.
• Followers of Jainism are called Jains.
• J ainism came into prominence in the 6th century B.C, when Lord Mahavira propagated the religion.
• There were 24 great teachers, the last of whom was Lord Mahavira.
• The first Tirthankara was Rishabnatha.

The correct answer is Ministry of Culture

In News

• Union Minister for Culture and Tourism Gajendra Singh Shekhawat inaugurated Kalagram this evening at Mahakumbh Nagar in Prayagraj. Ministry of Culture has created Kalagram which will showcase the rich and vibrant culture of the country.

Key Points

• Kalagram showcases India's vibrant culture through Craft, Cuisine, and Culture.
• Over 14,600 artists will perform at Kalagram during the 45-day event.
• The initiative offers visitors a chance to explore India's cultural heritage.
• Mahakumbh symbolizes unity and devotion, expecting 45 crore devotees and 15 lakh foreign tourists over the 45 days.

The correct answer is India Exposition Mart Ltd, Greater Noida.

In News

• Shri Chirag Paswan, Union Minister of Food Processing Industries, will inaugurate the 8th Edition of Indusfood 2025 at India Exposition Mart Ltd, Greater Noida, on January 8, 2025.

Key Points

• Indusfood 2025 is Asia’s premier annual F&B trade exhibition, organized by the Trade Promotion Council of India (TPCI) with support from the Department of Commerce, Government of India.
• This edition will host 2,300 exhibitors from over 30 countries and over 7,500 international buyers.
• Concurrent events include Indusfood Manufacturing and Indusfood Agritech, to be held in Yashobhoomi Dwarka, New Delhi, from January 9-11, 2025.
• The event format promotes integration across the farm-to-fork value chain and offers networking and knowledge-sharing opportunities.

Additional Information

• Indusfood Manufacturing: Focuses on food processing, packaging, and hospitality technology.
• Indusfood Agritech: Showcases agricultural, fisheries, dairy, and poultry farming technology.
• Asia President’s Forum: Hosted in India for the first time, bringing together presidents of national chef associations from over 30 Asian countries.

Let the original price of the sugar for 1kg be ‘x’.

Number of kgs = 36/x.

After 20% decrease in price of sugar he can buy 500g more sugar for Rs. 36.

(\Rightarrow \left( {\frac{{36}}{x} + \frac{1}{2};} \right) × \left( {x - \frac{{20}}{{100}}x} \right) = 36)

⇒ 36(0.8) + 0.5(0.8x) = 36

⇒ 0.5(0.8x) = 36 – 36(0.8) = 7.2

⇒ 0.4x = 7.2

⇒ x = 18

∴ The original price of sugar per kg = Rs. 18

20% = 20/100 = 1/5

If Initial price = 5 

then Final price = 4

Quantity α 1/Price

So Initial quantity : Final Quantity = 1/5 : 1/4 = 4 : 5

According to question (5 - 4) = 1 = 500 grams = 0.5 kg

So the initial quantity 4 × 0.5 = 2 Kg

∴ Initial (Original) price per kg = 36/2 = Rs. 18

Let the width of floor be x m

⇒ Length of the floor = x × 125/100 = 1.25x

As we know,

Area of the floor = length × width

According to the question

x × 1.25x = 20

⇒ x² = 20/1.25

⇒ x² = 16

⇒ x = √16

⇒ x = 4

∴ Sum of length and width of the floor = x + 1.25x = 2.25x = 2.25 × 4 = 9 m

Given:

Total chair = 7 + 5 + 8 = 20

Formula used:

Average = Sum of terms/Number of terms

Calculation:

Cost price of 1 chair = Rs. 3500

Cost price of 8 chair = 3500 × 8 = Rs. 28000

Cost price of 1 chairs = Rs. 3000

Cost price of 7 chairs = 3000 × 7 = Rs. 21000

Cost price of 1 chairs = Rs. 2200

Cost price of 5 chairs = 2200 × 5 = Rs. 11000

Total cost of all 20 chairs = (28000 + 21000 + 11000) = 60000

Average cost of chair = 60000/20 = Rs. 3000

∴ Average cost of chair is Rs. 3000

Total profit in 6 years by company B = (30 + 20 – 10 + 20 – 20 – 10) lakh = 30 lakh

Total profit in 6 years by company A = (20 + 10 – 10 + 0 + 20 + 30) lakh = 70 lakh

∴ Required ratio = 30 : 70 = 3 : 7

Concept used:

For a number to be divisible by 11, the difference between the sum of digits at an even place and odd place either be 0 or 11.

Calculation:         

For a number A9257B684

Sum of digits at even place = 9 + 5 + B + 8 = 22 + B

Sum of digits at odd place = A + 2 + 7 + 6 + 4 = 19 + A

Case (1) - When both sums are equal

A + 19 = B + 22

⇒ A - B = 3

Case(2) - When the difference of the sums is 11

A + 19 - (B + 22) = 11    

⇒ A + 19 - B- 22 = 11

⇒ A - B - 3 = 11

⇒ A - B = 14 

Case(3) - When the difference of the sums is 11

B + 22 - (A + 19) = 11    

⇒ B + 22 - A - 19 = 11

⇒ B - A + 3 = 11

⇒ A - B = -8 

∴ The smallest value of (A - B) will be -8.

Let D = 100

C = 100 × 110/100 = 110

B = 110 × 80/100 = 88

A = 88 × 125/100 = 110

From option 1

B is less than A by (110 – 88)/110 × 100 = 20%

option 1 is not true

Let the MP of the table be x

x × (9/10) × (8/10) = 18x/25

Single equivalent discount (\left( {\frac{{{\rm{x;}}-{\rm{;}}\frac{{18{\rm{x}}}}{{25}}}}{{\rm{x}}}{\rm{}} × {\rm{}}100} \right)) = [7x/25x] × 100 = 28%

ALTERNATIVE METHOD :

Equivalent Discount = a + b – a × b/100

⇒ 20 + 10 – 20 × 10/100

⇒ 28%

Shortcut Trick

Total sum of P, Q and R = 150 × 3 = 450 cms

Sum of P and Q = 150 × 2 = 300 cms

Sum of Q and R = 155 × 2 = 310 cms

Height of Q = (Sum of P&Q) + (Sum of Q&R) − (Sum of P, Q & R)

Height of Q = 300 + 310 − 450 = 160 cms

∴ The correct answer is 160 cms.

Alternate Method

Given:

Average height of P, Q, and R = 150 cms

Average height of P and Q = 150 cms

Average height of Q and R = 155 cms

Formula Used:

Total Sum = Average × Number of observations

⇒ Sum (P + Q + R) = 150 × 3 = 450 cms --- (i)

⇒ Sum (P + Q) = 150 × 2 = 300 cms --- (ii)

⇒ Sum (Q + R) = 155 × 2 = 310 cms --- (iii)

⇒ Adding (ii) and (iii): P + 2Q + R = 300 + 310 = 610 cms

⇒ (P + Q + R) + Q = 610 cms

⇒ Substituting (i) in the above equation:

⇒ 450 + Q = 610

⇒ Q = 610 − 450

⇒ Q = 160 cms

∴ The correct answer is 160 cms.

Additional Information

Fundamental Average Formula

The average of n observations is the ratio of the sum of observations to the total number of observations: Average = Sum ÷ n.

Finding a Common Element

When a group is divided into two overlapping subgroups, the common element is calculated as: Common Value = (Sum of Subgroup 1 + Sum of Subgroup 2) − Total Sum.

Effect of Constant Addition

If a constant value k is added to every observation in a set, the new average will also increase by k.

Let the cost price and selling price of per article are CP and SP.

Given, Loss = 8 × SP

Also,

Loss = 72 × CP – 72 × SP

⇒ 8 × SP = 72 × CP – 72 × SP

⇒ 80 × SP = 72 × CP

⇒ CP/SP = 80/72

Loss percentage = (80 - 72)/80 × 100 = 10%

Let SP of an article = Re 1

Hence, total SP = 72 and loss = 8

now, CP = SP + loss = 80

Loss percentage = (8/80) × 100 = 10%

Shortcut Trick

Total work = LCM(8, 12) = 24 units.

Combined efficiency of Kira and Kiki = 24 ÷ 8 = 3 units/day.

Kiki's efficiency = 24 ÷ 12 = 2 units/day → Kira's efficiency = 3 − 2 = 1 unit/day.

Work done in 4 days together = 3 × 4 = 12 units.

Remaining work = 24 − 12 = 12 units.

Kira's time for remaining work = 12 ÷ 1 = 12 days.

∴ The correct answer is 12 days.

Alternate Method

Given:

Time taken by Kira and Kiki together = 8 days

Time taken by Kiki alone = 12 days

Formula Used:

Total Work = Efficiency × Time

Efficiency = Total Work ÷ Time

Calculations:

⇒ Efficiency of Kira = (Efficiency of Kira + Kiki) − Efficiency of Kiki

⇒ Efficiency of Kira = 3 − 2 = 1 unit/day

⇒ Work done by both in 4 days = Combined Efficiency × Time

⇒ Work done = 3 × 4 = 12 units

⇒ Remaining work = Total Work − Completed Work

⇒ Remaining work = 24 − 12 = 12 units

⇒ Time taken by Kira to finish remaining work = Remaining Work ÷ Kira's Efficiency

⇒ Time = 12 ÷ 1 = 12 days

∴ The correct answer is 12 days.

Additional Information

Work and Wages

Wages are distributed in the ratio of the efficiency of the workers if they work for the same amount of time, or in the ratio of the actual work done by each.

Negative Work (Pipes & Cisterns)

When a person or pipe undoes the work (like a leak), its efficiency is taken as negative in the combined efficiency calculation.

Alternate Day Work

For alternate work, calculate the total work done in one complete cycle (e.g., 2 days) and then find the number of cycles required to reach the total work.

Given:

A truck drove 40 km starting at 9 pm and met with an accident at 11 pm, due to which It reduced its speed by 50% and reached the destination in 9 hours

Formula:

Distance = speed × time

Calculation:

The truck drove 40 km in 2 hours.

⇒ Speed of truck = 40/2 = 20 km/hr

⇒ Reduced speed of truck = 10 km/hr

It took further 9 hours

⇒ Distance travelled = 10 × 9 = 90 km

⇒ Total distance of journey = 40 + 90 = 130 km

 the required time when no accident had occurred = 130/20 = 6.5 hours

∴ Required time = 130/20 = 6.5 hours

Shortcut Trick

Use the constant ratio formula: SP₁ / (Qty₁ × %Value₁) = SP₂ / (Qty₂ × %Value₂)

Here, %Value = (100 − Loss%) or (100 + Gain%)

60 / (50 × 90) = 20 / (n × 120)

1 / 75 = 1 / 6n

6n = 75 ⇒ n = 12.5

∴ The correct answer is 12.5.

Alternate Method

Given: SP₁ = ₹60, Qty₁ = 50 lemons, Loss = 10%, Target Profit = 20%, Target SP₂ = ₹20.

Formula: CP = SP × 100 / (100 − Loss%) | New SP = CP × (100 + Gain%) / 100

CP (100%) Loss 10% SP1 = 90% CP Gain 20% SP2 = 120% CP Quantity ∝ 1/Price (for same total SP)

⇒ SP of 1 lemon (Case 1) = 60 ÷ 50 = ₹1.2

⇒ CP of 1 lemon = 1.2 × 100 ÷ 90 = 120 ÷ 90 = ₹4/3

⇒ Required SP per lemon for 20% gain = (4/3) × 120 ÷ 100 = 4 × 1.2 ÷ 3 = ₹1.6

⇒ Total lemons to be sold for ₹20 = Total Amount ÷ SP per lemon

⇒ Number of lemons = 20 ÷ 1.6 = 200 ÷ 16 = 12.5

∴ The correct answer is 12.5.

Additional Information

Unitary Method for Quantity

When the total expenditure remains constant, the ratio of quantities is inversely proportional to the ratio of price per unit.

Profit/Loss on Selling Price

CP = (SP × 100) ÷ (100 ± P/L%). If SP and CP are known, Profit% = (SP − CP) ÷ CP × 100.

Successive Percentage for Profit

If an item is sold at a loss and then a profit is desired, the total change factor is (1 ± r₁/100) × (1 ± r₂/100).

Shortcut Trick

Effective rate for half-yearly compounding = 20% ÷ 2 = 10%.

Ratio of Amount to Principal = 13310 ÷ 10000 = 1331 : 1000.

Since 1331 : 1000 = (11 : 10)³, there are 3 half-yearly periods.

Time = 3 ÷ 2 = 1.5 years = 1½ years.

∴ The correct answer is 1½ years.

Alternate Method

Given:

Principal (P) = ₹10,000

Amount (A) = ₹13,310

Rate (R) = 20% per annum

Compounding: Half-yearly

Formula Used:

A = P(1 + r/100)ⁿ

Where r = R ÷ 2 (half-yearly rate) and n = 2 × Time in years.

Calculations:

⇒ Half-yearly rate (r) = 20% ÷ 2 = 10%

⇒ 13310 = 10000(1 + 10/100)ⁿ

⇒ 13310 ÷ 10000 = (110/100)ⁿ

⇒ 1331 ÷ 1000 = (11/10)ⁿ

⇒ (11/10)³ = (11/10)ⁿ

⇒ n = 3 half-years

⇒ Time = 3 ÷ 2 years = 1.5 years

∴ The correct answer is 1½ years.

Additional Information

Half-Yearly Compounding Rule

When interest is compounded half-yearly, the annual rate is divided by 2 and the time is multiplied by 2 for calculation in the standard formula.

Quarterly Compounding Rule

When interest is compounded quarterly, the annual rate is divided by 4 and the time is multiplied by 4.

Compound Interest Formula

Total Amount (A) = P(1 + r/100)ⁿ, and Interest (CI) = A − P.

Given:

Time taken by the train to cover 610 m = 50 sec

Time taken by the train to cover 450 m = 42 sec

Formula used:

Time = Distance/Speed

1 m/s = (18/5) km/h

Calculation:

Let the speed of the train be s m/s and the length be l.

Time taken by the train to cover 610 m = 50 sec

⇒ (l + 610)/s = 50

⇒ l + 610 = 50s

⇒ l = 50s - 610

Time taken by the train to cover 450 m = 42 sec

⇒ (l + 450)/s = 42 sec

⇒ l + 450 = 42s

⇒ l = 42s - 450

Now, 50s - 610 = 42s - 450

⇒ 50s - 42s = 610 - 450

⇒ 8s = 160 

⇒ s = 20 m/s

⇒ s = 20 × (18/5) km/h

⇒ s = 72 km/h

Again, l = 50s - 610

⇒ 50 × 20 - 610

⇒ 1000 - 610 

⇒ 390 m

∴ The statement I is correct.

Let the the number of C be 100

Number of B = 100 × (200/100) = 200

Number of A = 100 × (150/100) = 150

A get number less than B by = 200 – 150 = 50

A get number less than B by (in %) = 50/200 × 100 = 25%

Shortcut Trick

For a period of 3 years, the difference (D) between Compound Interest and Simple Interest is given by the formula: D = P(R/100)² × (3 + R/100)

Given: Principal (P) = ₹1000, Rate (R) = 5%

D = 1000 × (5/100)² × (3 + 5/100)

D = 1000 × (1/400) × (3.05) = 2.5 × 3.05 = ₹7.625

Rounding to the nearest option, we get ₹7.6.

∴ The correct answer is ₹7.6.

Alternate Method

Given:

Principal (P) = ₹1000

Rate (R) = 5% per annum

Time (T) = 3 years

Formula Used:

Simple Interest (SI) = (P × R × T) / 100

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

Calculations:

⇒ SI = (1000 × 5 × 3) / 100 = ₹150

⇒ CI = 1000[(1 + 5/100)³ − 1]

⇒ CI = 1000[(21/20)³ − 1]

⇒ CI = 1000 × (9261/8000 − 1) = 1000 × 1261/8000

⇒ CI = 1261/8 = ₹157.625

⇒ Difference = CI − SI = 157.625 − 150 = ₹7.625

⇒ Difference ≈ ₹7.6

∴ The correct answer is ₹7.6.

Additional Information

Difference for 2 years

The difference between CI and SI for 2 years is D = P(R/100)².

Effective Rate for CI (3 Years)

The effective interest rate for CI over 3 years is 3R + 3R²/100 + R³/10000 percent.

Finding Principal from Difference

If the 3-year difference (D) is known, Principal (P) = (D × 10⁶) / [R² × (300 + R)].

Calculation:

The total number of illiterates in A, B and C is  20 + 14 + 22 = 56%

The total number of illiterates in D is 44%

The required percentage is (56 /44) × 100 = 127.27 %

∴ The correct option is 2

Given:

4.(\overline {31} ) + 5.(\overline {12} ) + 3.(\overline {21} )

Calculations:

According to the question, we have

Let the value of x, y and z be 4.(\overline {31} ) + 5.(\overline {12} ) + 3.(\overline {21} )

⇒ x = 4.3131...      ----(1)

Multiply both sides by 100

⇒ 100x = 100 × 4

⇒ 100x = 431.31...      ----(2)

Subtract (1) from (2), we have

⇒ 100x – x = 431.31 - 4.31

⇒ 99x = 427

⇒ x = 427/99      ----(3)

Similarly, we can solve other two values

y = 5.(\overline {12} ) = 507/99      ----(4)

And, z = 3.(\overline {21} ) = 318/99      ----(5)

Now, add the values of (3), (4) and (5), we get

⇒ x + y + z = (427/99) + (507/99) + (318/99)

⇒ x + y + z = 1252/99

∴ The value of 4.(\overline {31} ) + 5.(\overline {12} ) + 3.(\overline {21} ) is 1252/99

We can solve this question by short method:

Write the number and subtract the non-repeated part and divide the result by as many as 9 as repeat part followed by and as many as 0 as non-repeating decimal

 ⇒ 4.(\overline {31} ) = (431 – 4)/99 = 427/99

⇒ 5.(\overline {12} ) = (512 – 5)/99 = 507/99

⇒ 3.(\overline {21} ) = (321 – 3)/99 = 318/99

Now, add them

⇒ (427/99) + (507/99) + (318/99)

⇒ 1252/99

∴ The value of 4.(\overline {31} ) + 5.(\overline {12} ) + 3.(\overline {21} ) is 1252/99

Given:

Production of company A in 2015 = 3 thousand numbers

Production of company A in 2016 = 2.5 thousand numbers

Concept:

The percentage decrease is calculated by the formula:

Formula Used:

Percentage Decrease = [(Initial Value - Final Value) / Initial Value] × 100

Calculation:

⇒ Initial Value = 3

⇒ Final Value = 2.5

⇒ Percentage Decrease = [(3 - 2.5) / 3] × 100

⇒ Percentage Decrease = [0.5 / 3] × 100

⇒ Percentage Decrease = 0.1667 × 100

⇒ Percentage Decrease = 16.67%

∴ The approximate percentage decrease in production from 2015 to 2016 is 17%.

Answer: None of the given options match exactly, but the closest is Option 3) 15%

CALCULATION:

Annual snow falls of S3 = 20% of 700

Annual snow falls of S2 = 15% of 700

⇒ Difference = (20 – 15)% of 700

∴ Difference = 5% of 700 = 35 cm

Divisibility rule of 9: A number divisible by 9 if the sum of its digit is divisible by 9.

Divisibility rule of 8: A number divisible by 8 if the last three digit of the number is divisible by 8

If 10 digit number 897359y7x2 is divisible by 72. So, we can say number also divisible by 9 and 8

⇒ 7x2 is divisible by 8 if x = 9

⇒ 897359y792 is divisible by 9 if y = 4

⇒ 3x – y

⇒ 3 × 9 – 4

⇒ 27 – 4

⇒ 23

Shortcut Trick

Side of square = √121 = 11 cm.

Perimeter of square = 4 × 11 = 44 cm.

Circumference of circle = Perimeter = 44 cm.

Memory trick: For a circle, if Circumference = 44 cm, then Radius = 7 cm and Area = 154 sq. cm.

∴ The correct answer is 154 sq. cm.

Alternate Method

Given: Area of square = 121 sq. cm.

Formula: Area of square = side²; Perimeter = 4 × side; Circumference = 2πr; Area of circle = πr².

Square (Area = 121)side = 11 cmr = 7Circle (Circum = 44)Area = 154 sq. cm

⇒ Side of square = √121 = 11 cm

⇒ Perimeter of square = 4 × 11 = 44 cm

⇒ Circumference of circle = 2 × (22/7) × r = 44

⇒ r = (44 × 7) ÷ 44 = 7 cm

⇒ Area of circle = (22/7) × 7 × 7 = 154 sq. cm.

∴ The correct answer is 154 sq. cm.

Additional Information

Circle Formulas

Area = πr² and Circumference = 2πr. When r = 7, Area = 154 and Circumference = 44.

Square Formulas

Area = side² and Perimeter = 4 × side. The diagonal of a square is side√2.

Perimeter-Area Comparison

For a given perimeter, a circle has the maximum area compared to any other polygon like a square or rectangle.

Given:

The ratio of boys and girls in a college was 5 : 4. New students admitted and the number of boys went up by 20% and the number of girls went up by 50%

Calculation:

Let the number of boys and girls initially be 5x and 4x.

Hence, after new students admitted, number of boys = 5x × 120% = 6x

And, number of girls = 4x × 150% = 6x

New ratio of boys and girls = 6x : 6x = 1 : 1

∴ the correct answer is 1 : 1.

Concept used:

Calculation:

(1\frac{2}{5}; \div \left[ {\frac{5}{8}of;\left( {\frac{2}{3} - \frac{2}{{15}}} \right)} \right]; + ;\frac{1}{{15}})

( \Rightarrow \frac{7}{5}; \div \left[ {\frac{5}{8}{\rm{;}} \times {\rm{;}}\left( {\frac{{10; - ;2}}{{15}}} \right)} \right]; + ;\frac{1}{{15}})

( \Rightarrow \frac{7}{5}; \div \left[ {\frac{5}{8}{\rm{;}} \times {\rm{;}}\frac{8}{{15}}} \right]; + ;\frac{1}{{15}})

( \Rightarrow \frac{7}{5}; \div \frac{1}{3}; + ;\frac{1}{{15}})

( \Rightarrow \frac{7}{5}{\rm{;}} \times {\rm{;}}3; + ;\frac{1}{{15}})

( \Rightarrow \frac{{21}}{5}; + ;\frac{1}{{15}})

( \Rightarrow \frac{{63; + ;1}}{{15}})

⇒ 64/15

∴ The value is 64/15.

Given:

Principal = Rs. 600

Time = 4 years

Amount after 4 years = Rs. 720

Formula used:

SI = Amount – Principal

SI = PRT/100

Where, P = Principal

R = Rate of interest

T = Time 

Calculation:

SI = Rs. (720 – 600)

⇒ Rs. 120

Now, according to the question

Rs. 120 = (600 × R × 4)/100

⇒ R = 5%

Now, 5% of 5 = 0.25%

⇒ New rate of interest is (5 + 0.25) = 5.25%

Required SI = Rs. (600 × 5.25 × 4)/100

⇒ Rs. 126

Required amount = Rs. (600 + 126)

⇒ Rs. 726

∴ The required amount is Rs. 726

Mistake Points

Here, it is said that the interest rate is increased by 5% of itself, which means we are increasing 5% on the existing 5% interest. So, we take 5% of 5% according to the question. If we take any other way, the solution will be wrong.

Shortcut Trick

When Selling Price (SP) is same for two articles, and one is sold at x% profit and another at x% loss, there is always a net loss.

Net Loss % = (x ÷ 10)² %

Given x = 20%

Net Loss % = (20 ÷ 10)² = 2² = 4%

∴ The correct answer is 4% loss.

Alternate Method

Given: SP of cycle 1 = ₹6000, SP of cycle 2 = ₹6000, Gain% = 20%, Loss% = 20%

Formula Used: Cost Price (CP) = SP × [100 ÷ (100 ± P/L %)]

CP1: ₹5000

+20% Gain

SP: ₹6000 (Each)

CP2: ₹7500

−20% Loss

Total CP: ₹12500 → Total SP: ₹12000 (Loss = 4%)

⇒ CP of first cycle = 6000 × (100 ÷ 120) = ₹5000

⇒ CP of second cycle = 6000 × (100 ÷ 80) = ₹7500

⇒ Total CP = 5000 + 7500 = ₹12500

⇒ Total SP = 6000 + 6000 = ₹12000

⇒ Total Loss = 12500 − 12000 = ₹500

⇒ Loss % = (500 ÷ 12500) × 100 = 4%

∴ The correct answer is 4% loss.

Additional Information

Same Cost Price Case

If two articles are bought at the same CP and one is sold at x% profit and another at x% loss, the net result is always No Profit No Loss.

Successive Percentage Change

If a value is changed by a% and then by b%, the effective net change is [a + b + (a × b) ÷ 100] %.

Dishonest Dealer Formula

Profit % = [ (Error) ÷ (True Value − Error) ] × 100, where error is the weight difference.

Given:

Time taken by A to complete the work = 10 days 

Time taken by B to complete the work = 12 days 

Time taken by C to complete the work = 15 days 

Concept used:

Total work = LCM 

Efficiency = (Total work)/(Total time)

Calculations:

Total work = LCM(10, 12, 15) = 60

Total efficiency of A, B and C together = 6 + 5 + 4 = 15 

Work done by A, B and C in 2 days = 15 × 2 = 30 units  

Remaining work = 60 – 30 = 30 units

According to the question, B left the job 3 days before the work was completed.

So, in the last 3 days, only C was working 

So, work done by C in 3 days = 4 × 3 = 12 units 

Remaining work = 30 – 12 = 18 units 

These 18 unit work is completed by B and C together

Total efficiency of B and C = 5 + 4 = 9

So, time taken by B and C to complete 18 units of work = 18/9 = 2 days

Total time to complete the work = 2 + 2 + 3 = 7 days 

Total work = LCM(10, 12, 15) = 60

Let the total number of days taken to finish the work be x.

C worked for all X days.

B worked for (X - 3) days

A worked for 2 days.

Total work by all together = 60 untis

4 × X + 5 × (X - 3) + 6 × 2 = 60

Or, 9X = 63

Or, X = 7 

∴ Total time to complete the work is 7 days

Given,

A man rows 9 km upstream in = 3 hrs

10 km downstream distance in = 3 hrs

Formula:

If the speed of boat and stream are x km/hr and y km/hr respectively, then

Upstream speed = (x - y) km/hr

Downstream speed = (x + y) km/hr

Calculation:

Let the speed of boat and stream be x km/hr and y km/hr respectively, then

Upstream speed = (x - y)

Downstream speed = (x + y)

According to the question

(x - y) = 9/3

(x - y) = 3   ---(1)

(x + y) = 18/3

(x + y) = 6   ---(2)

Add equation (1) and equation (2)

2x = 9

⇒ x = 9/2

⇒ x = 4.5 km/hr

∴ Speed of boat in still water is 4.5 km/hr.

Let the sum = P

⇒ (4P = P \times {\left( {1 + \frac{R}{{100}}} \right)^2})

(\Rightarrow 4 = {\left( {1 + \frac{R}{{100}}} \right)^2})             

⇒ (2 = 1 + 0.01R \Rightarrow R = 100)            (1)

When sum becomes 16 times:

⇒ (16P = P \times {\left( {1 + \frac{R}{{100}}} \right)^n})

(\Rightarrow ;16 = {\left( {1 + \frac{{100}}{{100}}} \right)^n})           

⇒ ({2^4} = {2^n})

∴ n = 4 years

Given:

Difference between 3/8 and smaller number = 1/5

Calculation:

Let the another number be 'x'

⇒ (3/8) - x = 1/5

⇒ (3/8) - (1/5) = x

⇒ x = (15 - 8)/40

⇒ x = 7/40

∴ The another number is 7/40.

GIVEN:

39 students having average weight = 51 kg

39 students and teachers combined average weight = 51.2 kg 

FORMULA USED :

Average = (( sum of all the values)\over( number of all values ))

CALCULATION :

Average of students = (\frac{sum}{no.of students}) =  51 

⇒ sum/39 = 51 

⇒ sum  of weight of  students = ( 39 × 51) = 1989.

⇒Average of students and teachers including  = (sum \over( no. of students and teachers)) = 51.2

⇒ sum/40 = 51.2 

⇒ sum of the weight of students and teachers = 2048. 

weight of teacher = (sum of the weight of teacher and students - the sum of the weight of students )

⇒ ( 2048 - 1989) = 59 kg.

∴ The weight of the teacher is 59 kg.

Shortcut TrickAverage weight increases by .2 kg and .2 kg are increased in every 39 students.

so the weight of the teacher = .2× 39 + 51.2 = 59kg

Given-   

Two successive discounts =10% and 20%

Concept Used -

Discounted Value = Actual Value(1 - Discount%)

Calculation-  

Let the MP be 100

After 1st discount of 10% price becomes 100 -10

⇒ 90

After 2nd discount of 20% price becomes 90 - 18

⇒ 72

∴ The net discount offered to the buyer is 100 - 72

⇒ 28% 

∴ Net discount is 28%.

Given:

(12.3 ÷ 0.03) ÷ 2.05 + 2.05

Concept used:

Calculation:

(12.3 ÷ 0.03) ÷ 2.05 + 2.05

⇒ ((\frac{123}{10} ÷ \frac{3}{100}) ÷ 2.05 + 2.05)

⇒ ((\frac{123}{10} \times \frac{100}{3}) ÷ 2.05 + 2.05)

⇒ (410 ÷ \frac{205}{100} + 2.05)

⇒ (410 \times \frac{100}{205} + 2.05)

⇒ 200 + 2.05

⇒ 202.05

∴ Required answer is 202.05.

Shortcut Trick

When the time intervals are equal (T₁ = T₂ = 3 hr), the Average Speed is simply the Arithmetic Mean of the speeds.

Average Speed = (30 + 50) ÷ 2 = 40 km/h

Average of Speeds = (30 + 50) ÷ 2 = 40 km/h

Required Percentage = (40 ÷ 40) × 100 = 100%

∴ The correct answer is 100%.

Alternate Method

Given:

Speed 1 (v₁) = 30 km/h, Time 1 (t₁) = 3 hr

Speed 2 (v₂) = 50 km/h, Time 2 (t₂) = 3 hr

Formula Used:

Total Distance = (v₁ × t₁) + (v₂ × t₂)

Average Speed = Total Distance ÷ Total Time

Calculations:

⇒ Distance for first part = 30 × 3 = 90 km

⇒ Distance for second part = 50 × 3 = 150 km

⇒ Total Distance = 90 + 150 = 240 km

⇒ Total Time = 3 + 3 = 6 hr

⇒ Average Speed = 240 ÷ 6 = 40 km/h

⇒ Average of Speeds = (30 + 50) ÷ 2 = 80 ÷ 2 = 40 km/h

⇒ Percentage = (Average Speed ÷ Average of Speeds) × 100

⇒ Percentage = (40 ÷ 40) × 100 = 100%

∴ The correct answer is 100%.

Additional Information

Average Speed (Equal Distances)

If a person covers two equal distances at speeds x and y, the average speed is 2xy ÷ (x + y).

Average Speed (Equal Time Intervals)

If a person travels at speeds x and y for equal time intervals, the average speed is (x + y) ÷ 2.

General Formula

Average Speed = (Total Distance) ÷ (Total Time) = (d₁ + d₂ + ...) ÷ (t₁ + t₂ + ...).

Unit Conversion

To convert km/h to m/s, multiply by 5/18. To convert m/s to km/h, multiply by 18/5.

Shortcut Trick

Ratio of Amount to Principal for 2 years = 17745 : 10500

Simplify the ratio (divide by 105): 169 : 100

For a 2-year period, take the square root of the ratio: √169 : √100 = 13 : 10

Rate % = (Difference / Base value) × 100 = (13 − 10) / 10 × 100 = 3 / 10 × 100 = 30%

∴ The correct answer is 30%.

Alternate Method

Given:

Principal (P) = ₹10500

Amount (A) = ₹17745

Time (n) = 2 years

Formula Used:

A = P(1 + R/100)ⁿ

Calculations:

⇒ 17745 = 10500(1 + R/100)²

⇒ 17745 / 10500 = (1 + R/100)²

⇒ 1.69 = (1 + R/100)²

⇒ √1.69 = 1 + R/100

⇒ 1.3 = 1 + R/100

⇒ R/100 = 1.3 − 1 = 0.3

⇒ R = 0.3 × 100 = 30%

∴ The correct answer is 30%.

Additional Information

Compound Interest (CI) Basic Formula

Interest is calculated on the initial principal and also on the accumulated interest of previous periods. Formula: CI = P[(1 + R/100)ⁿ − 1].

Effective Rate for 2 Years

The effective interest rate for two years can be calculated using the successive percentage formula: R_eff = x + y + (xy/100).

Difference between CI and SI for 2 Years

The difference between compound interest and simple interest for a period of 2 years is given by the formula: Difference = P(R/100)².

Quarterly and Half-Yearly Compounding

If interest is compounded half-yearly, the rate becomes R/2 and time becomes 2n. For quarterly, the rate is R/4 and time is 4n.

Calculation:

Let the capacity of the tank = 72 litres

Efficiency of pipe P = 72/24 = 3 litres/hour

Efficiency of pipe Q = 72/18 = 4 litres/hour

According to the question,

Total time in which tank has filled = 15 hours

Let the pipe P was closed at after n hours

According to the question

⇒ 3 × (n) + 4 × 15 = 72

⇒ 3n + 60 = 72

⇒ 3n = 12

⇒ n = 4

So, 4 hours after 11:00 am. that means 3:00 pm

∴ the tap P should be closed at 3 : 00 pm

Confusion Points

Not asking about after how many hours the tap should be stopped. It is asking about the time (in p.m.) when the tap will be stopped. [Which is mentioned in the question]

Start at 11 a.m + 4 hours = 3 p.m

Given:

70% of (A – B) = 49% of (A + B)

Calculation:

According to question:

70 × (A - B)/100 = 49(A + B)/100

⇒ 70(A - B) = 49 (A + B)

⇒ 10(A - B) = 7(A + B)

⇒ 10A – 10B = 7A + 7B

⇒ 10A – 7B = 7A + 10B

⇒ 3A = 17B

⇒ A/B = 17/3

∴ A ∶ B = 17 ∶ 3

The correct option is 1 i.e. 17 ∶ 3

Shortcut Trick

The required ratio is (x/y) : (y/x), which simplifies to (x/y) ÷ (y/x) = (x/y) × (x/y) = (x/y)².

Given x : y = 5 : 4, substitute the values directly into the squared form.

Required Ratio = (5/4)² = 25/16.

∴ The correct answer is 25 : 16.

Alternate Method

Given:

The ratio x : y = 5 : 4

Formula Used:

Ratio of a : b is written as a/b. To simplify (a/b) : (c/d), we cross-multiply to get (a × d) : (b × c).

Calculations:

⇒ x/y = 5/4

⇒ y/x = 4/5

⇒ Required Ratio = (x/y) : (y/x)

⇒ Required Ratio = (5/4) : (4/5)

⇒ To remove fractions, multiply both sides by the LCM of 4 and 5 (which is 20):

⇒ (5/4 × 20) : (4/5 × 20)

⇒ 25 : 16

∴ The correct answer is 25 : 16.

Additional Information

Duplicate Ratio

The duplicate ratio of two numbers a : b is the ratio of their squares, which is a² : b².

Inverse Ratio

The inverse ratio of a : b is 1/a : 1/b, which simplifies directly to b : a.

Compounded Ratio

The compounded ratio of a : b and c : d is (a × c) : (b × d).

Shortcut Trick

Area of two paths = w(L + B − w) where w is path width and L, B are square sides.

Area = 2.2 × (25 + 25 − 2.2) = 2.2 × 47.8 = 105.16 m².

Convert area to dm²: 1 m² = 100 dm² ⇒ 105.16 × 100 = 10516 dm².

Total cost = 10516 × ₹1 = ₹10,516.

∴ The correct answer is ₹10,516.

Alternate Method

Given: Side of square park (a) = 25 m, Width of path (w) = 2.2 m, Cost = ₹1/dm².

⇒ Area of Path 1 (Horizontal) = length × width = 25 × 2.2 = 55 m²

⇒ Area of Path 2 (Vertical) = length × width = 25 × 2.2 = 55 m²

⇒ Common Intersection Area = width × width = 2.2 × 2.2 = 4.84 m²

⇒ Total Path Area = (55 + 55) − 4.84 = 105.16 m²

⇒ Conversion: 1 m = 10 dm ∴ 1 m² = 100 dm²

⇒ Total Area in dm² = 105.16 × 100 = 10,516 dm²

⇒ Total Cost = Area in dm² × Rate = 10,516 × 1 = ₹10,516

∴ The correct answer is ₹10,516.

Additional Information

Path area formulas

For paths outside a rectangle: Area = 2w(L + B + 2w). For paths inside a rectangle: Area = 2w(L + B − 2w).

Unit conversion

1 meter = 10 decimeters (dm). Therefore, 1 square meter = 10² = 100 square decimeters (dm²).

Central cross paths

When paths intersect at the center, always subtract the square of the width (w²) once as it is counted twice in the calculation.

Shortcut Trick

15% of 120 = 18

Given: 30% of Number = 18 + 21 = 39

If 30% → 39, then 10% → 13

So, 100% → 130

∴ The correct answer is 130.

Alternate Method

Given:

15% of 120 = (15 ÷ 100) × 120 = 18

Let the unknown number be 'x'.

⇒ 30% of x = 15% of 120 + 21

⇒ 0.30 × x = 18 + 21

⇒ 0.30x = 39

⇒ x = 39 ÷ 0.30

⇒ x = 3900 ÷ 30

⇒ x = 130

∴ The correct answer is 130.

Additional Information

Percentage Change

To find a value after a percentage increase: Final Value = Initial Value × (1 + r/100).

Base Change Rule

If A is x% more than B, then B is [x/(100+x)] × 100% less than A.

Fraction Equivalents

Always remember common fractions: 15% = 3/20 and 30% = 3/10 for faster calculation.