Previous Year Question Paper

GDS To MTS Question Paper 2025 Uttar Pradesh Circle

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GDS To MTS Question Paper 2025 Uttar Pradesh Circle questions and answers

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Question 1

#501

According to the PO Guide Part-1, what action must be taken if a postal employee suspects that a parcel contains prohibited items such as explosives or noxious substances?

A

Immediately return the parcel to the sender without opening it

B

Deliver it as usual but mark it for inspection

C

Detain the parcel and report it to the Head of the Office for further action

D

Open the parcel on the spot and verify its contents without informing superiors

Correct answer keyC

Explanation

In any case in which a postmaster has good reason to suspect that the contents of any postal article are likely to injure the mails or harm the person of any one engaged in the postal service he is directed to detain the suspected article and to refer the case at once for the orders of the Head of the Circle.

Article fastened with pins will be returned at once to the senders, if the irregularity is detected at the office of posting.

If detected subsequently, they will be returned through the Returned Letter Office, the pins being first removed.

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Question 2

#502

Which of the following Articles are not delivered through a post box?

A

Aerogramme

B

Inland letter Cards

C

Registered letters

D

Registered Newspapers

Correct answer keyC
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Question 3

#503

International Financial System (IFS) Money Order IFS-MO is operational in which of the following countries/Postal Operators?

A

Only with La Poste France

B

Only With UAE

C

Both La Poste France and UAE

D

None of the Above

Correct answer keyC

Explanation

India Post, the Universal Postal Union's International Financial System (IFS) Money Order (IFS-MO) service is currently operational in just two countries: France (La Poste Group) and the UAE (Emirates Post).

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Question 4

#504

Which of the following statement is correct with respect to Gyan Post?

A

The minimum weight shall be 300 gms. and the maximum weight shall be 5 (five) kg.

B

The minimum weight shall be 100 gms. and the maximum weight shall be 5 (five) kg.

C

The minimum weight shall be 300 gms. and the maximum weight shall be 10 (ten) kg.

D

The minimum weight shall be 100 gms. and the maximum weight shall be 10 (ten) kg.

Correct answer keyA
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Question 5

#505

Which of the following statement is correct with respect to Gyan Post?

A

The item posted as Gyan Post shall be address specific and shall be transmitted through surface mode.

B

The item posted as Gyan Post shall be addressee specific and shall be transmitted through Air mode.

C

The item posted as Gyan Post shall be addressee specific and shall be transmitted through surface mode.

D

The item posted as Gyan Post shall be address specific and shall be transmitted through Air mode.

Correct answer keyA
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Question 6

#506

Which of the following statement is correct with respect to Literature for Blind transmitted via India Post?

A

Postage shall be chargeable, but air mail fee shall be not chargeable for transmission by air.

B

No postage shall be chargeable; Air mail fee shall be also be not chargeable for transmission by air.

C

Postage shall be chargeable, as well as air mail fee shall be chargeable for transmission by air.

D

No postage shall be chargeable, but air mail fee shall be chargeable for transmission by air.

Correct answer keyD
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Question 7

#507

Which of the following is not typically a duty of a Post Office Counter Clerk according to the India Post operations guide?

A

Booking articles and accepting deposits.

B

Preparing accounts and statistical registers.

C

Delivering mail at the recipient's doorstep.

D

Handling payment of Money Orders.

Correct answer keyC
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Question 8

#508

Who is the administrative head of the Department of Posts in India?

A

Director General (Postal Services)

B

Chief General Manager

C

Secretary (Posts)

D

Member (Operations)

Correct answer keyA

Question 9

#509

According to the PO Guide Part I, what are the standard business hours of a post office, excluding weekly holidays?

Removed from evaluation

This question is deleted, so it is shown here only for reference.

A

9:00 AM to 3:00 PM

B

10:00 AM to 4:00 PM

C

9:00 AM to 2:00 PM

D

9:30 AM to 5:30 PM

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Question 10

#510

Which of the following is not a duty of a Letter Box Peon as per PO Guide Part-1?

A

Collecting letters from all letter boxes at scheduled times

B

Opening and checking the contents of the collected letters

C

Ensuring the letter boxes are securely locked after clearance

D

Reporting any damage or tampering of letter boxes to the postmaster

Correct answer keyB
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Question 11

#511

Which of the following articles is conditionally transmissible by post only if specific packing and declaration requirements are fulfilled, as per PO Guide Part-1?

A

Explosives and gunpowder

B

Live animals

C

Liquids and semi-liquids

D

Gold in any form

Correct answer keyC
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Question 12

#512

A customer approaches a post office to send a parcel containing a bottle of hair oil, some prescription medicine, and a metal tool by ordinary parcel. According to the PO Guide Part-1, what should the postal booking clerk do?

A

Accept the parcel without any special

B

Refuse the parcel outright, as all listed items are prohibited

C

Accept the parcel only if the customer provides a written declaration and uses proper packaging

D

Accept the parcel only if it is sent by Speed Post

Correct answer keyC
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Question 13

#513

Maximum limit of weight for international tracked packet service is:

A

20 kg

B

5 kg

C

10 kg

D

35 kg

Correct answer keyB

Explanation

The maximum weight limit for the International Tracked Packet Service (ITPS) is 5 kg, effective from April 1, 2025. However, for certain countries, the maximum weight limit remains 2 kg. Prior to this update, the general maximum weight limit for this service was 2 kg.

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Question 14

#514

Which of the following statements is correct regarding the payment of postage in the Indian Postal System, as per the PO Guide Part-1?

A

Postage must always be paid using adhesive postage stamps only.

B

Official correspondence must always bear postage stamps for accountability.

C

Postage can be paid using stamps, impressions, or in cash under permitted conditions.

D

Stationery with impressed stamps cannot be used for registered or insured articles.

Correct answer keyC
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Question 15

#515

According to the PO Guide Part-1, what is the prescribed treatment for unpaid or insufficiently paid postal articles found in the post?

A

They are immediately returned to the sender without delivery.

B

They are delivered at the discretion of the postmaster.

C

They are delivered only after charging double the deficiency from the addressee.

D

They are delivered free of cost if addressed to government offices.

Correct answer keyC
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Question 16

#516

According to the Postal Manual, which of the following statements about the use of a franking machine for postage payment is correct?

A

Franking machines can be used only by government departments.

B

Franking machines can be used by customers under agreement, and payment must be made in advance.

C

Franking machines are used only for international mail services.

D

Payment for franking is made after dispatch of the mail.

Correct answer keyB
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Question 17

#517

Which of the following is not a valid condition for the acceptance of articles franked with a franking machine?

A

The franked articles will be tendered at the counter bundled in separate bundles according to the value of the franks

B

The impressions of the franking machines recorded on postal articles should, as far as possible, be on the right top corner on the address side of the article itself or an address wrapper or an address label firmly attached to it.

C

There may be more than one impression of the licence die but only one of the value die on each article.

D

Articles should be given for acceptance in separate bundles of fixed number like 50 for each value of frank.

Correct answer keyC
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Question 18

#518

Consider the below given two statements P & Q wrt to franked articles and franking machine:

P. The re-setting of franking machine may be done at the premises of the holders of the machines and the machine need not be brought to the post office for this purpose.

Q. Machine franked articles posted in letter boxes shall be treated as unpaid articles.

A

Both P & Q are correct

B

Both P & Q are incorrect

C

P is correct but Q is incorrect

D

Q is correct but P is incorrect

Correct answer keyA
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Question 19

#519

If an Indian Postal Order is not presented for payment within six months from the last day of the month of issue, what is charged?

A

A penalty fee

B

The order becomes void

C

A second commission at prescribed rates

D

The amount is forfeited

Correct answer keyC

Explanation

Based on the traditional Post Office Guide Part-I (Clause 252), if an Indian Postal Order (IPO) is not presented for payment within its initial currency period (which was historically six months), a second commission at the prescribed rates is charged, which must be paid by affixing postage stamps to the back of the order.

Important Update for Latest Exams:
Please note that under the new Post Office Regulations 2024 (Regulation 158), the initial currency period has been extended. Currently, an IPO is valid for 24 months from the last day of the month of issue without any additional charge.

If it is not presented within those 24 months, it can still be encashed up to 36 months by paying the second commission. After 36 months, the order becomes void and the amount is forfeited.

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Question 20

#520

The transmission by the Inland post of the undermentioned articles is not prohibited:

A

Any sharp instrument not properly protected.

B

Any newspaper having on it or on the cover thereof, any words, marks or design of grossly offensive nature.

C

Lottery ticket

D

Gold coin or bullion or both of a value not exceeding Rs. 10,000.

Correct answer keyD

Explanation

According to the updated postal rules, the transmission of gold coin or bullion is only prohibited if its value exceeds Rs. 5,00,000 (Five Lakh)

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Question 21

#521

What is the minimum amount by which a domestic Philatelic Deposit Account should be replenished when it approaches exhaustion?

A

Rs. 25/-

B

Rs. 50/-

C

Rs. 100/-

D

Rs. 200/-

Correct answer keyD

Explanation

According to the updated postal guidelines, this deposit should be replenished by a sum of not less than Rs. 200/-.

If the balance in the account falls below the value of a single order plus handling charges, the account becomes inoperative. To bring the account back into operation, a fresh deposit of a minimum of Rs. 200/- must be made.

(Note: The older 1985 Post Office Guide originally set this minimum replenishment amount at Rs. 50.)

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Question 22

#522

Which of the following was a key objective of the IT Modernization Project?

A

Implementing green energy solutions for post offices

B

Developing software applications for counter operations, postal banking, and HR

C

Establishing foreign postal connections

D

Setting up an e-commerce platform

Correct answer keyB
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Question 23

#523

Holy Blessings - Temple Prasadam service is not available for which of following temples as per India Post Website?

A

Shri Kashi Vishwanath Mandir Varanasi

B

Shri Banke Bihari Ji Mandir, Vrindavan

C

Shri Hanuman Garhi temple Ayodhya

D

Sabarimala Swamy Prasadam, Kerala

Correct answer keyB
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Question 24

#524

What is the renewal fee for expired license of a franking machine?

A

375/-

B

475/-

C

350/-

D

325/-

Correct answer keyB

Explanation

According to the rules regarding franking machine licenses, the standard fee for a license (which is valid for 5 years) is ₹375. However, in the case of a late renewal (when the license has expired), an additional penalty of ₹100 is charged, making the total renewal fee ₹475.

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Question 25

#525

What can be the maximum weight for a book packet?

A

5 Kg

B

3 Kg

C

2 Kg

D

10 Kg

Correct answer keyA
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Question 26

#526

What is discount percentage for Speed Post customer whose monthly booking revenue lies between 500001/- to 2500000/-:

A

5%

B

10%

C

15%

D

20%

Correct answer keyC
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Question 27

#527

What is additional discount for booking International tracked package through Dakghar Niryat Kendra (DNK)?

A

2%

B

3%

C

1%

D

5%

Correct answer keyA
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Question 28

#528

Which class student can participate in Deen Dayal SPARSH Yojana, Scholarship scheme of Department of Posts.

A

Class V

B

Class VI

C

Class X

D

All of Above Classes

Correct answer keyB

Explanation

The Deen Dayal SPARSH Yojana (Scholarship for Promotion of Aptitude & Research in Stamps as a Hobby) is a scholarship scheme designed by the Department of Posts to promote philately among children. According to the scheme's guidelines, it specifically targets and awards students in the class category of Standard VI to IX.

Therefore, out of the given options, only a Class VI student is eligible to participate, as Class V and Class X fall outside the eligible range.

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Question 29

#529

What minimum quantity can be accepted under 'Direct Post' service?

A

1000

B

500

C

1500

D

2000

Correct answer keyA
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Question 30

#530

The amount or value of money order unpaid beyond how many years from the date of booking shall be forfeited after expiry of the said period, such amount or value shall be treated as revenue to the Government of India.

A

Three Year

B

Two Year

C

One Year

D

Six Months

Correct answer keyA
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Question 31

#531

Which of the following is not a Fundamental Right provided by Constitution of India.

A

Protection of language and culture of Minorities.

B

Right of Minorities to establish Educational Institutions.

C

Right to manage religious affairs and give religious instructions in certain institutions.

D

Right to discriminate on the grounds of Religion.

Correct answer keyD

Explanation

The Constitution of India explicitly prohibits discrimination on the grounds of religion under Article 15.

The other relevant Fundamental Rights are:

  • Article 29: Protects the interests of minorities by safeguarding their language, script, and culture.
  • Article 30: Grants minorities the right to establish and administer educational institutions.
  • Article 26: Allows every religious denomination to manage its own religious affairs.

Extra Exam Facts:

  • Fundamental Rights are enshrined in Part III of the Constitution (Articles 12–35).
  • The concept of Fundamental Rights in the Indian Constitution was inspired by the Bill of Rights of the U.S. Constitution.
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Question 32

#532

Which of the following Provision is Borrowed from Canadian Constitution in Indian Constitution?

A

The Power of Judicial Review

B

The Directive Principles of State Policy

C

The Institution of Speaker and Its Powers

D

The Concept of Residual Power

Correct answer keyD

Explanation

The concept of vesting residual powers in the Centre is borrowed from the Canadian Constitution.

Other important constitutional borrowings:

  • Judicial Review – Borrowed from the United States (USA).
  • Directive Principles of State Policy (DPSP) – Borrowed from Ireland.
  • Office of the Speaker and their role – Influenced by the British Parliamentary System.

Extra Exam Facts:

  • From Canada, India also borrowed:

    • The concept of a federation with a strong Centre.
    • The appointment of State Governors by the Centre.
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Question 33

#533

Which of the following is Highest (in Lakhs Tonnes) Soyabean Producing state as per Third Advance estimate 2024-25?

A

Madhya Pradesh

B

Uttar Pradesh

C

Rajasthan

D

Maharashtra

Correct answer keyD

Explanation

According to the Third Advance Estimate 2024-25, Maharashtra has emerged as the highest soybean producing state. Extra Exam Facts: Madhya Pradesh historically held the title of the 'Soyabean State' of India, but Maharashtra has frequently overtaken it in recent production estimates due to favorable yields and expanded acreage. India is among the top 5 soybean producers globally.

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Question 34

#534

The famous Khajuraho temples, renowned for their intricate sculptures and unique architectural style, were primarily built by which dynasty?

A

Gupta Dynasty

B

Maratha Dynasty

C

Maurya Dynasty

D

Chandela Dynasty

Correct answer keyD

Explanation

The Khajuraho group of monuments was built by the Chandela dynasty between 950 AD and 1050 AD.

Extra Exam Facts: Located in Madhya Pradesh, Khajuraho is a UNESCO World Heritage site known for its Nagara-style architectural symbolism and erotic sculptures. The Kandariya Mahadeva Temple is the largest and most famous temple in the complex.

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Question 35

#535

In the Mimamsa school of Indian philosophy, ethical action is primarily justified on which of the following bases?

A

The pursuit of liberation (moksha) as the highest goal.

B

The intrinsic value of non-violence (ahimsa) as universal law.

C

The realization of the self (atman) as identical with Brahman.

D

The authority of Vedic injunctions (vidhi) as the source of dharma.

Correct answer keyD

Explanation

The Mimamsa school, one of the six orthodox (astika) schools of Indian philosophy, strongly emphasizes the authority of the Vedas. Ethical action (dharma) is dictated by Vedic commands (vidhi) and rituals.

Extra Exam Facts: Purva Mimamsa was founded by Sage Jaimini. Unlike Vedanta (Uttara Mimamsa) which focuses on Moksha (liberation) and Brahman, Purva Mimamsa focuses strictly on Dharma through the adherence to Vedic rituals and duties.

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Question 36

#536

Which of the following best represents Mahatma Gandhi's Theory of Trusteeship in the context of modern capitalism?

A

Nationalization of private property to ensure equitable wealth distribution.

B

Voluntary renunciation of all material wealth by the rich in favor of the poor.

C

Legal redistribution of wealth through compulsory taxation and welfare programs.

D

Moral stewardship of wealth by the rich for the welfare of society, without coercive state control.

Correct answer keyD

Explanation

Gandhi's Theory of Trusteeship posits that wealthy individuals should act as 'trustees' of their wealth, holding and using it for the welfare of the community rather than for selfish desires, emphasizing moral conscience over state coercion.

Extra Exam Facts: This socio-economic philosophy aimed to bridge the gap between the rich and the poor without resorting to violence or extreme state control (like communism). It heavily influenced several Indian industrialists of his time, such as Jamnalal Bajaj.

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Question 37

#537

Which of the following statements best describes the primary reason for Mahatma Gandhi's decision to suspend the Non-Cooperation Movement in 1922?

A

The British government made concessions to Indian demands, including the release of political prisoners.

B

The movement had successfully achieved all its major objectives.

C

The Muslim League withdrew its support, weakening the movement's unity.

D

The occurrence of violent incidents, like the Chauri Chaura incident, indicated a deviation from the principle of non-violence.

Correct answer keyD

Explanation

Mahatma Gandhi abruptly called off the Non-Cooperation Movement after the Chauri Chaura incident in February 1922, when a violent mob set fire to a police station, killing 22 policemen.

Extra Exam Facts:

  • Gandhi was a staunch advocate of Ahimsa (non-violence) and believed that the masses were not yet ready for a completely non-violent mass movement.
  • The suspension of the movement led to the formation of the Swaraj Party by C.R. Das and Motilal Nehru.
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Question 38

#538

Tropic of Cancer does not pass through which of the following States in India.

A

Gujarat

B

Uttar Pradesh

C

Jharkhand

D

West Bengal

Correct answer keyB

Explanation

The Tropic of Cancer does not pass through Uttar Pradesh.

Extra Exam Facts:

  • The Tropic of Cancer (23.5° North latitude) passes through 8 Indian states:

    1. Gujarat
    2. Rajasthan
    3. Madhya Pradesh
    4. Chhattisgarh
    5. Jharkhand
    6. West Bengal
    7. Tripura
    8. Mizoram
  • It effectively divides India into the tropical and sub-tropical climatic zones.

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Question 39

#539

Which of the following is incorrect about the passes of the North & Northeastern mountains of India?

A

Zoji La Passes lies on Great Himalayas

B

Banihal Passes Lies on Pir Panjal

C

Khardung La lies on Pir Panjal

D

Photu La lies on Zaskar

Correct answer keyC

Explanation

The statement "Khardung La lies on the Pir Panjal Range" is incorrect because Khardung La is located on the Ladakh Range, north of Leh.

Extra Exam Facts:

  • Khardung La is one of the highest motorable mountain passes in the world and serves as the gateway to the Shyok and Nubra Valleys.
  • Zoji La connects Srinagar with Leh.
  • Banihal Pass connects the Kashmir Valley with the outer Himalayas and the plains.
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Question 40

#540

Which is the Longest River amongst Tapi, Mahi, Pennar & Suvernrekha?

A

Tapi

B

Mahi

C

Pennar

D

Suvernrekha

Correct answer keyA

Explanation

Among the given options, the Tapi (Tapti) River is the longest, with a length of approximately 724 km.

Extra Exam Facts:

  • The Tapi is a major west-flowing river of peninsular India.

  • It originates in the Satpura Range in Madhya Pradesh and empties into the Arabian Sea.

  • Approximate lengths of the other rivers are:

    • Pennar597 km
    • Mahi580 km
    • Subarnarekha395 km
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Question 41

#541

A train travels from Station A to Station B at a speed of 60 Km/hrKm/hr and returns from Station B to Station A at a speed of 40 Km/hr.40~Km/hr. What is the average speed of the train for the entire journey?

A

48 Km/hr48~Km/hr

B

50 Km/hr50~Km/hr

C

52 Km/hr52~Km/hr

D

54 Km/hr54~Km/hr

Correct answer keyA

Explanation

To find the average speed when the distances are equal, we use the formula: Average Speed=2xyx+y\text{Average Speed} = \frac{2xy}{x + y}. Here, x=60 km/hrx = 60\text{ km/hr} and y=40 km/hry = 40\text{ km/hr}. Substituting the values: Average Speed=2×60×4060+40=4800100=48 km/hr\text{Average Speed} = \frac{2 \times 60 \times 40}{60 + 40} = \frac{4800}{100} = 48\text{ km/hr}.

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Question 42

#542

If 15 workers can complete a task in 24 days, working 8 hours a day, in how many days will 20 workers complete the same task if they work 6 hours a day?

A

18 Days

B

20 Days

C

24 Days

D

22 Days

Correct answer keyC

Explanation

We can use the work formula: M1×D1×H1=M2×D2×H2M_1 \times D_1 \times H_1 = M_2 \times D_2 \times H_2, where MM is workers, DD is days, and HH is hours. Substituting the given values: 15×24×8=20×D2×615 \times 24 \times 8 = 20 \times D_2 \times 6. Simplifying this gives: 2880=120×D22880 = 120 \times D_2. Therefore, D2=2880120=24 daysD_2 = \frac{2880}{120} = 24\text{ days}.

Question 43

#543

A sum of money becomes 2,400 in 3 years and 2,880 in 5 years at simple interest. What is the rate of interest per annum?

Removed from evaluation

This question is deleted, so it is shown here only for reference.

A

5%

B

10%

C

6%

D

8%

Explanation

Let the Principal = P and the Rate of Interest = R.

  • Amount after 3 years = ₹2400
  • Amount after 5 years = ₹2880

Step 1: Interest for 2 years (from the 3rd to the 5th year):

  • ₹2880 − ₹2400 = ₹480

Step 2: Simple Interest for 1 year:

  • ₹480 ÷ 2 = ₹240

Step 3: Simple Interest for 3 years:

  • ₹240 × 3 = ₹720

Step 4: Principal:

  • P = ₹2400 − ₹720 = ₹1680

Step 5: Rate of Interest:

  • R = (240 ÷ 1680) × 100 = 100/7 ≈ 14.28%

Conclusion:
The rate of interest is 14.28% (approximately).

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Question 44

#544

What is the correct value of the expression: 8+6×(53)2÷2=?8+6\times(5-3)^{2}\div2=?

A

20

B

26

C

14

D

18

Correct answer keyA

Explanation

Using BODMAS rule to solve the expression 8+6×(53)2÷28 + 6 \times (5 - 3)^2 \div 2. First, solve the brackets: (53)=2(5 - 3) = 2. Next, solve the exponent: 22=42^2 = 4. The expression becomes 8+6×4÷28 + 6 \times 4 \div 2. Then, perform division: 4÷2=24 \div 2 = 2. The expression is now 8+6×28 + 6 \times 2. Next, perform multiplication: 6×2=126 \times 2 = 12. Finally, addition: 8+12=208 + 12 = 20.

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Question 45

#545

What is the value of the expression: 36÷3×(4+2)5=?36\div3\times(4+2)-5=?

A

67

B

19

C

66

D

17

Correct answer keyA

Explanation

Using BODMAS rule for the expression 36÷3×(4+2)536 \div 3 \times (4 + 2) - 5. First, solve the bracket: (4+2)=6(4 + 2) = 6. The expression becomes 36÷3×6536 \div 3 \times 6 - 5. Next, perform division: 36÷3=1236 \div 3 = 12. The expression is now 12×6512 \times 6 - 5. Next, multiply: 12×6=7212 \times 6 = 72. Finally, subtract: 725=6772 - 5 = 67.

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Question 46

#546

A shopkeeper marks an item at 800 and offers a discount of 10%. If he still makes a profit of 20%, what was the cost price of the item?

A

576

B

640

C

720

D

600

Correct answer keyD

Explanation

Marked Price (MP) = 800. Discount = 10% of 800 = 800×10100=80800 \times \frac{10}{100} = 80. Selling Price (SP) = MP - Discount = 80080=720800 - 80 = 720. The shopkeeper makes a profit of 20%, so SP=CP+20% of CP=1.2×CPSP = CP + 20\% \text{ of } CP = 1.2 \times CP. Therefore, 1.2×CP=7201.2 \times CP = 720, which means CP=7201.2=600CP = \frac{720}{1.2} = 600. The cost price was 600.

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Question 47

#547

The average weight of 8 people is 65 kg. If one person leaves and a new person joins, the average becomes 64.5 kg. The person who left had a weight of 70 kg. What is the weight of the new person?

A

65 Kg

B

67 Kg

C

68 Kg

D

66 Kg

Correct answer keyD

Explanation

Let the initial total weight be 8×65=520 kg8 \times 65 = 520\text{ kg}. Let the weight of the new person be xx. After one person of 70 kg leaves and the new person joins, the new total weight is 52070+x=450+x520 - 70 + x = 450 + x. The new average for the 8 people is given as 64.5 kg, so 450+x8=64.5\frac{450 + x}{8} = 64.5. Multiplying by 8 gives 450+x=516450 + x = 516. Therefore, x=516450=66 kgx = 516 - 450 = 66\text{ kg}.

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Question 48

#548

The price of a mobile phone was first increased by 20% and later decreased by 25%. What is the overall percentage change in the price?

A

5% increase

B

10% decrease

C

10% increase

D

5% decrease

Correct answer keyB

Explanation

Let the initial price be 100. After a 20% increase, the price becomes 100+20=120100 + 20 = 120. Then, the price is decreased by 25%. A 25% decrease on 120 is 120×25100=30120 \times \frac{25}{100} = 30. The new price is 12030=90120 - 30 = 90. The overall change from the initial price of 100 to the final price of 90 is a decrease of 10. Therefore, the overall percentage change is a 10% decrease.

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Question 49

#549

A and B together can complete a piece of work in 12 days. B and C can do it in 15 days, and A and C can do it in 20 days. In how many days can A alone complete the work?

A

30 days

B

20 days

C

40 days

D

24 days

Correct answer keyA

Explanation

Let the rates of work of A, B, and C be 1A,1B, and 1C\frac{1}{A}, \frac{1}{B}, \text{ and } \frac{1}{C} respectively. We have: 1A+1B=112\frac{1}{A} + \frac{1}{B} = \frac{1}{12} (Eq 1), 1B+1C=115\frac{1}{B} + \frac{1}{C} = \frac{1}{15} (Eq 2), and 1A+1C=120\frac{1}{A} + \frac{1}{C} = \frac{1}{20} (Eq 3). Adding all three equations: 2(1A+1B+1C)=112+115+120=5+4+360=1260=152(\frac{1}{A} + \frac{1}{B} + \frac{1}{C}) = \frac{1}{12} + \frac{1}{15} + \frac{1}{20} = \frac{5+4+3}{60} = \frac{12}{60} = \frac{1}{5}. Thus, 1A+1B+1C=110\frac{1}{A} + \frac{1}{B} + \frac{1}{C} = \frac{1}{10}. To find A's rate, subtract Eq 2 from this sum: 1A=110(1B+1C)=110115=3230=130\frac{1}{A} = \frac{1}{10} - (\frac{1}{B} + \frac{1}{C}) = \frac{1}{10} - \frac{1}{15} = \frac{3 - 2}{30} = \frac{1}{30}. A alone can complete the work in 30 days.

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Question 50

#550

A man covers a certain distance by walking at 5 km/h5~km/h and returns by cycling at 15 km/h.15~km/h. If the total time taken for the whole journey is 4 hours, what is the distance (in km) between the two points?

A

10 Km

B

15 Km

C

12 Km

D

14 Km

Correct answer keyB

Explanation

Let the distance between the two points be dd km. The time taken to walk the distance at 5 km/h5\text{ km/h} is d5\frac{d}{5} hours, and the time to return by cycling at 15 km/h15\text{ km/h} is d15\frac{d}{15} hours. The total time taken is 4 hours, so we set up the equation: d5+d15=4\frac{d}{5} + \frac{d}{15} = 4. Finding a common denominator (15), we get 3d+d15=4\frac{3d + d}{15} = 4, which simplifies to 4d15=4\frac{4d}{15} = 4. Dividing both sides by 4 gives d15=1\frac{d}{15} = 1, so d=15d = 15. The distance between the two points is 15 km15\text{ km}.