Tuesday, 18 July 2017

English Questions


Directions (1-5): In each of the following questions, there are four sentences or parts of sentences that form a paragraph. Identify the sentence(s) or part(s) of sentence(s) that is/are correct in terms of grammar and usage (including spelling, punctuation and logical consistency). Then, choose the most appropriate option.

Q1. A. Sometimes, we think we are only the people with problems.
B. Our problems override other considerations; we can't think beyond our own vexations.
C. When we see a small dampness on our wall we scurry to get them repaired and corrected,
D. but we don't think of people whose homes have been washed away by the rage of the rain gods.
(a) A and B
(b) B and D
(c) C only
(d) C and D
(e) None of the above

Q2. A. Chen Jianping repeated again on twitter something her fiancé said
B. about anti-Japan protests getting violent, and added, "Charge, angry youth!"
C. For this she was sentenced one year in a labour camp.
D. Twitter is banned in China, but its easy to use blocked sites with simple internet tricks.
(a) A only
(b) B only
(c) C only
(d) B and D
(e) None of the above

Q3. A. The Great Pacific Garbage Patch, is gyre of marine litter in the central North Pacific Ocean.
B. The patch extends over a very wide area, with estimates ranging from area
C. the size of the state of Texas to one larger as the continental United States;
D. however, the exact size is unknown.
(a) A and D
(b) B and C
(c) C only
(d) D only
(e) None of the above

Q4. A. At media agency Mindshare's Mumbai office
B. sit a team of ninety-three individuals
C. who's only focus is the consumer giant Hindustan Unilever.
D. In fact, this unit occupies an area the size of most mid-sized agency's in this country.
(a) A only
(b) A and C
(c) A and D
(d) B and C
(e) None of the above

Q5. A. One of the classroom exercise I conduct with my Persuasive Communication students
B. at IIMA is taken from Kurukshestra war.
C. I ask a student to be Kunti, other to be Karna.
D. Kunti has to persuade Karna to leave Duryodhana and join the Pandavas.
(a) A only
(b) A and B
(c) C and D
(d) D only
(e) None of the above

Directions (6-10): In each of the following questions, a statement and five choices are given. Select from among the choices, the most logical complement and mark its number as your answer.

Q6. Electricity is the backbone of industrial development
(a) Many of our new electric projects are lying abandoned.
(b) The authorities are exploring the possibility of starting non-conventional energy sources.
(c) Reliable and uninterrupted power is a prerequisite for development.
(d) People demand some urgent measures to improve the situation.
(e) Hydroelectric projects are unable to meet the demand.

Q7. Our country is rapidly becoming a consumer nation.
(a) The nation must stand on its own legs.
(b) For financial progress we must reduce import and increase export.
(c) We want to become financially strong.
(d) We are not yet Independent because we depend on other countries in certain fields.
(e) India must become self – sufficient and reduce importing goods.

Q8. Children find it difficult to get admission to primary schools as demand exceeds supply.
(a) The government is against starting new schools.
(b) Primary education has been declared compulsory.
(c) The government schools offer better education than the private schools.
(d) The private sector is exerting influence upon the ruling party to recommend the opening of new schools.
(e) The private schools make the most of the situation and charge hefty fees.

Q9. The C.B.I. presented an incriminating report about the minister’s foreign connection.
(a) The Newspapers published a lot of nonsense.
(b) The court ordered a judicial enquiry into the whole affair.
(c) People believe all sorts of hearsay without going into their merits.
(d) The party-connection emboldens everybody to do whatever he likes.
(e) The C. B. I need to look into all aspects before arresting a senior politician.

Q10. The author’s new book was widely accepted by the common people but it angered those in power.
(a) The book was acclaimed for the political criticism it contained.
(b) The author has employed all his power of observation to prepare the book.
(c) People in the Gulf countries arranged a number of meetings to welcome him.
(d) To secure a valid passport the author had to force a lot of political intervention.
(e) The author’s new book is not available in any of the book shops.


Directions (11-15): Rearrange the following SIX sentences (A), (B), (C), (D), (E) and (F) in the proper sequence to form a meaningful paragraph; then answer the questions given below them.

A. Indeed, one recent study found that spending money on others is more rewarding than spending it on oneself.
B. It feels good to be good.
C. The paradoxical finding here is that one great trick to being happy is to forget about being happy and instead try to increase the happiness of others.
D. The effects of our kindness are not zero-sum.
E. Those who receive charity have their lives improved, but those who provide it also benefit.
F. It’s not just short-term pleasure: those who donate wealth and time to others tend to be a lot happier in their entire lives than those who do not.

Q11. Which of the following will be the FIRST sentence after rearrangement?
(a) B
(b) C
(c) D
(d) E
(e) F

Q12. Which of the following will be the SECOND sentence after rearrangement?
(a) A
(b) B
(c) C
(d) D
(e) E

Q13. Which of the following will be the THIRD sentence after rearrangement?
(a) B
(b) C
(c) D
(d) E
(e) A

Q14. Which of the following will be the SIXTH sentence after rearrangement?
(a) A
(b) B
(c) C
(d) D
(e) F

Q15. Which of the following will be the FOURTH sentence after rearrangement?
(a) B
(b) C
(c) D
(d) E
(e) A

Solutions

S1. Ans.(b)
Sol. Answer Option B. B and D. In A ‘only’ is misplaced; “we are the only people…” In C, the pronoun ‘them’ is inconsistent (in number) with its antecedent’ a small dampness’; ‘it’ is the correct pronoun.

S2. Ans.(b)
Sol. Answer Option B. B only. In A ‘repeated again’ is redundant. ‘repeated’ is correct. In C, ‘sentenced one year…’ is incorrect; ‘sentenced to one year…’ will make it correct. In D, its is used instead of it’s.

S3. Ans.(d)
Sol. Answer Option D. D only. In A ‘gyre’ needs a determiner before that ‘a gyre’ would be correct. In B ‘ranging from an area…’ would be correct. In ‘as large as’ or ‘larger than’ would correct the part. “larger as” is incorrect.

S4. Ans.(a)
Sol. Answer Option A. A only. In B, The verb ‘sit’ for the subject ‘team’ is incorrect. It should be ‘sits’. In C, who’s has to be replaced with ‘whose’. In D agency’s is incorrect, it should be agencies.

S5. Ans.(d)
Sol. Answer Option D. D only. A should be corrected to ‘one of the …exercises’. B has to include the definite article” the Kurukshetra war”. C should be corrected “another to be…” D has no error.

S6. Ans.(c)
Sol. Reliable and uninterrupted power is a prerequisite for development. Other options do not follow the idea expressed in the question statement logically. Either they distort the message or introduce new idea.

S7. Ans.(b)
Sol. For financial progress we must reduce import and increase export. Other options do not follow the idea expressed in the question statement logically. Either they distort the message or introduce new idea.

S8. Ans.(e)
Sol. Since demand is higher than supply in schools for admission, the private schools make the most of the situation and charge hefty fees.

S9. Ans.(b)
Sol. The court ordered a judicial enquiry into the whole affair. Since report was submitted to the court hence judge ordered an enquiry into the case. Hence option C logically follow course of action.

S10. Ans.(a)
Sol. the book was acclaimed for the political criticism it contained.



S11. Ans.(c) 
Sol. The logical and correct order of the sentences of the given paragraph will be DEBAFC.
S12. Ans.(e) 
Sol. The logical and correct order of the sentences of the given paragraph will be DEBAFC.
S13. Ans.(a) 
Sol. The logical and correct order of the sentences of the given paragraph will be DEBAFC.
S14. Ans.(c) 
Sol. The logical and correct order of the sentences of the given paragraph will be DEBAFC.
S15. Ans.(e) 
Sol. The logical and correct order of the sentences of the given paragraph will be DEBAFC.

Quant Quiz


Quant Quiz

Directions (Q. 1-5): Each question below is followed by two statements A and B. You are to determine whether the data given in the statement is sufficient to answer the question. You should use the data and your knowledge of Mathematics to choose the possible answers. Give answer
1) if the statement A alone is sufficient to answer the question but the statement B alone is not sufficient.
2) if the statement B alone is sufficient to answer the question but the statement A alone is not sufficient.
3) if both statements A and B together are necessary to answer the question.
4) if either statement A alone or statement B alone is sufficient to answer the question.
5) if you cannot get the answer from the statements A and B together, but need even more data.


1. What is a three-digit number?
(A) The three-digit number is an exact multiple of 19.
(B) The first and the third digit are 7 and 9 respectively.

2. What is the age of T in the group of P, Q, R, S and. T whose average age is 55 gears?
(A)The average age of P and Q is 65 years.
(B)The average age of R and S is 60 years.

3. How many women can complete a piece of work in 25 days?
(A)35 women can complete the same piece of work in 15 days.
(B)25 men complete the same piece of work in 15 days.

4. What is the age of Sandeep?
(A)Sandeep is two times younger than Ramesh.
(B)Suresh's age is four times that of Ramesh.

5. What is the perimeter of a semicircle?
(A)The radius of the semi-circle is equal to half the side of a square.
(B)The area of the square is 169 sq cm.

Directions (Q. 6-10): What will come in place of question mark (?) in the following questions?
6. (42)^2 - (38)^2  - (17)^2= ? / 0.1
1)4.1
2)3.1
3)5.1
4)6.1
5) None of these

7. 702 ÷ 27 + 108 x 0.75 = ?
1)79
2)89
3)98
4)107
5)99

8. 348 x 9 x ? = 37584
1) 11
2) 12
3) 14
4) 16
5) None of these

9. 1234.131-93.12 -431.1 -?= 8.432
1) 411.072
2) 369.497
3) 701.479
4) 356.479
5) 405.521

10. (54% of 3845) - (36% of 2755) = ?
1) 1340.65 
2) 1284.5 
3) 1084.5
4) 1410.75 
5) 1348.5




1. 3
2. 3
3. 1
4. 5
5. 3
6. 2
7. 4
8. 2
9. 3
10. 3

QUIZ-18


Q1. World No Tobacco Day is observed around the world every year on _______________.
Answer: 31 May

Q2. The Minister of Defence and National Security of Fiji, Ratu Inoke Kubuabola signed an MoU with the Minister of Defence, Finance and Corporate Affairs, Shri Arun Jaitley, recently. What is the capital of Fiji?
Answer: Suva

Q3. According to India Development Report released by World Bank on the female participation in the workforce, what is the ranking of India in that Report?
Answer: 120th

Q4. Barcelona striker Lionel Messi won the European Golden Shoe for a record equaling fourth time having scored 37 goals in the Spanish league. He drew level with _________________.
Answer: Cristiano Ronaldo

Q5. Name the Indian Union Minister who has been chosen for WHO Director-General Special Recognition Awards for accelerating India’s tobacco control initiatives and taking bold measures to protect people against hazards of tobacco use.
Answer: Jagat Prakash Nadda

Q6. India has signed a loan agreement of 36 million dollars with the World Bank for Public Financial Management Capacity Building Program of which Indian states?
Answer: Himachal Pradesh

Q7. The Prime Minister Narendra Modi has signed seven agreements with Spain to strengthen bilateral cooperation to fight against terrorism after the visit from Germany. Who is the current Prime Minister of Spain?
Answer: Mariano Rajoy

Q8. World Milk Day is observed around the globe on ___________.
Answer: 1 June

Q9. India's Gross Domestic Product (GDP) grew at what percent during the January-March quarter of 2017, according to government data?
Answer: 6.1%

Q10. To attract more passengers to buy online train tickets, Indian Railways has introduced a new service called ___________________.
Answer: Buy Now, Pay Later

Q11. India and Russia have signed Saint Petersburg Declaration as a roadmap to enhance cooperation after the annual bilateral summit. This was the _______ edition of the Summit.
Answer: 18th

Q12. The Telangana Government has launched a digital wallet named _____________, which doesn’t charge transaction fee from consumers.
Answer: T-Wallet

Q13. The 29th state of India Telangana was formed on __________.
Answer: 2 June 2014

Q14. Japan recently launched a satellite to help build a high-precision geolocation system that will complement the US-operated GPS. A 'H-IIA' rocket blasted off from _________________.
Answer: Tanegashima Space Center

Q15. NAAC has received Asia Pacific Quality Network Award 2017 for International Co-operation in Quality Assurance. What does 'AA' stands for in NAAC?
Answer: Assessment Accreditation

Monday, 17 July 2017

Daily GK Update 17th July 2017



1. Roger Federer lifts a record 8th Wimbledon title beating Marin Cilic in Men’s singles

i. Roger Federer won a record eighth Wimbledon title and became the tournament’s oldest champion with a straight-sets victory over Marin Cilic. Federer claimed his 19th Grand Slam title.
ii. The 36-year old Federer is also Wimbledon’s oldest men’s winner of the modern era, succeeding Arthur Ashe, who was almost 32 when he won in 1976. This was his 11th Wimbledon final and 29th title at the majors.
iii. With this victory, Federer also became the first player since Bjorn Borg in 1976 to win Wimbledon without dropping a set in the entire tournament.

Important Takeaways from Above News-
  • Roger Federer is from Switzerland.
  • Wimbledon is the oldest tennis tournament in the world held in England.

2. India’s Harinder Pal Sandhu wins Victorian Open squash tournament by defeating Rex Hedrick

i. India's Harinder Pal Sandhu has won the second title in two weeks, beating top-seed Rex Hedrick of Australia in a 77-minute final of Victorian Open squash, a PSA Tour event, in Melbourne, Austraila.
ii. Third-seeded Sandhu had recently won the South Australian Open. In the Women’s PSA W10 final, Hong Kong’s Tsz-Ling showed every bit of her undoubted class in a straight games victory over fourth seed, Amanda Landers-Murphy.

Important Takeaways from Above News-
  • The Capital of Australia is Canberra.
  • Malcolm Turnbull is the PM of Australia.

3. Lewis Hamilton won Formula One's fifth British Grand Prix

i. Mercedes’ Lewis Hamilton won the British Grand Prix for the fifth time – matching the record of Jim Clark and Alain Prost to cut Sebastian Vettel’s championship lead to just a single point.
ii. They allowed Valtteri Bottas to grab second from Kimi Raikkonen to secure a Mercedes one-two, as Vettel trailed home seventh.

Important Takeaways from Above News-
  • Valtteri Bottas who races for Mercedes stood second in the race.

4. I H Manudev wins 1st National Masters snooker tournament title

i. I H Manudev has won the first National Masters snooker tournament title in Chennai. Alok Kumar, a former national men’s champion, had been in fine form coming into the summit clash but found Karnataka’s Manudev a tough proposition.


5. MobiKwik Partnered with Samsung Pay Mini

i. Digital payments company MobiKwik has partnered Samsung Pay, under which consumers will be able to make payments with a single tap using select Samsung handsets.
ii. Samsung had unveiled a 'Mini' version of the platform that integrates UPI and mobile wallets to work on mid-range priced smartphones.

Important Takeaways from Above News-
  • CEO of Mobikwik is Bipin Preet Singh.
  • Samsung Group is a South Korean multinational conglomerate headquartered in Seoul.

6. Five P Venture inks pact with Central Silk Board

i. Erode-based Five P Venture India Private Ltd and Central Silk Board (CSB) inked an agreement for development and commercialization of handloom silk products.
ii. This MoU signed at the first-ever mega trade fair for the textile sector organized by the Ministry of Textiles at Gandhinagar. This step will also help revive the heritage skills of the handloom weavers in Chennimalai belt.

Important Takeaways from Above News-
  • Headquarter of Central Silk Board (CSB) is in Bengaluru.

7. Justice Gopal Prasad Parajuli to be the new Chief Justice of Nepal

i.Justice Gopal Prasad Parajuli will be the new Chief Justice of Nepal. The Parliamentary Hearing Special Committee (PHSC) unanimously endorsed Justice Parajuli’s name for the post of Chief Justice of Supreme Court.
ii. After endorsement by PHSC the President will now appoint him as the Chief Justice. He will head the Judiciary till April 28, 2018.

Important Takeaways from Above News-
  • The Capital of Nepal is Kathmandu.
  • Sher Bahadur Deuba is the newly appointed Prime minister of Nepal.

8. Shri R K Pachnanda takes charge as Director General, ITBP
i. Shri R K Pachnanda, an IPS officer, took charge as the new Director General of Indo-Tibetan Border Police (ITBP), recently.
ii. Shri Krishna Chaudhary, DG who retired on superannuation, handed over the customary baton to Shri Pachnanda. Shri Pachnanda is the 29th Chief of the ITBP.

Important Takeaways from Above News-
  • The Capital of Tibet is Lhasa.

9. Former Sikkim CM Nar Bahadur Bhandari passes away

i. Nar Bahadur Bhandari, one of the longest-serving chief ministers of Sikkim has died recently. Mr. Bhandari, a three-term former Chief Minister was 77 years old.
ii. He became the Chief Minister of Sikkim for the first time in 1979 on a Janata Parishad ticket and then again in 1984 and 1989 on a Sikkim Sangram Parishad ticket.

Important Takeaways from Above News-
  • The Capital of Sikkim is Gangtok.
  • The present Chief Minister Sikkim is Pawan Kumar Chamling.

10. Indonesia renames part of South China Sea

i. Indonesia has named waters in its exclusive economic zone that overlap with China’s expansive claim to the South China Sea as the North Natuna Sea.
ii. The part of the renamed area falls in China’s “nine-dash line” waters extending hundreds of miles to the south and east of China’s island province Hainan.

Important Takeaways from Above News-
  • In 2011, the Philippines renamed the waters as the “West Philippine Sea” 
  • The Capital of Indonesia is Jakarta.

Quant Quiz


Quant Quiz

1. If the compound interest on an amount of Rs. 29000 in two years is Rs. 9352.5, what is the rate of interest?

(1) 11  (2) 9 (3) 15  (4) 18 (5) None of these

2. Three friends A, B and C start running around a circular stadium and complete a single round in 8, 18 and 15 seconds respectively. After how many minutes will they meet again at the starting point for the first time?

(1) 12  (2) 6 (3) 8  (4) 15 (5) 18

3. The perimeter of a square is equal to the radius of a circle having area 39424 sq cm, what is the area of square?

(1) 1225 sq cm (2) 441 sq cm (3) 784 sq cm (4) Can’t say (5) None of these

Directions—(Q. 4 and 5) Study the following information carefully to answer the questions that follow—A committee of five members is to be formed out of 5 Males, 6 Females and 3 Children. In how many different ways can it be done if—?
4. The committee should consist of 2 Males, 2 Females and 1 Child?
(1) 450  (2) 225 (3) 55  (4) 90 (5) None of these
5. The committee should include all the 3 Childs?
(1) 90  (2) 180 (3) 21  (4) 55 (5) None of these
6. Thirty men can complete a work in 36 days. In how many days can 18 men complete the same piece of work?
(1) 48  (2) 36 (3) 60  (4) 72 (5) None of these

7. Ram spends 50% of his monthly income on household items, 20% of his monthly income on buying clothes, 5% of his monthly income on medicines and saves remaining Rs. 11,250 . What is Ram’s monthly income?

(1) Rs. 38,200  (2) Rs. 34,000 (3) Rs. 41,600  (4) Rs. 45,000 (5) None of these

8. The number obtained by interchanging the two digits of a two digit number is lesser than the original number by 54. If the sum of the two digits of the number is 12, then what is the original number?
(1) 28 (2) 39 (3) 82 (4) Can’t say (5) None of these

9. At present Geeta is eight times her daughter’s age. Eight years from now, the ratio of the ages of Geeta and her daughter will be 10 : 3 respectively. What is Geeta’s present age ?

(1) 32 years (2) 40 years (3) 36 years (4) Can’t say (5) None of these

10. In how many different ways can 4 boys and 3 girls be arranged in a row such that all the boys stand together and all the girls stand together ?

(1) 75  (2) 576 (3) 288  (4) 24 (5) None of these

ANSWERS
1. (3)
P = 29000 CI = 9352.5 N = 2 years  A = P + I = 38,352.5
Substituting the values in
A = P(1 + R/100)^n
Solving we get R = 15%.
2. (2)
The required time will be the LCM of 8, 18 and 15 which is 360 sec or 6 minutes.
3. (3)
Π R^2 = 39424
R = 112
Perimeter of square = 4a = 112
Side of square = 112/4 = 28
Area of square = 28^2 = 784 cm2.
4. (1)
Number of ways = 5C2 * 6C2 *3C1 = 450
5. (4)
Number of ways = 11C2 * 3C3 = 55.
6. (3)
Required number of days = (30 * 36)/18 = 60
7. (4)
Let total income of Ram be x. Then
(100 – 50 – 20 – 5)% of x = 11250
x = 45000.
8. (5)
Let the number be xy
(10x + y) – (10y + x) = 54
x – y = 6 And  x + y = 12
Solving the equations we get x = 9 and y = 3
So the number is 93.
9. (1)
Let the age of Geeta’s daughter be x. Then Geeta’s age is 8x.
(8x + 8)/(x + 8) = 10/3
x = 4
Geeta’s present age = 8x = 32 years.
10. (3)
Required number of ways = 4! * 3! * 2! = 288.


Average


Average
An average or more accurately an arithmetic mean is, in crude terms, the sum of n different data divided by n.

 Averages of a group is defined as the ratio of sum of all the items in the group to the number of items in the group.


Average = (Sum of all items in the group)/ Number of items in the group



Now, sum of all items can be ‘the sum of number of quantities like apple, people etc’ or ‘sum of values of the item like 10 coins of 2Rs each etc’.


Some Important Concepts:

1.Average =total of data/No.of data

2.If the value of each item is increase by the same value a, then the average of the group or items will also increase by a.

3.If the value of each item is decreased by the same value a, then the aveage of the group of items will also decrease by a.

4.If the value of each item is multiplied by the same value a, then the average of the group or items will also get multiplied by a.

5.If the value of each item is multiplied by the same value a, then the average of the group or items will also get divided by a.

6.If we know only the average of the two groups individually, we cannot find out the average of the combined group of items.

7.Average of n natural no's=(n+1)/2

8.Average of even No'=(n+1)

9.Average of odd No'= n

10.General Formula=(1st number +Last number)/2

Quant Quiz on Average

1.The average marks obtained by 120 cndidates in a certain examinationis 35.if the average marks of passed candidate is 39 and that of the failed candidates is 15,what is the number of candidates who passed the examination
(a)110
(b)115
(c)120
(d)100
(e)none of these

2.The average age of 8 persons in a committee is increased by 2 years when two men aged 35 years and 45 years are substituted by two women.Find the average age of these two women.
(a)48
(b)36
(c)42
(d)29
(e)none of these

3.In a class, there are 20 boys whose average age is decreased by 2 months, when one boy aged 18 years is replaced by a new boy.Find the age of new boy.
(a)19 years
(b)14 years 6 month
(c)15 years
(d)14 years 8 month
(e)12 years

4.One -third of certain journey is covered at the rate of 25kmph,one-fourth at the rate of 30kmph and the rest at 50 kmph.Find the average speed for the whole journey.
(a)33.33 kmph
(b)36
(c)42
(d)27
(e)none of these

5.The average salary of the entire staff in a office is Rs 120 per month.The average salary of officers is Rs 460 and of non officers is Rs 110. If the number of officers is 15,then find the No of non-officers in the office.
(a)480
(b)500
(c)600
(d)430
(e)510

6.There were 35 students in a hostel.If the number of students increased by 7, the expenses of the mess increases by Rs. 42 per day,while the average expenditure per head diminishes by Rs.1.Find the original expenditure of the mess.
(a)420
(b)400
(c)480
(d)460
(e)none of these

7.The average weight of A,B,and C is 84 kg. If D joins the group, the average weight of the group becomes 80 kg.If another man E who weights is 3 kg more than D Replaces A, Then the average of B,C,Dand E becomes 79 kg. What is the weight of A?
(a)64
(b)72
(c)75
(d)100
(e)80

8.In an exam, the average was found to be 50 marks. After deducting computational errors the marks of the 100 candidates had to be changed from 90 to 60 each and average came down  to 45 marks. Total No of candidates who took the exam were.
(a)300
(b)600
(c)200
(d)150
(e)none of these

9. Find the average of all even No's up to 100 or average of first 50 even No's.
(a)50
(b)50.5
(c)51
(d)49
(e)none of these

10. The average of 8 No's is 20. The average of first two No's is 15.5 and that of next three No's is 64/3.if the 6th No be less than the seventh and eight No. by 4 and 7 respectively, then find eight No.
(a)26
(b)25.5
(c)27
(d)25
(e)none of these

Answers with Explanation:

1. (d) Let No. of passed candidates are x
So, x * 39 + (120 – x) 15= 120 * 35
x = 100
2.(a) Total increase = 8 * 2 = 16 years
So, total age of two women = 35 + 45 +16= 96
Average age of two women=96/2=48 years
3(d) Total decrease = 20 * 2 = 40 month
= 3 years 4 month
So, age of new boy  = 18 years – 3 years 4 month
= 14 years 8 month

4.(a) Average speed = total distance / total time
LCM = 3, 4 = 12
Average speed = 12 / (1/3*12*1/25 + ¼ * 12*1/30 +5/50)
= 12/ (4/25 + 3/30+ 5/30
= 150*12/54 = 33.333 kmph

5.(e) Let no. of non- officers be x
15 * 460 + x * 110 = (x + 15) 120
x = 510

6.(a) Let average expenditure per head be = x
So, (35 + 7) (x -1) – 35 x = 42
42 (x -1) – 35x = 42
X =12
Original expenditure of mess = 12 * 35 = 420

7.A + B + C = 3 *84 = 252
A + B + C + D = 4 * 80 = 320 ---- (i)
So, D =   68& E = 68 + 3 = 71
B + C + D +E = 79 * 4 = 316 --- (ii)
From Eq. (i) & (ii)
A-E = 320 – 316 = 4
A = E +4 = 71 + 4 = 75

8.(b) Let the total no. of candidates =  x
So, (50x-100 (90-60)) / x = 45
x = 600

9.(c) 2, 4, 6, ………… 100
Average = (1st No. + Last No.) /2 = (2+100)/2 = 51

10.(c) Total Sum of 8 nos.  = 20 * 8 = 160
Sum of 1st two nos. = 2 * 15.5 = 31
Sum of next three nos. = 3 * 64/3 = 64
Let 6th no. be x 
31 +  64 + x + (x+4) + (x+7) = 160
x = 18
8th no. = 18 + 7 = 25