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Given:

Average age of 10 persons = 32 years 

Average age of 11 persons including instructor = 34 years

Formula used:

Average age = Sum of the ages of persons/No of persons 

Calculation:

Total age of 10 persons = 32 years × 10 = 320 years

Total age of 11 persons including instructor = 34 years × 11 = 374

∴ The age of instructor = 374 - 320 = 54 years

Given:

25% of a number is 20

Calculation:

Let the number be = a 

25% × a = 20 

⇒ 25/100 × a = 20 

⇒ a = 20 × 100/25 = 80 

∴ 40% of a = 40/100 × 80 = 32

Alternate Method 25% = 1/4 

⇒ 1/4 = 20

⇒ 4 = 20 × 4 = 80

∴ 40% of the number = 2/5 × 80 = 32

A girl is facing south direction. She turns 60° in clock wise direction and turns 100° in the anticlock wise direction.

The diagram are given below -

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

Formula used:

Sum of n natural numbers = n(n + 1)/2 

Calculation:

Sum of 50 natural numbers = 50 × 51/2 

∴ Sum of 50 natural numbers is 1275.

Given:

Cost price of 2 tables and 3 chairs = Rs.3500 

Cost price of 3 tables 2 chairs = Rs.4000

Calculation:

Let the cost price of a table be = t 

⇒ Cost price of a chair = c

2t + 3c = 3500       (1)

3t + 2c = 4000       (2) 

By 2 × (1) and 3 × (2) and solving them 

⇒ 4t + 6c = 7000       (3)

⇒ 9t + 6c = 12000     (4)

By (4) - (3):

9t + 6c - 4t - 6c = 12000 - 7000 

⇒ 5t = 5000 

⇒ t = 1000

∴ The cost of one table is Rs.1000.

Given:

Time taken by 12 machines working 7 hours a day = 18 days 

Formula used:

(M1 × D1 × H1)/W1 = (M2 × D2 × H2)/W2 

Calculation:

By using the above formula for calculating the no of days:

(12 × 18 × 7)/1 = (16 × D2 × 9)/2

⇒ 12 × 18 × 7 × 2/(16 × 9) = D2 

⇒ D2 = 21 days 

∴ 16 machines working 9 hours a day finish twice the work in 21 days.

Given:

Average age of A & B four years ago = 18 years 

Present age of A, B & C = 24 years 

Formula used:

Average age = Sum of the ages/No of persons 

Calculation:

Sum of the ages of A and B, 4 years ago = 18 × 2 = 36 years 

Sum of the present age of A and B = 4 + 4 + 36 = 44 years 

Sum of the present ages of A, B and C = 24 × 3 = 72 years 

⇒ Present age of C = 72 - 44 = 28 years

∴ C's age after 4 years = 28 + 4 = 32 years.

The correct answer is President.

Key Points

• Administration of Union Territories
• President is the de-jure or constitutional head of the state.
• Article 52 says that there shall be a president of India.
• President is the first citizen and the supreme commander of the defence forces of India.
• The President of India is responsible for the administration of a Union Territory which does not have its own elected Legislative Assembly.
• As per article 239 of the Indian constitution President of India is the chief administrator of union territories. Hence, Option 3 is correct.
• He appoints an administrator or lieutenant governor for each Union Territories.
• The election of the president is conducted by the election commission of India.
• Dr Rajendra Prasad was the first President of India.

Additional Information

• Union Home Minister
• Amit Shah was born to Smt. Kusumben and Shri Anilchandra Shah, in an affluent Gujarati family on 22^nd October 1964.
• Amit Shah represents the emerging New India in every sense of the term.
• Leading the Party from the front for the last five years, he has been remarkably successful in expanding BJP’s organizational footprint, securing one electoral victory after the other in State assembly elections.
• During his tenure, Party has become the world’s largest political party with over 10 crores of registered members.
• Lieutenant Governor
• A Lieutenant Governor also has the same powers.
• Only three Union Territories — Andaman and Nicobar, Delhi and Puducherry — have Lt. Governors.
• These powers are in place to ensure checks and balances for the state government and its functioning.
• The President of India is the head of the Indian state and is also the first citizen of India.
• Article 52 of the Indian Constitution mentions that there shall be a President of India.
• Droupadi Murmu is an Indian politician who has been serving as the 15^th president of India since 25 July 2022. She is the first person belonging to the tribal community and also the second woman after Pratibha Patil to hold the office.
• The detailed information about the election of the president in India.
• The President is an integral part of the union executive along with the Vice President, Prime Minister, the council of ministers, and attorney journal.

The correct answer is Dhaka.

Key Points

• March 16, 2012, will be etched in the minds of cricket fans across the globe as the day when Sachin Tendulkar scored his 100^th international century.
• During the Asia Cup clash against Bangladesh at the Sher-e-Bangla National Stadium Dhaka, Tendulkar played a brilliant knock of 114 to bring up his 49^th ODI century. Hence, Option 2 is correct.
• The maestro already had 51 hundred to his name in the longest format.
• His century was also special in the sense that he breached the three-figure mark after a gap of one year.

Important Points

• Dhaka
• It is the capital city of Bangladesh, in southern Asia.
• Set beside the Buriganga River, it’s at the centre of the national government, trade, and culture.
• The 17^th-century old city was the Mughal capital of Bengal, and many palaces and mosques remain.
• American architect Louis Khan’s National Parliament House complex typifies the huge, fast-growing modern metropolis.
• Kolkata (formerly Calcutta)
• It is the capital of India's West Bengal state.
• Founded as an East India Company trading post, it was India's capital under the British Raj from 1773–1911.
• Today it’s known for its grand colonial architecture, art galleries, and cultural festivals.
• It’s also home to Mother House, headquarters of the Missionaries of Charity, founded by Mother Teresa, whose tomb is on site.
• Chittagong
• It is a large port city on the southeastern coast of Bangladesh.
• The Ethnological Museum has exhibits about the many different ethnic tribes across the country.
• Zia Memorial Museum, inside the former Old Circuit House, displays items belonging to former president Ziaur Rahman, who was assassinated on the site in 1981.
• The landmark Chandanpura Mosque has many onion-shaped domes and brightly painted minarets.
• Karachi
• It is the largest city in Pakistan and the twelfth-largest city in the world.
• It is the capital of the Pakistani province of Sindh.
• Ranked as a beta global city, it is Pakistan's premier industrial and financial centre, with an estimated GDP of $164 billion as of 2019$.

The correct answer is Porbandar.

Key Points

• M.K. Gandhi
• He was born on October 2, 1869, in Porbandar in what is today India’s western state of Gujarat. Hene, Option 3 is correct.
• Upon return to British-controlled India in January 1915, Gandhi had acquired the skills both of an accomplished lawyer and a community organizer dedicated to peaceful protest.
• In South Africa (1893-1915), he had successfully fought the racist regime with a novel method of mass agitation, which he called satyagraha.
• The idea of satyagraha emphasized the power of truth and the need to search for truth.
• The International Day of Non-Violence is observed on 2^nd October, the birthday of Mahatma Gandhi.
• Gandhi's Peace Prize is given for social, economic, and political transformation through non-violence and other Gandhian methods.
• He returned to India from South Africa on 9^th January 1915.
• Pravasi Bharatiya Divas (PBD) is celebrated on 9^th January every year to mark the contribution of the Overseas Indian community to the development of India.
• Rajkot
• It is a city in the western Indian state of Gujarat.
• In central Jubilee Garden are the Lang Library, with Gujarati literature, and the Watson Museum, with paintings and artifacts documenting British colonial rule.
• Kaba Gandhi No Delo, the house where Mahatma Gandhi spent part of his childhood, displays photos of the Indian leader and his belongings.
• The Rotary Dolls Museum exhibits dolls from around the world.
• Porbandar
• It is a city in the Indian state of Gujarat, perhaps best known for being the birthplace of Mahatma Gandhi and Sudama.
• It is the administrative center of the Porbandar District and it was the former capital of the Porbandar princely state.
• Ahmedabad
• In western India, is the largest city in the state of Gujarat.
• The Sabarmati River runs through its center.
• On the western bank is the Gandhi Ashram at Sabarmati, which displays the spiritual leader’s living quarters and artifacts.
• Across the river, the Calico Museum of Textiles, once a cloth merchant's mansion, has a significant collection of antique and modern fabrics.
• Gandhinagar
• It is a planned city in the western Indian state of Gujarat.
• The Akshardham is a massive Hindu temple with ornate carvings and sculpted pillars, plus a water show in its sprawling gardens.
• Dandi Kutir museum traces the life of leader Mahatma Gandhi, who was born in Gujarat.
• South, along the Sabarmati River, the Indroda Nature Park has a zoo and botanical gardens, plus an adjacent dinosaur and fossil park.