MP Police Constable : (25 Nov 2025, Shift 1) Memory-Based Paper (Previous Year Paper)

The correct answer is 1784.

 Key Points

• In 1784, Sir William Jones founded the Asiatic Society of Bengal.
• Asiatic Society of Bengal, scholarly society founded on Jan. 15, 1784, by Sir William Jones, a British lawyer and Orientalist, to encourage Oriental studies.
• At its founding, Jones delivered the first of a famous series of discourses.

Additional Information

• The Asiatic Society had the support and encouragement of Warren Hastings, the governor-general (1772–85) of Bengal, though he declined its presidency.
• Indians were first admitted as members in 1829.
• Headquarters are in Kolkata.
• The society owns an art collection that includes paintings by Peter Paul Rubens and Joshua Reynolds.
• The society’s library contains some 100,000 general volumes, and its Sanskrit section has more than 27,000 books, manuscripts, prints, coins, and engravings.

In the above statement, the mother is crying in the hospital as her only son died in a road accident while driving his bike. Here both the assumptions are not implicit as there is no information given about whose fault it is in the accident. The mother is in grief because his son died in the accident, there might be possible that because of the carelessness of his son while driving. With the given information, We cannot predict her intentions towards God.

Hence, “neither 1 nor 2 is implicit” is the correct answer.

Shortcut Trick

Volume remains constant: π × R² × H = π × r² × h

Convert radius to same unit (cm): 2 mm = 0.2 cm

1.2² × 22 = 0.2² × h

1.44 × 22 = 0.04 × h ⇒ h = 36 × 22 = 792 cm

∴ The correct answer is 792 cm.

Alternate Method

Given:

Radius of rod (R) = 1.2 cm

Length of rod (H) = 22 cm

Radius of wire (r) = 2 mm = 0.2 cm (since 10 mm = 1 cm)

Formula Used:

Volume of cylinder = πr²h

Calculations:

⇒ Volume of metallic rod = π × (1.2)² × 22

⇒ Volume of cylindrical wire = π × (0.2)² × L

⇒ π × 1.44 × 22 = π × 0.04 × L

⇒ 1.44 × 22 = 0.04 × L

⇒ L = (1.44 × 22) ÷ 0.04

⇒ L = 36 × 22

⇒ L = 792 cm

∴ The correct answer is 792 cm.

Additional Information

Recasting Concept

When a 3D solid is melted and recast into another shape, its Total Volume remains constant, provided there is no wastage.

Cylinder Properties

Curved Surface Area (CSA) = 2πrh | Total Surface Area (TSA) = 2πr(h + r).

Unit Conversion

Always ensure all dimensions are in the same unit. 1 cm = 10 mm | 1 m = 100 cm.

The correct answer is adrenaline.

Key Points

• Blood pressure may be referred to as the pressure exerted by the blood on the arteries and veins.
• Adrenaline hormone is administered to a person suffering from a marked fall in blood pressure.
• It is an emergency hormone secreted by adrenal medulla.

Explanation:

• The adrenal medullary hormones, namely adrenaline (epinephrine) and noradrenaline (norepinephrine), have the same effect as the sympathetic stimulation.
• Adrenaline increases the rate of heart beat and promotes cardiac output, thus increasing blood pressure.
• It also increases the strength of heart contraction, rate of respiration, and metabolic rate.

Hence, the correct option is (2) Adrenaline.

Additional Information

• Insulin-
• It is a peptide hormone secreted by β-cells of the Islets of Langerhans of pancreas.
• Insulin plays significant role in the regulation of glucose homeostasis.
• Thyroxine-
• Thyroxine (T₄) is secreted by the thyroid gland.
• It regulates basal metabolic rate, controls metabolism of carbohydrates, fats and proteins.
• Vasopressin-
• It is synthesized by hypothalamus and released by posterior pituitary or neurohypophysis.
• It mainly acts at the kidney and stimulates reabsorption of water and electrolytes by DCT.
• Vasopressin is also called as anti-diuretic hormone.

According to the given information,

Hence, R is to the “South” of X.

Given:

Side of cube: 5 cm

Concept Used**:**

Total surface area of the resulting cuboid is 2lw + 2lh + 2wh, where l is length, w is width, and h is height.

Solution:

⇒ Here, length l = 5 x 3 = 15 cm (since three cubes are joined end to end), width w = 5 cm, height h = 5 cm

⇒ 2lw + 2lh + 2wh = 2(15 x 5) + 2(15 x 5) + 2(5 x 5)

⇒ 150 + 150 + 50 = 350 cm²

Therefore, the total surface area of the resulting cuboid is 350 cm².

The correct answer is rise a little higher.

Key Points

• Buoyant force
• ​The buoyant force is an upward force on an object that is wholly or partially immersed in a fluid.
• Due to the force of buoyancy, a body partially or wholly immersed in a liquid tends to lose its weight, that is, it appears to be lighter.
• Sea water is denser than river water.
• A ship experiences more buoyant force in seawater than in river and hence the volume of the ship submerged in water decreases to balance the weight of the ship.
• In Sea water density is higher than river water that's why a ship experiences more buoyant force in sea water.
• So when it goes from the river to the sea it ​rises a little higher.

The logic followed here is :-

Hence, the correct answer is "NROS".

Given:

Circumference of the base of cylinder = 22 cm

Height (h) = 4 × radius(r)

Concept used:

Circumference of circle = 2 × π × r

The lateral surface area of cylinder = 2 × π × r × h

Calculation:

Circumference of circle = 2 × π × r

⇒  2 × (22/7) × r = 22

⇒ r = 3.5 cm

Height (h) = 4 × radius(r)

⇒ h = 4 × 3.5 = 14 cm

The lateral surface area of cylinder = 2 × π × r × h

⇒ 22 × 14 = 308 cm2

∴ The correct answer is 308 cm2.

The correct answer is Palk Strait.

Key Points

A strait is a narrow channel of water that joins two water bodies and separates two land masses.

• Palk Strait
• The strait is between southeastern India and northern Sri Lanka.
• The southwestern portion of the strait is also called Palk Bay.
• The strait is named after Robert Palk, who was a governor of Madras during the Company Raj period.
• The strait is 40 to 85 miles (64 to 137 km) wide, 85 miles long, and less than 330 feet (100 meters) deep.
• It receives several rivers, including the Vaigai (India), and it contains many islands on the Sri Lankan side.
• The port of Jaffna, the commercial center for northern Sri Lanka, lies on the strait.

Additional Information

Important Points

Decoding the information, 

Given:

15 C 7 B (24 D 8) A 16 C 4 B 21 D 3

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

15 × 7 - (24 ÷ 8) + 16 × 4 - 21 ÷ 3

= 15 × 7 - 3 + 16 × 4 - 7

= 105 - 3 + 64 - 7

= 169 - 10

= 159

Hence, “159” is the correct answer.

Shortcut Trick

Let Total capacity = LCM(5, 10, 30) = 30 units.

Efficiency of Pipe A = 30 ÷ 5 = 6 units/hr.

Efficiency of Pipe B = 30 ÷ 10 = 3 units/hr.

Efficiency of Pipe C = 30 ÷ 30 = 1 unit/hr.

Total Time = Total capacity ÷ Combined Efficiency = 30 ÷ (6 + 3 + 1) = 3 hours.

∴ The correct answer is 3 hours.

Alternate Method

Given:

Time taken by Pipe A = 5 hours

Time taken by Pipe B = 10 hours

Time taken by Pipe C = 30 hours

Formula Used:

Efficiency = Total Work ÷ Time Taken

Total Time = Total Work ÷ Combined Efficiency

Calculations:

⇒ Total Efficiency = 6 + 3 + 1 = 10 units/hr

⇒ Time required when all pipes are open = Total Work ÷ Total Efficiency

⇒ Time required = 30 ÷ 10

⇒ Time required = 3 hours

∴ The correct answer is 3 hours.

Additional Information

Inlet vs Outlet Pipes

An inlet pipe fills the tank (positive work), while an outlet pipe empties it (negative work).

Two Pipes Working Together

If Pipe A and Pipe B fill a tank in x and y hours respectively, together they take (x × y) ÷ (x + y) hours.

Work Equivalence Method

Taking the LCM of all given times as the total capacity helps avoid fractional calculations when finding individual efficiencies.

Concept

The two main ways of changing physical state:

• By changing pressure.
• By changing temperature.freezing

Examples of physical change

• It includes changes in the size or shape of matter.
• Changes of state. for example, from solid to liquid or from liquid to gas-are also physical changes.
• Some of the processes that cause physical changes include cutting, bending, dissolving, , boiling, and melting.

Explanation :

• A change in the physical state can be brought about When energy is either given to or taken out of the system.
• Changing states of matter occur when matter loses or absorbs energy.
• When a substance absorbs energy; the atoms and molecules move more rapidly and this increased kinetic energy pushes particles far enough that they change form. This energy is usually heat or thermal energy.
• The heating or cooling of matter can shift its condition from one to another**.**
• For instance, heating ice causes it to turn into water, and heating water causes it to turn into steam.
• The intermolecular forces of attraction between the molecules are broken by the heat source, which is why this occurs.

The correct option is 3 which is A change in the physical state that can be brought about when energy is either given to or taken out of the system.

According to the given information:

1. Out of seven, three are girls.

2. No girl is wearing black, yellow, or brown.

3. 'U' is the sister of 'T' and is wearing pink, while 'T' is wearing brown.

4. 'P' is wearing blue, while his sister 'Q' is not wearing green.

5. 'R' is wearing yellow, while his best friend 'W' is a boy.

Final arrangement: 

So, groups Q, S and U represents only girls.

Hence, the correct answer is "Q, S and U".

Shortcut Trick

Total Cost Price (CP) = 650 + 50 = ₹700

To earn 20% Profit, the Selling Price (SP) must be 120% of the CP.

SP = 700 × 1.2 = 840

∴ The correct answer is ₹840.

Alternate Method

Given:

Purchase price of television set = ₹650

Overhead expenses (Transportation) = ₹50

Required Profit = 20%

Formula Used:

Total Cost Price (CP) = Purchase Price + Overhead Expenses

Selling Price (SP) = CP × (100 + Profit%)/100

Calculations:

⇒ Total Cost Price = 650 + 50 = ₹700

⇒ Profit amount = 20% of 700 = (20/100) × 700 = ₹140

⇒ Selling Price = Total Cost Price + Profit amount

⇒ Selling Price = 700 + 140 = ₹840

∴ The correct answer is ₹840.

Additional Information

Overhead Charges

Any extra expenditure incurred on transportation, repairs, or labor after buying an article is added to the Original Cost Price to find the Total Cost Price.

Profit and Loss Percentage

Profit % = (Profit / CP) × 100 and Loss % = (Loss / CP) × 100. Both are always calculated on the Cost Price (CP).

Marked Price and Discount

Selling Price (SP) = Marked Price − Discount. Discounts are always calculated on the Marked Price (MP).

The correct answer is Alfred Cobban.

Key Points

• Alfred Bert Carter Cobban was an English historian and Professor of French History who advocated a classical liberal view of the French Revolution.
• Alfred Cobban argued that excessive dependence upon facts and failure to correlate facts with theory as well as ideological reductionism led to the decline of political theory.

Thus It was Alfred Cobban who has discussed the 'Decline of Political Theory

The position of letters according to alphabetic series is,

The pattern followed here is,

• FINE : GKQI

• MOST : NQVX

• SEAL : TGDP

Hence, the correct answer is option 4.

Shortcut Trick

Rate = 8\(\frac{1}{3}\)% = 1/12. Ratio of Principal to Installment for Year 1 = 12 : 13.

For Year 2, the ratio is 12² : 13² = 144 : 169.

Equating installments (making them 169), Year 1 ratio becomes (12 × 13) : (13 × 13) = 156 : 169.

Total Principal = 156 + 144 = 300 parts.

Given 300 parts = Rs. 1200 ⇒ 1 part = 4.

Annual installment = 169 parts × 4 = Rs. 676. ∴ The correct answer is Rs. 676.

Alternate Method

Given:

Loan Amount (P) = Rs. 1200

Rate of Interest (R) = 8&frac{1}{3}% = 25/3% ⇒ Fractional value = 1/12

Time = 2 years

Let each equal annual payment be x.

Formula Used:

P = x / (1 + R/100) + x / (1 + R/100)²

Calculations:

⇒ 1200 = x / (1 + 1/12) + x / (1 + 1/12)²

⇒ 1200 = x / (13/12) + x / (13/12)²

⇒ 1200 = (12x / 13) + (144x / 169)

⇒ 1200 = (156x + 144x) / 169

⇒ 1200 = 300x / 169

⇒ x = (1200 × 169) / 300

⇒ x = 4 × 169

⇒ x = 676

∴ The correct answer is Rs. 676.

Additional Information

Compound Interest Installment

For a loan P paid in n equal annual installments x at rate R: P = x/(1+R/100) + x/(1+R/100)² + ... + x/(1+R/100)ⁿ

Simple Interest Installment

The annual payment x that will discharge a debt A due in n years at simple interest rate R is: x = (100 × A) ÷ [100n + n(n−1)R/2]

Effective Compound Interest Rate for 2 Years

The net effective rate for 2 years at R% per annum is given by: (2R + R²/100)%

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 5^th 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 6^th 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 image obtained when the paper is unfolded is,

Hence, the correct answer is "Option 2".

Shortcut Trick

Substitute the standard trigonometric values: cosec 30° = 2, sin 45° = 1/√2, sec 60° = 2, and tan 30° = 1/√3.

Expression = 2² + (1/√2)² + 2² + (1/√3)²

Expression = 4 + 1/2 + 4 + 1/3

Expression = 8 + (3 + 2) ÷ 6 = 8 + 5/6 = 53/6

∴ The correct answer is 53/6.

Alternate Method

Given: cosec² 30° + sin² 45° + sec² 60° + tan² 30°

Formula Used: Values of Trigonometric Ratios for specific angles.

⇒ cosec 30° = 2

⇒ sin 45° = 1/√2

⇒ sec 60° = 2

⇒ tan 30° = 1/√3

⇒ Value = (2)² + (1/√2)² + (2)² + (1/√3)²

⇒ Value = 4 + 1/2 + 4 + 1/3

⇒ Value = 8 + (3 + 2) ÷ 6

⇒ Value = 8 + 5/6 = 53/6

Thus, the final calculated value corresponds to option (3).

∴ The correct answer is 53/6.

Additional Information

Trigonometric Table Values

Values for common angles: sin 30° = 1/2, sin 45° = 1/√2, cos 60° = 1/2, tan 30° = 1/√3, and cot 45° = 1.

Reciprocal Relations

cosec θ = 1 ÷ sin θ | sec θ = 1 ÷ cos θ | cot θ = 1 ÷ tan θ.

Square Identities

sin²θ + cos²θ = 1 | sec²θ − tan²θ = 1 | cosec²θ − cot²θ = 1.

The correct answer is option 1.

In News

• The HINDU: Indian Navy’s mission-deployed warship INS Teg, assisting in a search-and-rescue (SAR) operation.

Key Points INS Teg:

• INS Teg is a Talwar-class frigate of the Indian Navy.
• These frigates are known for their stealth capabilities and advanced weapon systems.
• The Talwar-class frigates are an improved version of the Krivak III-class frigates of Russia, designed to carry out a variety of roles, including anti-ship warfare, anti-submarine warfare, and anti-aircraft warfare.

Additional Information

• BrahMos Missile: Equipped with the BrahMos supersonic cruise missile for powerful surface strike capabilities.
• Russian Built: Constructed by Yantar Shipyard in Kaliningrad, Russia, and commissioned in the Indian Navy in April 2012.
• Operational Role: Actively involved in Operation Sankalp for protecting Indian merchant vessels in the Strait of Hormuz.

The correct answer is Option 2: Will announce to find the owner of the note.

• Qualities Projected in this situation:  (Sense of responsibility and determination).

Key Points

• Checklist for attempting SRT questions:

1. Read the question and options carefully.
2. Look for options that are realistic, optimistic, and reflect officer-like qualities.
3. Do not skip any situation.
4. Relegate the negative sentences and choose the most logical option among the remaining. As time is an important factor, hence your thinking ability should be swift.
5. React quickly and be logical.

Given:

Speed of four successive distances = 10 km/hour, 20 km/hour, 30 km/hour and 60 km/hour.

Total Distance = 7 km.

Formula used:

Average Speed = Total Distance /Total Time

Calculation:

For the first 7 km at a speed of 10 km/hour:

time₁ = \(\dfrac{7}{10}\)

For the next 7 km at a speed of 20 km/hour:

time₂ = \(\dfrac{7}{20}\)

For the next 7 km at a speed of 30 km/hour:

time₃ =\(\dfrac{7}{30}\)

For the last 7 km at a speed of 60 km/hour:

time₄ = \(\dfrac{7}{60}\)

Total time = \(\dfrac{7}{10} + \dfrac{7}{20} + \dfrac{7}{30} + \dfrac{7}{60} \) 

⇒ \( \dfrac{42 +21 +14 +7 }{60} \) ⇒ \(\dfrac{84 }{60} \) 

Total distance covered = 7 km + 7 km + 7 km + 7 km = 28 km

Average speed = \( \dfrac{28}{ \dfrac{84}{60} } \) = 20 km/hour

∴ The average speed over this distance is 20 km/hour.

The correct answer is C.K. Mishra Committee.

Key Points

• The Union Environment Ministry has constituted a 7-member committee to continuously monitor the short-term and long-term solutions to air pollution.
• It will be headed by C.K Mishra, the Secretary of the Ministry of Environment, Forest and Climate Change (MoEFCC).

Additional Information

Mistake Points

The question is asking to find the NOT Related numbers, so we need to find the wrong option, so Solve accordingly.

The logic followed here is:-

(64, 91, 118)

The difference between the second and first numbers is 27 and the difference between the third and second numbers is also 27.

91 - 64 = 27

118 - 91 = 27

From option 1:-

(46, 73, 101)

73 - 46 = 27

101 - 73 = 28

It does not follow because both differences are not 27.

From option 2:-

(48, 75, 102)

75 - 48 = 27

102 - 75 = 27

It is follow.

From option 3:-

(72, 99, 126)

99 - 72 = 27

126 - 99 = 27

It is follow.

From option 4:-

(45, 72, 99)

72 - 45 = 27

99 - 72 = 27

It is follow.

Hence, "option 1" is the correct answer.

Shortcut Trick

For three numbers a, b, and c, the fourth proportional is given by (b × c) ÷ a.

Here, a = 10, b = 12, and c = 15.

Fourth proportional = (12 × 15) ÷ 10 = 180 ÷ 10 = 18.

∴ The correct answer is 18.

Alternate Method

Given: Three numbers are 10, 12, and 15.

Formula Used: If a, b, c, and d are in proportion, then a : b = c : d or a × d = b × c.

⇒ Let the fourth proportional be x.

⇒ 10 : 12 :: 15 : x

⇒ 10 ÷ 12 = 15 ÷ x

⇒ 10 × x = 12 × 15

⇒ 10 × x = 180

⇒ x = 180 ÷ 10

⇒ x = 18

∴ The correct answer is 18.

Additional Information

Mean Proportional

The mean proportional between two numbers a and b is defined as √(a × b).

Third Proportional

For two numbers a and b, the third proportional c is such that a : b :: b : c, calculated as c = b² ÷ a.

Rule of Proportion

In any proportion a : b :: c : d, the product of the extremes (a × d) is always equal to the product of the means (b × c).

The correct answer is Ribs.

Key Points

• Flat bones are bones whose principal function is either extensive protection or the provision of broad surfaces for muscular attachment.
• These bones are expanded into broad, flat plates, as in the cranium (skull), the ilium (pelvis), sternum and the rib cage.
• The ribs are a series of curved bones that attach to the spine in the back and to the sternum (breastbone) in the front.
• They form a cage around the lungs and heart, protecting them from injury.
• The other options are not flat bones.
• The ankle bones are called tarsals.
• They are small bones that form the ankle joint.
• The wrist bones are called carpals.
• They are small bones that form the wrist joint.
• The pelvic bones are called coxal bones.
• They are large bones that form the pelvis.

Important Points

Correct option 2. Only argument I is strong.

Statement asks if human beings have become intolerant.

Argument I suggests that there has been an increase in the incidents of mob lynchings. This form of violence indicates that we are lacking tolerance. Therefore, argument I is strong.

Argument II suggests that it is natural and intrinsic to an animal to dominate over the weaker species. This is not justified. We call ourselves evolved species, we follow the man-made codes of conduct and are not governed by the laws of the jungle. Therefore, argument II is not strong.

Hence, option 2 is correct.

Given: number = 294

Concept Used: Factorization

Calculation:

294 = 2 × 3 × 7 × 7 = 2¹ × 3¹ × 7²

Hence, to make '294 a perfect square. We have to multiply with 2 × 3 = 6.

Required Answer : 6

The Indian National Congress was founded in Bombay in December 1885.

• The years from 1885-1905 were known as the period of the moderates because they dominated the Indian National Congress.
• The Moderates used petitions, prayers, meetings, leaflets, pamphlets, memorandums, and delegations to present their demands to the British government.
• Their only notable achievements were the expansion of the legislative council by the Indian Councils Act of 1892.
• This created dissatisfaction among the people.

Important Points

The Surat Split was the splitting of the Indian National Congress into two groups - the Extremists and the Moderates - at the Surat session in 1907. 

• The 1907 INC meeting was to be held in Nagpur.
• Gopal Krishna Gokhale moved the meeting place from Nagpur to Surat fearing that in Nagpur, Bal Gangadhar Tilak would win.
• An INC meeting was shifted from Nagpur to Surat. Since Surat was in the home province of Bal Gangadhar Tilak, he could not preside over the meeting.
• But what outraged the extremists was that he was not even given permission to speak.
• This led to a violent altercation between the two factions and the meeting being canceled.

Additional Information

Surat Split:

• The Surat split was a big jolt to the Indian National Congress. In fact, the difference between the moderates and the extremists presented an opportunity to the British.
• The moderates were quite reluctant to pass the motion on the demand for Swaraj. The Arya-samaj notion of Swaraj and Swadeshi was the hallmark of the program of the extremists.
• In the initial days, there were many Congress leaders who opposed the notion of Swaraj, the demand for Swaraj, and extremist politics, but at the beginning of the 20^th Century, some of the veteran Congress leaders like Dadabhai Naoroji, and G.K. Gokhale, had the word, ‘Swaraj’ in their minds.
• In 1907, Surat Session: The two main objectives placed by the extremists were that:
• Demand for the resolution of Swaraj
• Lala Lajpat Rai to be made the President of the INC
• These two demands were not acceptable to the moderates. Thus, instead of Lala Lajpat Rai (November 17, 1928), the moderates supported the idea of Rash Behari Ghosh as the President.
• This was the first time that there was to be an election in the INC for Presidentship.
• In between the election, the extremists were expelled from the INC, and the moderates had complete command over the affairs of the INC.
• Rash Behari Ghosh became the President of the Surat session.

Given:

• Number of floors: 7 such that  The floors were numbered 1 to 7 from bottom to top, floor 1 being the ground floor.
• Number of men: 7; A, B, C, D, E, F, and G

Explanation:

• C lives on the fifth floor.
• There are Three floors between C and E.

• B lives at an odd numbered floor.
• B lives immediate below D.
• Two person live between D and A​

• G does not live at any prime numbered floor.

​As the only man left is F, he will be positioned at the only floor left vacant i.e at the second floor.

Thus, according to the final arrangement B lives immediate above F.

Hence, "B" is correct answer.

Shortcut Trick

Ratio of the two numbers = 7 : 11

Sum of the ratio parts = 7 + 11 = 18 units

Since HCF is the common factor, 1 unit = HCF = 28

Total sum of the numbers = 18 × 28 = 504

∴ The correct answer is 504.

Alternate Method

Given:

Ratio of numbers = 7 : 11

HCF of numbers = 28

Formula Used:

If two numbers are in the ratio a : b and their HCF is x, then the numbers are ax and bx.

7 Units (Number 1)
11 Units (Number 2)

Sum = 7 + 11 = 18 Units
Common Factor (HCF) = 28

Calculations:

⇒ Let the first number be 7x and the second number be 11x.

⇒ HCF of 7x and 11x is x (since 7 and 11 are co-prime).

⇒ x = 28

⇒ Sum of the numbers = 7x + 11x = 18x

⇒ Sum = 18 × 28

⇒ Sum = 504

∴ The correct answer is 504.

Additional Information

Relationship between Numbers, HCF and Ratio

If HCF of two numbers is H and they are in ratio a:b, then the numbers are aH and bH, and their LCM = a × b × H.

Product of Numbers

Product of two numbers = HCF × LCM. For the given problem, Product = (7 × 28) × (11 × 28).

Co-prime Numbers

Numbers that have only 1 as their common factor (HCF = 1) are called co-prime numbers. In a reduced ratio a:b, a and b are always co-prime.

The correct answer is Sikkimese.

Key Points 

• The Losoong Festival is one of the most prominent events in Sikkim, a state in North East India.
• The Sikkimese New Year begins with Losoong, which is celebrated with tremendous enthusiasm and zeal throughout the province.
• The event takes place at the end of the harvesting season, providing much-needed joy and excitement for all of the farmers who have worked hard all year.
• Losoong festival was formerly restricted to the Bhutia people; however, it gradually extended to the Lepchas, and it is today celebrated by other minor tribes from Sikkim, Darjeeling, and Nepal.
• Cham dances performed by the Buddhist Monks are this festival’s main attraction.

Additional Information

2. It borders Tibet in the north and northeast, Bhutan in the east, Nepal in the west, and West Bengal in the south.
3. The Capital of Sikkim is Gangtok.
4. It was founded by the Namgyal dynasty in the 17^th century.
5. Kangchenjunga the highest peak of India and third highest on Earth is in the State of Sikkim.
6. Sikkim became a state of India by the 36^th Amendment Act, 1975 on 26^th April, 1975 | | | | Rivers | 1. Teesta 2. Rangit | | | National Park | 1. Khangchendzonga National Parks 2. Fambong Lho Wildlife Sanctuary 3. Singba Rhododendron Sanctuary 4. Kyongnosla Alpine Sanctuary 5. Maenam Wildlife Sanctuary 6. Varsey Rhododendron Sanctuary | | | Festivals | 1. Saga Dawa 2. Lhabab Dunchen 3. Losar Festival 4. Phang Lhabsol 5. Bumchu 6. Losoong 7. Tihaar | | | Famous Personalities | 1. Baichung Bhutia (Indian footballer) 2. Danny Denzongpa (Bollywood Actor) | | | Mountain Passes | 1. Nathula Pass 2. Jelep La Pass | | | Lakes | 1. Tsomgo Lake 2. Cholamu Lake | | | Symbol of Sikkim | | | | State Animal | Red Panda(Ailurus fulgens) | | | State Bird | Blood Pheasant | | | State Flower | Nobile Orchid | | | State Tree | Rhododendron | |

A person is expected to be honest before the advocate as s/he needs to plan the argument accordingly. But even though it is expected to be honest, people can hide some facts to avoid trouble.

Thus, statement 1 is implicit.

Assumption 2 works contrary to the statement and hence is rejected.

Hence the correct answer is only assumption 1 is implicit.

Given:

The numbers 4, 8, 12, 16, and 20. 

Concept used:

Arithmetic mean = Average = (Sum of observations)/(Number of observations)

Calculation:

Sum of observations = 4 + 8 +12 + 16 + 20

Number of observations = 5

Arithmetic mean = \(\dfrac{60}{5}\) = 12

∴ The arithmetic mean is 12.

The correct answer is Indore.

Key Points

• Indore is the only city in India that's home to both an IIM (established in 1996) and an IIT (2009) .
• ​Indian Institute of Management Indore is an autonomous public business school located in Indore, Madhya Pradesh in India.
• Indian Institute of Technology Indore is an Institute of National Importance located in Indore, Madhya Pradesh, India.
• It was one of the eight new Indian Institutes of Technology launched by the Government of India in the year 2009.

The sequence of reaching school is as follow-

(1) E reaches immediately after A and is subsequently followed by G, Who is the second last to reach the school.

_ < G < E < A

(2) F reaches immediately before A but does not immediately follow D that means F follow B.

_ < G < E < A < F and G < E < A < F < B < D

(3) C is the last one to reach school.

C < G < E < A < F < B < D

In the final arrangement, F is the person who reaches third in school.

Hence, Option (4) is the answer.

Shortcut Trick

Let the Cost Price (CP) of the jute bag be 100%.

Selling Price (SP₁) at a 20% loss = 100% − 20% = 80%.

Target Selling Price (SP₂) for a 20% profit = 100% + 20% = 120%.

Given that the value of 80% = Rs. 48. Therefore, the value of 120% = (48 ÷ 80) × 120 = Rs. 72. ∴ The correct answer is Rs. 72.

Alternate Method

Given:

Selling Price (SP₁) at a loss = Rs. 48

Loss Percentage = 20%

Formula Used:

Cost Price (CP) = [SP × 100] ÷ (100 − Loss %)

Selling Price (SP) = [CP × (100 + Profit %)] ÷ 100

Calculations:

First, find the Cost Price (CP):

⇒ CP = (48 × 100) ÷ (100 − 20)

⇒ CP = (48 × 100) ÷ 80

⇒ CP = Rs. 60

Now, calculate the new Selling Price (SP₂) for a 20% profit:

⇒ SP₂ = [60 × (100 + 20)] ÷ 100

⇒ SP₂ = (60 × 120) ÷ 100

⇒ SP₂ = Rs. 72

∴ The correct answer is Rs. 72.

Additional Information

Cost Price & Selling Price

Cost Price (CP) is the base value at which goods are bought. Selling Price (SP) is the final amount received after a sale. Profit occurs when SP is greater than CP, and Loss happens when SP is less than CP.

Marked Price & Discount

Marked Price (MP) is the list price attached to the article. A discount is always provided on the Marked Price. Formula: SP = MP × (100 − Discount%) ÷ 100.

Successive Percentage Change

When two successive changes of x% and y% are applied on a base value, the net percentage change is given directly by the effective formula: Net Change = x + y + (x × y) ÷ 100.

The correct answer is Element.

Important Points

• The coil of an electric room heater is termed as an element.
• The heating coil of the electric room heater transfers the electric energy into heat energy.
• The coil of the electric heater is made up of nichrome.
• Nichrome consists of 80% nickel, 20% chromium.
• In an incandescent bulb, an electric current is passed through a metal filament.

Thus, the correct answer is option 4.

Shortcut Trick

Deepak's Salary = Savings × (100 ÷ 48) = 18000 × (100 ÷ 48) = ₹37500

Raju's Salary = Deepak's Salary × (100 ÷ 120) = 37500 × (10 ÷ 12) = ₹31250

∴ The correct answer is ₹31250.

Alternate Method

Given:

⇒ Deepak's savings = ₹18000

⇒ Savings percentage = 48% of Deepak's salary

⇒ Deepak's salary = 120% of Raju's salary

Calculations:

⇒ Let Deepak's salary be D.

⇒ 48% of D = 18000

⇒ D × (48 ÷ 100) = 18000

⇒ D = 18000 × (100 ÷ 48)

⇒ D = ₹37500

⇒ Let Raju's salary be R.

⇒ Since Deepak's salary is 20% more than Raju's salary, D = R × 120%

⇒ R × (120 ÷ 100) = 37500

⇒ R × 1.20 = 37500

⇒ R = 37500 ÷ 1.20

⇒ R = ₹31250

∴ The correct answer is ₹31250.

Additional Information

Percentage Change

Percentage change is calculated as: [(Final Value − Initial Value) ÷ Initial Value] × 100.

Base Concept in Percentage

When A is x% more than B, B is the base (100%). Therefore, A = B × (100 + x) ÷ 100. Always identify the correct base for percentage calculations.

Successive Percentage

When a value is successively changed by x% and y%, the net percentage change is given by: x + y + (x × y) ÷ 100.

The correct answer is 4.

Key Points

• Meiosis is a manner wherein a single cell divides two times to produce four cells containing half the original amount of genetic statistics.
• The chromosome pairs line up subsequent to every difference along the middle (equator) of the mobile.
• Meiosis produces 4 haploid cells.  Mitosis produces 2 diploid cells.

Additional Information

• The motive of meiosis is to supply gametes or intercourse cells.
• Meiosis takes place within the testes and ovaries of men and women, respectively, inside the primordial germ cells.
• The manner of meiosis become first defined in the mid-1870s by Oscar Hertwig.

Given series:

2 3 4 2 3 4 2 5 4 7 3 2 4 3 1 9 2 5 4 8 5 4 7 2 3 4 5 2 9 5 4 6

Condition to be checked:

1. 4's which is preceded by a 5.
2. 4's which is not followed by a 7.

5 → 4 → 7 (any number but not 7)

2 3 4 2 3 4 2 5 4 7 3 2 4 3 1 9 2 5 4 8 5 4 7 2 3 4 5 2 9 5 4 6

Hence, the correct answer is "Two".

Immediately preceded by means immediately before or to come just before.

Immediately followed by means immediately after or to come just after.

Given:

Speed without stoppage = 60 km/h

Speed with stoppage = 40 km/h

Formula used:

Speed = Distance/Time

Calculation:

Distance travel by man with the speed of 60 km/h in one hour,

Distance = speed × Time

⇒ Distance = 60 × 1 = 60 km

Distance travel by man with the speed of 40 km/h in one hour,

Distance = speed × Time

⇒ Distance = 40 × 1 = 40 km

Now, the time is taken to cover the extra 20 km with the speed of 60 km/h

Time = Distance/Speed

⇒ Time = 20/60

⇒ Time = 1/3 hour = (1/3) × 60

⇒ Time = 20 minutes

∴ A man stops for 20 minutes per hour.

Stoppage in min/hr = {(F - S)/F ×  60},

Where,

F is without stoppage,

S is with stippage,

Stoppage in min/hr,

⇒ (60 - 40)/60 × 60

⇒ 20/60 × 60 = 20

∴ A man stops for 20 minutes per hour.

The correct answer is Fossil National Park.

• Ghughva is the main site of Fossil National Park.

Key Points

• Fossil National Park is located between the Kanha and the Bandhavgarh national parks in the Mandla district.
• The National Park is rich in fossils which are said to be around sixty million years old.
• Ghughva is the main site of Fossil National Park.
• Three other associated sites with Ghughva are Umaria-Silther, Deori Khurd, and Barbaspur.
• The National Park was established in 1968.

Additional Information

• Madhav National Park is situated in Shivpuri, Madhya Pradesh.
• The National Park was established in 1958.
• Van Vihar National Park is situated in Bhopal, Madhya Pradesh 
• The National Park was established in 1979.
• Satpura National Park is situated in Hoshangabad, Madhya Pradesh.
• ​The National Park was established in 1981

The least possible venn diagram is shown below,

Conclusion:

I. Some L are U → False (No L is U implies that some L cannot be U).

II. Some C are not L → True (Some U are C and no L is U implies that some part of C which are U cannot be L).

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

2 × (7 + 2) – 6/2 + (5 – 1) = ?

⇒ ? = 2 × 9 – 3 + 4

⇒ ? = 18 – 3 + 4

∴ ? = 19

The correct answer is Ladakh.

Key Points

• Naropa is Annual festival of Ladakh.
• It is also known as the "Kumbh of Himalayas".
• Naropa Festivals takes place every 12 years in the Tibetan calendar.
• The Shandol Dance was performed by 408 women artists in traditional dresses.
• The Shandol Dance broke its record of 299 artists.
• The Shandol Dance is known as "Royal dance of Ladakh"
• The Last celebration was organized in the year 2016 for completion of 1000 years of Naropa Legacy.

Additional Information

By using the symbols in the table given below, we can draw the following family tree:

Z @ R & T # H @ K → Z is wife of R, R is brother of T, T is daughter of H, H is wife of K.

Clearly, K is father-in-law of Z.

Hence, ‘Father-in-law’ is the correct answer.

Shortcut Trick

If x² + 1/x² = k, then x + 1/x = √(k + 2)

Here, the given value of k is 98.

⇒ x + 1/x = √(98 + 2)

⇒ x + 1/x = √100 = 10

∴ The correct answer is 10.

Alternate Method

Given:

x² + 1/x² = 98

Formula Used:

(a + b)² = a² + b² + 2ab

Calculations:

⇒ (x + 1/x)² = x² + 1/x² + 2 × x × (1/x)

⇒ (x + 1/x)² = x² + 1/x² + 2

Substitute the given value of x² + 1/x² = 98:

⇒ (x + 1/x)² = 98 + 2

⇒ (x + 1/x)² = 100

Taking the square root on both sides:

⇒ x + 1/x = √100

⇒ x + 1/x = 10

∴ The correct answer is 10.

Additional Information

Square of Difference

If x − 1/x = k, then x² + 1/x² = k² + 2. Conversely, x − 1/x = √(x² + 1/x² − 2).

Cubes of Sum

If x + 1/x = k, then x³ + 1/x³ = k³ − 3k.

Cubes of Difference

If x − 1/x = k, then x³ − 1/x³ = k³ + 3k.

Higher Powers

To find x⁴ + 1/x⁴, square the value of x² + 1/x² and subtract 2.

The correct answer is option 1 i.e Wilhelm Röntgen

• Wilhelm Röntgen:
• Wilhelm Rontgen discovered the  X-rays for which he received the Nobel prize in 1901.
• He became the first scientist to receive the Nobel prize in Physics.

Nobel Prize:

• The Swedish chemist, engineer and industrialist Alfred Nobel, through his will, established the five Nobel prizes in 1895.
• It is awarded for outstanding contribution in the Six fields - chemistry, literature, peace, physics, economics and physiology or medicine.
• The first Nobel Prizes were awarded in the year 1901.

The logic followed here is:

⇒ The relationship between the words "Cockpit" and "Aeroplane" is that the cockpit is a part of an aeroplane. 

Let's check each option,

1) Student ∶ Class

→ Student is a part of Class. 

2) House ∶ Room

→ House is not a part of Room. Infact, Room is a part of House. Here, the order is incorrect.

3) Pencil ∶ Lead

→ Pencil is not a part of Lead. Infact, Lead is a part of Pencil. Here, the order is incorrect.

4) Bicycle ∶ Pedal

→ Bicycle is not a part of Pedal. Infact, Pedal is a part of Bicycle. Here, the order is incorrect.

Here, we can see that only Option 1 follow the logic.

Hence, the correct answer is " Student: Class ".

Shortcut Trick

The multiplying factor for a 10% discount is 90/100 or 9/10.

Selling Price (SP) = Marked Price × (9/10) × (9/10)

SP = 1600 × (81 / 100)

SP = 16 × 81 = 1296

∴ The correct answer is Rs.1,296.

Alternate Method

Given:

Marked Price of the toy (MP) = Rs.1,600

First discount (D₁) = 10%

Second cash discount (D₂) = 10%

Formula Used:

Selling Price (SP) = MP × (1 − D₁/100) × (1 − D₂/100)

Calculations:

⇒ Price after 1^st discount = 1600 − (10% of 1600)

⇒ Price after 1^st discount = 1600 − 160 = 1440

⇒ Price after 2^nd discount = 1440 − (10% of 1440)

⇒ Price after 2^nd discount = 1440 − 144 = 1296

⇒ Final Selling Price = Rs.1,296

∴ The correct answer is Rs.1,296.

Additional Information

Equivalent Successive Discount

For two successive discounts of D₁% and D₂%, the single equivalent discount percentage is D₁ + D₂ − (D₁ × D₂) / 100.

Marked Price (MP) vs Cost Price (CP)

All discounts are calculated strictly on the Marked Price (MP), whereas Profit and Loss percentages are based exclusively on the Cost Price (CP).

Markup Percentage

The percentage by which a seller increases the price of goods above the cost price. Markup % = (MP − CP) / CP × 100.

The correct answer is 4000.

Key Points

• Madhya Pradesh Mukhyamantri Kisan Kalyan Yojana is made on the terms of Pradhan Mantri Kisan Samman Nidhi Yojana.
• In PM Kisan Samman Nidhi Yojana 6000 is given to the beneficiary farmers and in this Scheme 4000 is given in 2 Equal Installments which will make it a total of 10000 to the farmers.
• This Scheme is launched by CM Shivraj Singh Chauhan on 26 Sept 2020.80 lakh farmers will be benefitted from this Scheme.
• This Scheme is under the Revenue Department of Madhya Pradesh. Madhya Pradesh government deposited Rs.800 crores in Co-operative Bank for this scheme and Kisan Credit Card.

Additional Information 

• ​​PM Kisan Samman Nidhi Yojana a Central Government sponsored Scheme the amount of Rs.6000 will be given to Beneficiary Farmers in Three Equal Installments.
• ​PM Kisan Samman Nidhi Yojana comes under the Ministry of Agriculture and Family Welfare.
• This Scheme came on the grounds of Telangana’s Rythu Bandhu Scheme. PM Narendra Modi launched the scheme in Gorakhpur, Uttar Pradesh in 2019.

Given:

• All 34 students in a class are standing in a straight line facing north.
• Kamini is 12^th from the right end while Poonam is 8^th from the left end.

Students between Kamini and Poonam:

=> Students between Kamini and Poonam = Total number of students - (Position of Kamini from the right + Position of Poonam from the left)

=> Students between Kamini and Poonam = 34 - (12 + 8) = 34 - 20 = 14

Hence, "Fourteen​" Students stand between Kamini and Poonam.

Shortcut Trick

Total Simple Interest for 4 years = ₹5,310 − ₹4,500 = ₹810

Simple Interest for 1 year = 810 ÷ 4 = ₹202.5

Rate % = (1-year Interest ÷ Principal) × 100

Rate % = (202.5 ÷ 4500) × 100 = 4.5%

∴ The correct answer is 4.5%.

Alternate Method

Given:

Principal (P) = ₹4,500

Amount (A) = ₹5,310

Time (T) = 4 years

Formula Used:

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

Amount (A) = P + SI

Calculations:

⇒ SI = A − P

⇒ SI = 5310 − 4500 = ₹810

⇒ 810 = (4500 × R × 4) ÷ 100

⇒ 810 = 45 × R × 4

⇒ 810 = 180 × R

⇒ R = 810 ÷ 180

⇒ R = 4.5%

∴ The correct answer is 4.5%.

Additional Information

Compound Interest

When interest is compounded annually, Amount A = P × (1 + R÷100)^T.

SI vs CI Difference

For 2 years, the difference between Compound Interest and Simple Interest on the same principal is P × (R÷100)².

Rule of 72

A simple rule to estimate the number of years required to double the invested money at a given annual interest rate (Time ≈ 72 ÷ R).

The Correct Answer is Betwa.

• The town of Vidisha is located east of the Betwa River, at the fork of the Betwa and Bes rivers, 9 km from Sanchi.
• The town of Besnagar that is located 3 km from the present-day Vidisha on the west side of the river became an important commercial center in the 5^th and 6^th century BC, under the Shungas, Nagas, Satavahanas, and Guptas, it was mentioned in the Pali scriptures.
• The Betwa is a river in northern India, a tributary of the Yamuna. It rises in the Vindhya range (Raisen) just north of Hoshangabad in Madhya Pradesh and flows northeast through Madhya Pradesh and Orchha to Uttar Pradesh.
• Almost half of its course, which is not navigable, passes through the Malwa Plateau.
• The confluence of the rivers Betwa and Yamuna is the district of Hamirpur in Uttar Pradesh, in the vicinity of Orchha.

Additional Information

• In honor of the Betwa River, the Indian Navy named one of its frigates INS Betwa.
• The Betwa River is being connected to the Ken River as a part of the Madhya Pradesh River project.

Given:

Statement: The number of complaints lodged by patients and their attendants in Hospital-A has increased during the last five years. Patients have to wait for hours before treatment is started as the number of doctors available is not sufficient to treat the increasing number of patients.

Courses of action:

I. More doctors should be recruited in the hospital to meet the needs of the increasing number of patients - True (Complaints by patients and their attendants have increased during the last five years as patients have to wait for hours before treatment because of the unavailability of doctors.)

II. Patients should be motivated not to report any case of complaint in order to reduce the number of complaints - False (It is not about the complaints, its about the patients lives as they came to the hospital for treatment and its hospital's responsibility that they should have enough doctors so that patient don't have to wait for a long time.)

So, only action I should take.

Hence, the correct answer is "Option 2".

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

⇒ 4 – 1 + 5 × 6 ÷ 2 – 1 =?

⇒ 4 – 1 + 5 × 3 – 1 =?

⇒ 4 – 1 + 15 – 1 =?

⇒ 19 – 2 = 17

⇒ 17 is the correct answer.

The correct answer is Solids can be compressed easily.

Key Points

• Solid is a form of matter that has structural rigidity and a firm shape which cannot be changed easily.
• It has a fixed shape and volume.
• The intermolecular force of attraction is strong as molecules of particles are closely attached.
• There is less Intermolecular space between particles.
• They are not easily compressible.
• It is difficult to change the shape of solids, so they are hard.​

Additional Information

The logic followed here is :

Second number = (First number)² - (First number)

For 18 : 306,

18² -18 = 324 -18 = 306.

Similarly,

For 19 : ?,

19² - 19 = 361 - 19 = 342.

Hence, the correct answer is "342".

Given:

The distance of chord MN from the center is 15 cm

The length of chord MN is 40 cm

Concept:

Chord length using perpendicular distance from the centre = 2 × √ (r2 – d2) [∵ r = radius, d = perpendicular distance]

Calculation:

Length of Chord = 2 × √ (r2 – d²)

40 =  2 × √ (r² – 15²) = 25 cm

∴ Option 4 is the correct answer.

The correct answer is Death.

Key Points

• Kushinagar(Uttar Pradesh) is the place where Buddhists believe Gautama Buddha attained Parinirvana after his death.
• Mahaparinirvana is a Sanskrit word meaning 'Final Death.
• After the death of Buddha, his followers built a stupa where the relics of Buddha were kept.

Additional Information

• Events related to Buddha and representing Symbol:

The logic is:

Hence, ‘GRQ’ is the correct answer.

Shortcut Trick

Let the total work be the LCM of 15 and 7.5 = 15 units.

Efficiency of A = 15 ÷ 15 = 1 unit/day.

Efficiency of A and B together = 15 ÷ 7.5 = 2 units/day.

Efficiency of B alone = 2 − 1 = 1 unit/day.

Time taken by B = Total work ÷ Efficiency of B = 15 ÷ 1 = 15 days.

∴ The correct answer is 15 days.

Alternate Method

Given:

Time taken by A alone = 15 days.

Time taken by A and B together = 7.5 days.

Formula Used:

Total Work = Efficiency × Time

Calculations:

⇒ Efficiency of B = (Efficiency of A + B) − Efficiency of A

⇒ Efficiency of B = 2 − 1 = 1 unit/day

⇒ Time taken by B = Total Work ÷ Efficiency of B

⇒ Time taken by B = 15 ÷ 1 = 15 days

∴ The correct answer is 15 days.

Additional Information

Pipes and Cisterns

Works on the same concept as time and work, but an outlet pipe is considered as doing negative work. Net efficiency = Inlet efficiency − Outlet efficiency.

Work and Wages

Wages are distributed in direct proportion to the actual amount of work done. If multiple people work for the exact same duration, their wages are divided in the ratio of their daily efficiencies.

Alternate Day Work

For alternate day completion, calculate the total work done in one complete cycle (e.g., a 2-day cycle for 2 people) and determine how many cycles are required to reach the total work.

The Correct Answer is Grass.

Key Points

• ​The grass is a producer, a self-sustaining organism that obtains its energy from the sun.
• All biological organisms play a part in the earth's ecosystem, but consumers get energy from eating other organisms and producers make energy on their own.
• A food chain always starts with a producer, which is an organism that makes food. This is usually a green plant, because plants can make their own food by photosynthesis.

Additional Information

• Bacteria:- 
• Bacteria are decomposers.
• Decomposers are made up of the FBI (fungi, bacteria and invertebrates—worms and insects). They are all living things that get energy by eating dead animals and plants and breaking down the wastes of other animals.
• Grasshopper:-
• Grasshopper is consumers.
• A grasshopper eats grass, hence the grasshopper is the primary consumer.
• Mushroom:-
• Mushrooms are decompoers.
• This group of consumers eats only dead organisms. They break down the nutrients in the dead organisms and return them to the food web. They may eat dead producers or consumers.

The logic is:

1. QIW → Q = 17, I = 9, W = 23 and 17 + 9 + 23 = 49

2. OYJ → O = 15, Y = 25, J = 10 and 15 + 25 + 10 = 50

3. FSX → F = 6, S = 19, X = 24 and 6 + 19 + 24 = 49

4. MTP → M = 13, T = 20, P = 16 and 13 + 20 + 16 = 49

The sum of the place value of the letters of all the options except ‘OYJ’ are 49, while that of ‘OYJ’ is 50.

Hence, ‘OYJ’ is the odd one out.

Shortcut Trick

Total weight increase = Total persons × Average increase

Total increase = 10 × 7.9 = 79 kg

New person's weight = Replaced person's weight + Total increase

New person's weight = 20 + 79 = 99 kg

∴ The correct answer is 99 kg.

Alternate Method

Given:

Number of persons = 10

Weight of replaced person = 20 kg

Increase in average weight = 7.9 kg

Formula Used:

Weight of new person = Weight of replaced person + (Total members × Increase in average)

Calculations:

⇒ Total weight increase of the group = 10 × 7.9

⇒ Total increase = 79 kg

⇒ Weight of the new person = 20 + 79

⇒ Weight of the new person = 99 kg

∴ The correct answer is 99 kg.

Additional Information

Replacement in Averages

When a new item replaces an old item, causing the average to increase, the value of the new item is calculated as: New Value = Old Value + (Total Items × Increase in Average).

Decrease in Average on Replacement

If the replacement causes the average to drop, it means the new item is smaller. The formula is: New Value = Old Value − (Total Items × Decrease in Average).

Addition of a New Member

When a completely new member joins the group (without replacing anyone) and changes the average: New Member's Value = Old Average + (New Total Members × Change in Average).