SSC GD Constable Previous Year Paper (Held on: 3rd March 2019 Shift 1)

According to the alphabetical positions of the letters,

The pattern followed here is:

M - 1 → L

N -1 → M

Q -1 → P

R - 1 → Q

Similarly, to get the required answer we have to add ‘1’.

R + 1 → S

S + 1 → T

V + 1 → W

W + 1 → X

Hence, ‘STWX’ is the correct answer.

The pattern followed here is :

Hence, ‘47’ is the correct answer.

Given:

 

Given Equation :

21 ÷ 8 + 2 − 12 × 3 =?

Arranging according to the given conditions:

21 - 8 × 2 + 12 ÷ 3 =?

Applying BODMAS rule:

21 - 8 × 2 + 12 ÷ 3 =?

21 - 8 × 2 + 4 = ?

21 - 16 + 4 = ?

25 -16 = ?

? = 9

Hence, ‘9’ is the correct answer.

The question figure is embedded in, 

Hence, option (d) is correct answer.

The mirror image would be as follows:

Hence, option 2 is the correct answer.

The logic is as follows:

Hence, figure 4 is the correct answer.

Dumb, Deaf and Blind are type of disabilities.

Whereas,

‘Sinus ’ is a disease which is related to nasal cavity.

Hence, ‘Sinus’ is the odd one among the given options.

The pattern followed here is:

Similarly,

Hence, the code for ‘GREAT’ is ‘FPBWO’.

The pattern followed here is :

R E D = R(18) + E(5) - D(4)

18 + 5 - 4 = 19

Similarly,

WED = W(23) + E(5) - D(4)

23 + 5 - 4 = 24

Hence**, ‘24’** is the correct answer.

The pattern followed here is :

Mango is a type of fruit.

Similarly,

Potato is a type of vegetable.

Hence, ‘Vegetable’ is the correct answer.

1. Sonam is older than Renu.

Sonam > Renu

2. Komal is younger than Renu.

Sonam > Renu > Komal

3. Priya is older than Sonam.

Priya > Sonam > Renu > Komal

Hence, Priya is eldest among all.

Logic: Each number is obtained by multiplying consecutive terms

• 42 : 72 = 6 × 7: 8 × 9

Similarly,

• 12 : 30 = 3 × 4 :  5 × 6

 Hence, ‘30’ is the correct answer

The pattern followed here is :

Hence, ‘54’ is the correct answer.

The least possible Venn diagram is as follows:

Conclusions:

I. Some mangoes are grapes → True ( some grapes are mangoes)

II. All apples are grapes → False ( it is possible but not defiant)

Hence, ‘Only Conclusion I follows’ is the correct answer.

The least possible Venn diagram is as follows:

Conclusions:

I. All trees are roses → False (As All roses are fruits and All fruits are trees)

II. Some fruits are roses → True (All roses are fruits)

Hence, ‘Only Conclusion II follows’ is the correct answer.

Given eight people P, M, D, A, F, H, R and B are sitting around a round table facing the centre.

1. R is fourth to the right of A, who is third to the right of P.

2. M is second to the left of H, who is second to the left of P.

3. D is third to the right of B.

Hence, ‘AF’ is the correct answer.

According to the alphabetical positions of the letters,

The pattern followed here is :

1. KMP : K + 2→ M; M + 3 → P

2. ACF : A + 2→ C ; M + 3 → F

3. TVY : T + 2→ V ; V + 3 → Y

4. BCG :B + 1→ C; C + 4 → G (does not follow the pattern)

Hence, ‘BCG’ is the odd one among all the options.

The paper when unfolded looks like,

Hence, option (a) is the correct answer.

According to the alphabetical positions of the letters,

The pattern followed here is :

Hence, ‘U’ is the correct answer.

Given eight people A, B, C, D, E, F, G, and H are sitting around a round table facing the centre.

1. D is fourth to the right of H and second to the left of B.

2. F is fourth to the right of B.

3. C is fourth to the right of E, who is not an immediate right of B or D.

4. A is not an immediate neighbour of D.

Hence, D is sitting between G and C.

The pattern followed here is :

Last digit of the number is sum of first three digit.

1. 2248 → 2 + 2 + 4 = 8

2. 3036 → 3 + 0 +3 = 6

3. 1258 → 1 + 2 + 5 = 8

4. 3196 → 3 + 1 + 9 = 13 (not followed the pattern)

Hence, ‘3196’ is the correct answer.

Key board, Mouse and Monitor all are different from each other, so the Venn diagram is :

Hence, option (2) is the correct answer.

When the question figure is merged with the figure in option C, the complete pattern can be seen.

Hence, the figure in option (c) will complete the pattern.

Telecast is happened on television.

Similarly,

Broadcast happened on radio.

Hence, ‘Broadcast’ is the correct answer.

The pattern followed here is :

1. 8 × 2 × 3 = 48

2. 6 × 3 × 4 = 72

3. 12 × 2 × 1 = 24

Hence, ‘24 ‘is the correct answer.

The Correct Answer is Hullabaloo in the Guava Orchard.

 

Key Points

• Hullabaloo in the Guava Orchard is a novel by Kiran Desai.
• It is her first book and won the top prize for the Betty Trask Awards in 1998.
• The book deals with a fictitious small town called Shahkot in North India.
• The story tells about Sampath Chawla, who just wants to be left alone, is forced into being a holy man in spite of himself.

 

Additional Information

• Selection Day is a 2016 sports fiction novel written by Booker Prize winner Aravind Adiga.
• An Equal Music (1999) is a novel by Vikram Seth.
• It Happens for a Reason is a novel written by Preeti Shenoy.

The Correct Answer is Indian National Congress (INC).

 

Key Points

• The Indian National Congress was founded in Bombay in December 1885.
• The Indian National Congress (INC) has seen a steady number of splits and breakaway factions.
• Some of the breakaway organizations have thrived as independent parties, some have become defunct, while others have merged with the parent party or other political parties.

 

Additional Information

• Communist Party of India — Marxist (CPI-M) emerged from a split from the Communist Party of India in 1964.
• The CPI(M) was formed in Calcutta from 31 October to 7 November 1964.
• The Nationalist Congress Party (NCP) was formed on 25 May 1999, by Sharad Pawar, P. A. Sangma, and Tariq Anwar after they were expelled from the Indian National Congress (INC) on 20 May 1999.
• The Bahujan Samaj Party (BSP) was founded in 1984 by Kanshi Ram.

The Correct Answer is ₹1,850 per quintal.

• The MSP for paddy (common grade) has been fixed at 1,815/quintal for 2018-19.

 

Key Points

• The MSP is announced by the Government of India for 25 crops currently at the beginning of each season viz. Rabi and Kharif.
• The government decides the support prices for various agricultural commodities after taking into account the following:
• Recommendations of the Commission for Agricultural Costs and Prices
• Views of State Governments
• Views of Ministries
• Other relevant factors

​ 

Additional Information

• The Department of Agriculture and Cooperation implements the Price Support Scheme for Oil Seeds and Pulses through the National Agricultural Cooperative Marketing Federation of India Ltd. (NAFED).

The Correct Answer is Amar Jiban.

 

Key Points

• Aamar Jiban is the first autobiography written by Rassundari Devi in 1876.
• It is the first-ever known autobiography of an Indian woman.
• It tells us about the status of women in 19th-century Indian society.

 

Important Points

• My Reminiscences (1911) was written by Rabindra Nath Tagore.
• It is an account of the first twenty-seven formative years of his life.
• Beyond the Jungle: A Tale of South India is a book by Sita Rathnamal.
• The City of Two Gateways: The Autobiography of an Indian Girl is a book written by Savitri Devi Nanda.

The Correct Answer is ​Inequalities exist in democracies.

 

Key Points

• India is a democratic country.
• In India, we can see that even today a small number of ultra-rich people enjoy a highly disproportionate share of wealth and incomes.
• On the other hand, the people who are at the bottom of society sometimes find it difficult to meet their basic needs of life like food, shelter, clothing, education, and health.
• So we can say that inequalities exist in democracies.

 

Additional Information

• A dictatorship can never be better than a democracy.
• History indicates that the combination of political, civil, and economic freedom is a better guarantee of ever-increasing prosperity than a dictatorship.
• Inequalities also exist in dictatorships and the citizens may not have opportunities to move up in a dictatorship.
• Democracy helps in the development and does not deter it.

The Correct Answer is Jupiter.

Key Points

• Jupiter's moon Ganymede is the largest satellite in the solar system.
• The satellite is even larger than Mercury and Pluto, and only slightly smaller than Mars.

Important Points

• Jupiter is the fifth planet from the Sun and the largest in the Solar System.
• It is a gas giant with a mass one-thousandth that of the Sun.
• Jupiter currently has 92 known satellites.

Additional Information

• Uranus currently has 27 known satellites.
• Neptune has 14 known moons, which are named for minor water deities in Greek mythology.
• Saturn has 146 moons.

The Correct Answer is CH₃CN.

 

Key Points

• Acetonitrile is a chemical compound with the formula CH₃CN.
• It is produced mainly as a byproduct of acrylonitrile manufacture.
• It is used as a polar aprotic solvent in organic synthesis and in the purification of butadiene.

 

Additional Information

• Methyl isocyanate (MIC) is an organic compound with the molecular formula CH₃NCO.
• Cyanogen is the chemical compound with the formula (CN)₂.
• It is a colorless, toxic gas with a pungent odor.
• Acrylonitrile is an organic compound with the formula CH₂CHCN.
• It is a colorless volatile liquid.
• It has a pungent odor of garlic or onions.

The Correct Answer is Ireland.

 

Key Points

• In the Sultan Azlan Shah Cup 2018, India beat Ireland 4-1 to finish in the fifth spot.
• Australia won the Sultan Azlan Shah cup 2018.

 

Important Points

Azlan Shah Hockey Tournament

• It is an annual international men’s field hockey tournament held in Malaysia.
• It has been named after the 9th king of Malaysia and ‘Father of Malaysian Hockey’ Sultan Azlan Shah.
• India had won it 4 times 1985, 1991, 1995, 2009 and shared it in 2010 with South Korea.

The Correct Answer is Chalcocite.

 

Key Points

• Chalcocite is one of the most important ores of copper.
• Chalcocite (Cu2S) belongs to a group of sulfide minerals formed at relatively low temperatures.

 

Important Points

Galena

• Galena, also called lead glance, is the natural mineral form of lead(II) sulfide (PbS).
• It is the most important ore of lead and an important source of silver.

Cassiterite

• Cassiterite, also called tinstone, is the major ore of tin.

Cinnabar

• Cinnabar is an important ore of mercury.

The Correct Answer is Mahi.

 

Key Points

• Mahi rises in Minda Village, in sardarpur district Madhya Pradesh.
• After flowing through the Vagad region of Rajasthan, enters Gujarat and flows into the Arabian Sea.
• It is one of only three major rivers in peninsular India that runs from east to west along with the Tapti River and the Narmada River.

 

Important Points

Krishna

• It originates near Mahabaleshwar (Satara) in Maharashtra.
• It runs from **four states Maharashtra (303 km), North Karnataka (480 km), and the rest of its 1300 km journey in Telangana and Andhra Pradesh before **It empties into the Bay of Bengal.
• Tributaries: Tungabhadra, Mallaprabha, Koyna, Bhima, Ghataprabha, Yerla, Warna, Dindi, Musi and Dudhganga.

Penna

• The Penna rises in the Nandi Hills in Chikkaballapur District of Karnataka.
• It runs north and east through the states of Karnataka and Andhra Pradesh to empty into the Bay of Bengal.

Rushikulya

• The Rushikulya River is one of the major rivers in the state of Odisha.
• It has a catchment area in the districts of Kandhamal and Ganjam of Odisha.
• It meets the Bay of Bengal at Purina Bandha in Ganjam.

The Correct Answer is ₹1,400 crore.

 

Key Points

• Growth of direct taxes in 2016-17 at 12.6% & for the financial year 2017-18 (up to 1 January 2018) at 18.7%.
• Allocation for the Ministry of Food Processing doubled to Rs.1400 crore.
• Agri-Market Infrastructure Fund allocated corpus of Rs.2000 crore
• Fisheries, aquaculture, and animal husbandry allocated corpus at Rs.10,000 crore.

 

Important Points

Budget:

• According to Article 112 of the Indian Constitution, the Union Budget of a year is referred to as the Annual Financial Statement (AFS).
• It is a statement of the estimated receipts and expenditure of the Government in a financial year (which begins on 01 April of the current year and ends on 31 March of the following year).

The Correct Answer is 2s = 2ut + at².

• The second equation of motion is : s = ut + 1/2at² = 2s = 2ut + at2.

 

 

• There are three equations for the motion of those bodies which travel with uniform acceleration.
• The first equation of motion is : v = u + at
• It gives the velocity acquired by a body in time t.
• The second equation of motion is : s = ut + 1/2 at².
• It gives the distance traveled by a body in time t.
• The third equation of motion is : v² = u² + 2as.
• It gives the velocity acquired by a body in traveling distance s.

The Correct Answer is Minicoy.

Key Points

• The Minicoy Island is the southern-most island of Lakshadweep.
• It is situated at a distance of 398 km (215 nautical miles) south-west of Kochi between 8° 15′ and 8° 20′ N latitude and 73° 01′ and 73° OS’ E longitude.
• It has an area of 4.80 sq km.
• This island lies near the 9 ⁰ Channel.

 

Important Points

• Bitra Island is the smallest inhabited island of Lakshadweep with a land area of 0.105 sq km.
• Kavaratti is the capital of the Union Territory of Lakshadweep.
• Amini Island is at a distance of 407 km (220 nautical miles) from Kochi and located between Kavaratti Island in the south and Kadmat Island in the north.

The Correct Answer is Monpa Tribe.

 

Key Points 

• The Losar Festivals are celebrated in Arunachal Pradesh.
• It is celebrated by the people of the Monpa Tribe who are said to be inhabitants of Arunachal Pradesh.
• Losar is a 3-day festival, which is celebrated with great pomp and show in Tawang.
• The festival is observed to ward off evil spirits and welcome the new year that shall be filled with happiness and prosperity.

 

Important Points

• The Khasis inhabit Central Meghalaya.
• The scheduled tribe populations (mainly belonging to Khasi, Jaintia, and Garo tribes) constitute 85.53% of the total population of Meghalaya.
• The Kodavas are a group of tribes from the region of Kodagu, Karnataka.
• The Mundas are one of the aboriginal peoples found in the Chota Nagpur region of eastern India.

The Correct Answer is Mahmud Lodi.

Key Points

• The Battle of Ghaghra was fought in 1529.
• The battle of Ghagra was fought between the Afgan king Mahmud Lodi and the Mughal emperor Babur.
• Lodi was supported by the Rajput kings of India.
• Mahmud Lodi was defeated in the battle, and Babur extended his frontier from the Oxus River in the west to the Ghagra River in the east and from the Himalayas to Gwalior.

 

Additional Information

• Yusuf Adil Shah was the founder of the Adil Shahi dynasty that ruled the Sultanate of Bijapur for nearly two centuries.
• Dilawar Khan Ghori was governor of the Malwa province of central India during the decline of the Delhi Sultanate.
• Qasim Barid I was prime-minister of the Bahmani sultanate and the founder of the Bidar Sultanate.

The Correct Answer is 6.75%.

 

Key Points

• The Economy survey 2017-2018  was authored by the chief economic adviser in the finance ministry Arvind Subramaniam.
• The real GDP growth projections for 2017-18 were expected to be around 6.75%.
• The survey also stated that the Major reforms initiated by the government would take the growth rate to 7-7.5% in 2018-19.

 

Important Points

• The Economic Survey is a detailed report of the country's economic performance during the past year.
• The Economic Survey also offers glimpses into the current state of the economy, and occasional insights into the economic outlook.
• The Economic Survey is prepared under the guidance of the Chief Economic Advisor.
• It is presented in both the houses of Parliament, a day before the announcement of the Union Budget.

 

Additional Information

• Krishnamurthy Venkata Subramanian is the current Chief Economic Adviser to the Government of India.

The Correct Answer is ​Dadabhai Naoroji.

 

Key Points

• Dadabhai Naoroji was the first Indian to become a member of the British Parliament.
• He was elected for the Liberal Party in Finsbury Central at the 1892 general election, was the first British Indian MP.

 

Important Points

Dadabhai Naoroji

• Dadabhai Naoroji was popularly known as 'The Grand Old Man of India'.
• He was also an intellectual and educator.
• For the betterment of his countrymen, he founded the Dnyan (Gyan) Prasarak Mandali to educate women.

 

Additional Information

Piloo Mody

• Piloo Mody was an Indian architect and politician and one of the founding members of the Swatantra Party.

Bhikaiji Cama

• Bhikaiji Cama is regarded as ” the mother of Indian revolutionaries”.
• She supported violent revolutionary means for achieving freedom.

Jamshetji Tata

• Jamsetji Nusserwanji Tata was an Indian pioneer industrialist, who founded the Tata Group.

The Correct Answer is Kolkata.

 

Key Points

• The regulating act of 1773 established a supreme court at Fort William, Calcutta.
• This Supreme Court consisted of one Chief Justice and three other regular judges or Puisne Judges.
• Sir Elijah Imphey was the first Chief Justice of this Supreme Court.

 

Important Points

The regulating act of 1773 

• It was the first step taken by the British Government to control and regulate the affairs of the East India Company in India.
• It recognized, for the first time, the political and administrative functions of the Company.
• It designated the Governor of Bengal as the ‘Governor-General of Bengal’ and created an Executive Council of four members to assist him.
• The first such Governor-General was Lord Warren Hastings.

The Correct Answer is face.

 

Key Points

• The mandible is the bone of the lower jaw.
• The mandible is located inferiorly in the facial skeleton.
• It is the largest and strongest bone of the face.
• It forms the lower jaw and acts as a receptacle for the lower teeth.
• It also articulates on either side with the temporal bone, forming the temporomandibular joint.

The Correct Answer is Novak Djokovic.

 

Key Points

• Novak Djokovic from Serbia won the 2018 US Open title of tennis in the men’s singles category.
• He defeated Argentina’s Juan Martín del Potro (world no 3).
• It was Djokovic’s third US Open title and overall 14th Grand Slam title.

 

Important Points

• Sir Andrew Barron Murray OBE is a British professional tennis player from Scotland.
• Rafael "Rafa" Nadal Parera is a Spanish professional tennis player.
• Roger Federer is a Swiss professional tennis player.

The Correct Answer is Gha To Kito.

 

Key Points

• Gha To Kito is a song-cum-dance of the Bhutia tribe in Sikkim.
• It depicts the riches of Sikkim such as Mount Kanchanjunga, religious places, hills, lakes, caves, and minerals.

 

Important Points

• Mando is a folk dance that originated in Goa.
• Khubakeshei is a dance form of Manipur.
• Dekhṇi is a semi-classical dance form of Goa.

 

Additional Information

• Singhi Chham is another folk dance of Sikkim which is also known as the Loin Dance.

The Correct Answer is Maach.

 

Key Points

• Maach is a form of folk theatre from the Malwa region of Madhya Pradesh.
• It is a sung drama with only occasional use of speech.
• The background of the play is set by curtains and the dancers usually double up as singers.

  

Important Points

Other dance of Madhya Pradesh

• Macha
• Lota
• Pandvan
• Tertali
• Charkula
• Jawara
• Matki dance
• Phulpatti dance
• Grida dance
• Gaur maria

 

Additional Information

• Lezim is a folk dance form, from the state of Maharashtra.
• Cheraw dance is a traditional cultural dance performed in Mizoram.
• Ottan Thullal is a Comedic dance and poetic performance form of Kerala.

The Correct Answer is Chandragupta.

 

 

• With the help of Chanakya (Vishnugupta/ Kautilya), Chandragupta Maurya defeated Dhana Nanda (322 BCE) and founded the Mauryan Dynasty.
• Chanakya encouraged Chandragupta Maurya and his army to take over the throne of Magadha.
• His vast empire included Bihar, Bengal, Deccan (except modern Kerala, Tamilnadu, and parts of Northeast India), Eastern Afghanistan, Baluchistan, and the area west of the Indus river.

 

 

bindusara

• Chandragupta was succeeded by his son Bindusara.
• Bindusara ruled for approximately 25-26 years and his succession was disputed which ultimately gave India a great king called Asoka.

Ashoka

• Asoka was the third and the greatest of the Mauryan rulers.
• Ashoka is referred to as Ashokavardhana.

Kunala

• Kunala was the son of Emperor Ashoka and Queen Padmavati and the presumptive heir to Ashoka.

The correct answer is magnetic flux.

 

Key Points

• Magnetic flux is a measurement of the total magnetic field which passes through a given area.
• Magnetic flux is the product of the average magnetic field times the perpendicular area that it penetrates.
• The SI unit of magnetic flux is Weber (Wb).

 

Important Points

• Conductance explains the ease with which electric current flows through a substance.
• Magnetic flux density is defined as the amount of magnetic flux in an area taken perpendicular to the magnetic flux's direction.
• Capacitance is the ability of a body to hold an electrical charge.

The Correct Answer is M Visvesvaraya.

Key Points

• Engineers day is observed on September 15 to commemorate the birth anniversary of M Visvesvaraya.
• Under his able Dewanship, the state of Mysore saw a major transformation in the realms of Agriculture, Irrigation, Industrialization, Education, Banking, and Commerce.

 

Important Points

• National Education Day on November 11 to commemorate the birth anniversary of Abul Kalam Azad.
• Abul Kalam Azad was appointed as India's first Minister for Education.
• Chandrasekhara Venkata Raman was born on November 7, 1888.
• His discovery of the Raman Effect had earned him the 1930 Nobel Prize for Physics.
• J.R.D. Tata, the patriarch of the biggest industrial house in India.

Formula used:

Sum of n number = n(n + 1)/2

Calculation:

first 8 multiple of 8 are 8, 16,....64

sum = 8 + 16 +...+ 64

⇒ 8(1 + 2 + 3....+8)

⇒ 8(8)(9)/2

⇒ 288

∴ Average = 288/8 = 36

Concept used:

We have to follow the BODMAS rule

Calculation:

⇒ 5 − 6.5 ÷ 13 + 2.3 × 0.8 + 0.4

⇒ 5 − 0.5 + 2.3 × 0.8 + 0.4

⇒ 5 − 0.5 + 1.84 + 0.4

⇒ 7.24 - 0.5

⇒ 6.74

∴ Answer is 6.74

Given:

The ratio between two natural number is 3 : 4

The smallest number which must be added so that the ratio becomes 4 : 5

The sum of the numbers will be 27

Calculation:

Let the two numbers be 3x and 4x and 'y' be the smallest number that has

⇒ $\% MathType!MTEF!2!1!+- \% feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn \% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr \% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 \% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x \% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 \% qadaWcaaWdaeaapeGaaG4maiaadIhacqGHRaWkcaGGGcGaamyEaaWd \% aeaapeGaaGinaiaadIhacaGGGcGaey4kaSIaaiiOaiaadMhaaaGaai \% iOaiabg2da9iaacckadaWcaaWdaeaapeGaaGinaaWdaeaapeGaaGyn \% aaaaaaa!461C! \frac{{3x + ;y}}{{4x; + ;y}}; = ;\frac{4}{5}$

⇒ 15x + 5y = 16x + 4y

⇒ x = y

Given sum of the numbers are 27

⇒ 3x + y + 4x + y = 27

⇒ 7x + 2y = 27

⇒ 9y = 27

⇒ y = 3

Therefore, x and y is 3

Given:

the ratio between 2 numbers is 4 : 5

the sum of their squares is 1025

Calculation:

let one umber is 4x and the second number is 5x

According to problem

(4x)² + (5x)² = 1025

⇒ 16x² + 25x² = 1025

⇒ 41x² = 1025

⇒ x² = 1025/41

⇒ x² = 25

⇒ x = 5

first number, 4x = 4 × 5

⇒ 20

second number, 5x = 5 × 5

⇒ 25

∴ the number are 20 and 25

Given:

A complete one round in 8 minutes

B Complete one round in 15 minutes

C Complete one round in 20 minutes

Concept used:

LCM method

Calculation:

according to problem

LCM of 8, 15 And 20 = 120

⇒ 120 minute = 120/60 

⇒ 2 hours

A, B and C start at 8 A.M 

∴ A, B and C will meet, 8 + 2 = 10 A.M

Given:

A car travels 60 km in the first hour

65 km in the second hour

70 km in the third hour

Formula used:

$\% MathType!MTEF!2!1!+- \% feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn \% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr \% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 \% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x \% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 \% qacaWGbbGaamODaiaadwgacaWGYbGaamyyaiaadEgacaWGLbGaaeiO \% aiaadohacaWGWbGaamyzaiaadwgacaWGKbGaeyypa0JaaeiOamaala \% aapaqaa8qacaWGubGaam4BaiaadshacaWGHbGaamiBaiaabckacaWG \% KbGaamyAaiaadohacaWG0bGaamyyaiaad6gacaWGJbGaamyzaaWdae \% aapeGaamivaiaad+gacaWG0bGaamyyaiaadYgacaqGGcGaamiDaiaa \% dMgacaWGTbGaamyzaaaaaaa!5B6C! Average{\rm{;}}speed = {\rm{;}}\frac{{Total{\rm{;}}distance}}{{Total{\rm{;}}time}}$

Calculation:

Distance in first hour = 60 × 1 = 60 km

Distance in second hour = 65 × 1 = 65 km

Distance in third hour = 70 × 1 = 70 km

Total distance = 60 + 65 + 70 = 195 km

Total time = 3 hours

Average speed = $\% MathType!MTEF!2!1!+- \% feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn \% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr \% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 \% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x \% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 \% qadaWcaaWdaeaapeGaaGymaiaaiMdacaaI1aaapaqaa8qacaaIZaaa \% aaaa!395C! \frac{{195}}{3}$

⇒ 65 km/hour

∴ The average speed of the car is 65 km/hour

Shortcut Trick

Present ratio of Arun and Anand is 3 : 1.

After 5 years, Arun's age = 2 × (Anand's age) + 5.

Substitute the ratio parts: 3x + 5 = 2(1x + 5) + 5.

Solving for 1 unit: 3x + 5 = 2x + 10 + 5 ⇒ x = 10.

Present age of Arun = 3 units = 3 × 10 = 30 years.

∴ The correct answer is 30 years.

Alternate Method

Given:

Ratio of present ages of Arun and Anand = 3 : 1

Let the present age of Arun be 3x and Anand be x.

Calculations:

After 5 years, Arun's age = 3x + 5

After 5 years, Anand's age = x + 5

According to the question:

⇒ 3x + 5 = 2(x + 5) + 5

⇒ 3x + 5 = 2x + 10 + 5

⇒ 3x + 5 = 2x + 15

⇒ 3x − 2x = 15 − 5

⇒ x = 10

Present age of Arun = 3x

⇒ 3 × 10 = 30 years.

∴ The correct answer is 30 years.

Additional Information

Ratio and Proportion in Ages

When a ratio a : b is given, values can be represented as ax and bx. The multiplier x represents the HCF of the actual ages.

Constant Age Difference

The numerical difference between the ages of two individuals always remains constant throughout their lives, regardless of the years added or subtracted.

Future and Past Ages

To calculate age 'n' years in the future, use (Present Age + n). For age 'n' years in the past, use (Present Age − n).

We have to follow the BODMAS rule

<br>

Calculation:

⇒$8; + ;3 - \left( {\frac{5}{2}; \times ;\frac{1}{3}} \right);$(of;\frac{{12}}{5}; + \left( {\frac{4}{3}; \times ;\frac{3}{8}} \right)\)

⇒$8 + 3 - \left( {\frac{5}{6}} \right);of;\frac{{12}}{5}; + ;\frac{1}{2}$

⇒$8 + 3 - \left( {\frac{5}{6}; \times ;\frac{{12}}{5}} \right) + ;\frac{1}{2}$

⇒$11 - 2 + \frac{1}{2}$

⇒9 + 0.5

⇒ 9.5

Therefore, the answer is 9.5

Calculation:

Sum of vehicles manufactured in the give years by company X = 119 + 99 + 141 + 78 = 437

Sum of vehicles manufactured in the given years by company Y = 139 + 120 + 100 + 128 = 487

Difference = 487000 - 437000

⇒ 50000

Therefore, difference between the total productions of the two companies from 1997 to 2000 is 50000

Given:

Ramu got a new table for 25% discount

Ramu would have had to pay Rs. 185 more.

Calculation:

Let the cost price be x

He got 25% discount

⇒ (100 - 25)%

⇒ 75%

So, he paid 0.75x 

According to question

given no discount then he would have paid 185 more

So, $\% MathType!MTEF!2!1!+- \% feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn \% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr \% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 \% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x \% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 \% qadaWcaaWdaeaapeGaamiEaaWdaeaapeGaaGinaaaacqGH9aqpcaaI \% XaGaaGioaiaaiwdaaaa!3B5F! \frac{x}{4} = 185$

⇒ x=740

So Ramu paid 740-185

⇒ Rs. 555

Therefore, Ramu pay for this table Rs. 555

Calculation:

Difference between the productions in 1997 = 139 - 119 = 20

Difference between the productions in 1998 = 120 - 99 = 21

Difference between the productions in 1999 = 141 - 100 = 41

Difference between the productions in 2000 = 128 - 78 = 50

Difference between the productions in 2001 = 120 - 107 = 13

Difference between the productions in 2002 = 159 - 148 = 11

Therefore, the difference between the productions was minimum in the year 2002.

Given:

Reduced SP by 39

The gain of 10% turns in to a loss of 3%

Formula used:

Loss% = (CP – SP)/CP × 100

Calculation:

Let the original price of the article be x

Initial SP = (110/100)x

⇒ 1.1x

If shop keeper reduced SP by 39 then,

New SP = 1.1x – 39

Loss% = (CP – SP)/CP × 100

⇒ 3 = (x – 1.1x + 39)x × 100

⇒ 0.03x = – 0.1x + 39

⇒ 0.03x + 0.1x = 39

⇒ x = 39/0.13

⇒ x = 300

∴ The original price of the article is 300

Shortcut Trick

Here the net change is 10 + 3 = 13%

13% change has occurred due to the change in selling price it means decreased by 39

13% of CP = 39

⇒ 100% = CP

⇒ CP = (39 × 100)/13

∴ CP = 300

Given:

The difference between the circumference and diameter of a circle is 60 cm

Formula used:

circumference of circle = 2πR

Calculation:

According to problem

⇒ 2πR – 2R = 60

⇒ 2R(π – 1) = 60

⇒ R(π – 1) = 30

⇒ R = 30/(π – 1)

⇒ R = $\frac{{30}}{{\frac{{22}}{7} - 1}} ~$ 

⇒ R = $\frac{30\times 7}{22-7}$

⇒ R = 210/15

⇒ R = 14

∴ The radius of the circle is 14 cm

Given:

Two cylindrical cans have the base of the same size

The diameter of each is 14 cm

The height of one can is 10 cm and another 20 cm

Formula used:

The volume of a cylinder = π r²h

Calculation:

If both the cylinders have the same radius then the only difference will be in their heights

The ratio of volumes will be in the ratio of their heights

Therefore the ratio of heights or volumes=10/20

⇒ 1:2

The ratio of their volume is 1:2

Shortcut Trick

Since the number of observations in all three groups is equal ('n'), the overall average is simply the arithmetic mean of their individual averages.

Overall Average = (Sum of all averages) ÷ (Number of groups)

Overall Average = (38 + 42 + 55) ÷ 3

Overall Average = 135 ÷ 3 = 45

∴ The correct answer is 45.

Alternate Method

n obs. Avg: 38

n obs. Avg: 42

n obs. Avg: 55

Total: 3n obs. Avg: ?

Given:

Three groups of observations, each containing 'n' observations.

Averages of the three groups are 38, 42, and 55 respectively.

Formula Used:

Sum of observations = Average × Number of observations

Overall Average = Total Sum of Observations ÷ Total Number of Observations

Calculations:

⇒ Sum of first 'n' observations = 38 × n = 38n

⇒ Sum of second 'n' observations = 42 × n = 42n

⇒ Sum of remaining 'n' observations = 55 × n = 55n

⇒ Total sum of all observations = 38n + 42n + 55n = 135n

⇒ Total number of observations = n + n + n = 3n

⇒ Overall average = 135n ÷ 3n

⇒ Overall average = 45

∴ The correct answer is 45.

Additional Information

Combined Average

When combining multiple groups with different numbers of items (n₁, n₂, ...), the combined average is given by the weighted average formula: A = (n₁A₁ + n₂A₂ + ...) ÷ (n₁ + n₂ + ...).

Equal Weights Shortcut

If the number of items in all combined groups is identical (n₁ = n₂ = n₃ ...), the combined average simplifies to the basic arithmetic mean of the individual averages: (A₁ + A₂ + A₃ + ...) ÷ Total Groups.

Net Deviation Method

Assume an arbitrary mean (e.g., 40). Find the net deviation of each group's average from it. The final average is calculated as: Assumed Mean + (Net Deviation ÷ Total Number of Items). This technique helps in fast mental calculations.

Shortcut Trick

When the Rate of interest (R) is numerically equal to the Time period (T), the formula is:

R = √((SI × 100) ÷ P)

R = √((2000 × 100) ÷ 8000) = √(200000 ÷ 8000) = √25

R = 5%

∴ The correct answer is 5%.

Alternate Method

Given:

Principal (P) = ₹8000

Simple Interest (SI) = ₹2000

Condition: Time (T) = Rate (R)

Formula Used: SI = (P × R × T) ÷ 100

Calculations:

⇒ 2000 = (8000 × R × R) ÷ 100

⇒ 2000 = 80 × R²

⇒ R² = 2000 ÷ 80

⇒ R² = 25

⇒ R = √25

⇒ R = 5

∴ The correct answer is 5%.

Additional Information

Simple Interest Concept

Simple Interest (SI) is calculated only on the Principal amount. The formula is SI = (P × R × T) ÷ 100.

Relationship when T = R

If the Time and Rate are numerically equal, then the Rate is the square root of 100 times the ratio of Interest to Principal.

Total Amount

The total Amount (A) at the end of the loan period is the sum of Principal and Interest: A = P + SI.

Shortcut Trick

Net annual growth rate = Birth rate − Death rate = 9% − 7% = 2%.

Effective growth for 2 years using successive formula (x + y + xy/100) = 2 + 2 + (2 × 2)/100 = 4.04%.

Final Population = 2,25,000 × (100 + 4.04)% = 2,25,000 × 1.0404 = 2,34,090.

∴ The correct answer is 234090.

Alternate Method

Given:

Initial population (P) = 2,25,000

Annual Birth Rate = 9%

Annual Death Rate = 7%

Time (n) = 2 years

Formula Used:

Net Rate (R) = Birth Rate − Death Rate

Final Population = P × (1 + R/100)ⁿ

⇒ Net Rate of growth (R) = 9% − 7% = 2% per annum

⇒ Population after 1st year = 2,25,000 × (1 + 2/100) = 2,25,000 × 1.02 = 2,29,500

⇒ Population after 2nd year = 2,29,500 × (1 + 2/100) = 2,29,500 × 1.02

⇒ Final Population = 2,34,090

∴ The correct answer is 234090.

Additional Information

Net Growth Rate

When both birth and death rates are given, the net annual growth is calculated by subtracting the death rate from the birth rate.

Population Change Formula

The population after 'n' years is given by P_n = P(1 ± R/100)ⁿ, where P is initial population and R is rate of change.

Successive Percentage Change

If a value changes by x% and then y%, the effective percentage change is (x + y + xy/100)%.

Given:

speed of car = 120 km/hr

time = 4 hours

Formula used:

Speed = distance/time

Calculation:

let distance be D

D = 120 × 4

⇒ 480 km

now the speed of the car to cover 480 km in 3 hours 20 minutes

3 hours 20 minutes = 10/3 hours

⇒ 480 = speed × (10/3)

⇒ speed = 144 km/hour

∴ The speed of the car to cover 480 km in 3 hours 20 minutes is 144 km/hour

Alternate MethodLet the required speed be x km/hr. We know that time α 1/distance.

3 hour 20 minutes = 10/3 hrs

⇒ 4/10/3 = x/120

⇒ x = (12/10) × 120

⇒ x = 144 km

∴ The speed of the car to cover 480 km in 3 hours 20 minutes is 144 km/hour

Given:

I sold an article for ₹8800 thus gained 10%.

What amount should sell it to get 15% profit

Calculation:

Selling Price = 8800

Profit percent = 10%

So, selling price(S.P.) = 100 + (100 × 10)/100

⇒ 100 + 10

⇒ 110

Therefore, 110 % C.P. = 8800

C.P. = (8800 × 100)/110

C.P. = 8000

We have profit percent = 15%

So, S.P. = 100 + (100 × 15)/100

⇒ 100 + 15

⇒ 115

According to question,

S.P. = 115% of C.P.

⇒  (115/100) × 8000

⇒ 9200

∴ The amount should sell by 9200 Rs.

Calculation:

The production of Company Y in 1998 = 120000

The production of Company X in 1998 = 99000

Required percentage = (120000/99000) × 100

⇒ (40/33) × 100%

⇒ 121.2%

∴ The production of Company Y in 1998 was approximately 121.2% of the production of Company X in the same year.

Given:

The length and breadth of a rectangle are in the ratio 8 : 3

The perimeter is 132 cm

Formula used:

Area of rectangle = length × breadth

Perimeter of rectangle = 2(length + breadth)

Calculation:

Let the length and breadth be 8x and 3x respectively

Perimeter of rectangle = 2(length + breadth)

⇒ 2(8x + 3x)

⇒ 2(11x)

⇒ 22x

Given 22x = 132

⇒ x = 6

So, Area of rectangle = length × breadth

⇒ 48 × 18

⇒ 864 sq cm

∴ The required area is 884 sq cm