From a close reading of the passage, it is clear that the topic of concern is the changing nature of education due to the internet and cloud computing. The passage goes in detail to describe the changes that will occur in the sector of education due to the same. 

Hence the correct option is 1. Cloud computing will change the nature of education.

The correct answer is option 5. All of these.

It is given in the following lines of the passage: The future is about access, anywhere learning and collaboration, both locally and globally. Teaching and learning are going to be social. Schools of the future could have a traditional cohort of students, as well as online-only students who live across the country or even the world. Things are already starting to move this way with the emergence of massive open online courses (MOOCs).

The correct answer is option 1. An ill-trained and under-confident staff of teachers who do not see the benefits of online education.

It is given in the following lines of the passage: Staff will also need training; you can't expect staff to use new technology if they are not confident users or creators. Any initiative is doomed to failure without well trained, confident staff who can see how technology can support and benefit teaching and learning.

Out of the given options, the best title is option 1, Cloud computing: The new era of global education.

From a close reading of the passage, we realize that the main idea that is being discussed in detail here is the changes that will come in the current model of education because of the advent of internet and cloud computing. 

All the other options are incorrect as they relate to only a particular aspect of the passage or are ambiguous.

The correct answer is option 4. Options 1, 2, and 3.

It is given in the following lines of the passage: School classrooms are going to change. With the cloud, the world will be our classroom. E-learning will change teaching and learning. Students can learn from anywhere and teachers can teach from anywhere.

Let us look at the meanings of all the words:

Massive: large and heavy or solid.

Puny: small and weak.

Humongous: huge; enormous.

Medium: about halfway between two extremes of size or another quality; average.

Elaborate: detailed and complicated in design and planning.

Hence option 1 is the correct answer.

Let us look at the meanings of all the words:

Ensure: make certain that (something) will occur or be the case.

Pressure: the continuous physical force exerted on or against an object by something in contact with it.

Assure: make (something) certain to happen.

Lure: tempt (a person or animal) to do something or to go somewhere, especially by offering some form of reward.

Procure: obtain (something), especially with care or effort.

Hence option 2 is the correct answer.

Let us look at the meanings of all the words:

Adopt: choose to take up, follow, or use.

Deny: a state that one refuses to admit the truth or existence of.

Accept: give an affirmative answer to (an offer or proposal); say yes to.

Affect: have an effect on; make a difference to.

Attempt: make an effort to achieve or complete (something difficult).

In a sentence, if the first of two or even more adjectives is the superlative degree, the others must also be of the superlative degree.

Therefore, 'most hard-working' will fill the blank.

The complete sentence will be: He is one of the best and most hard-working teachers that the school ever had. 

The correct option is 2.

The correct word here must be fewer.

Key Points

• When we are dealing with a number we must use 'fewer' and when we are dealing with 'quantity' we must use 'less.'
• The complete sentence will be: No fewer than fifty girls took part in the dance competition for the University's anniversary celebration.  

Hence the correct option is 3.

In the given sentence, the word 'preferable' already has the force of a comparative degree and hence does not require 'more' or 'much' in front of it.

'The most preferable' is an incorrect option as it is a superlative degree that cannot be used for comparing two entities.

So we must use 'preferable' alone. 

So, option 1 is correct. 

The complete sentence will be: Before long, we will all be old and realize that health is preferable to wealth.

Here we need not write 'roses' because 'rose' a singular noun represents the whole class of flowers.

Since the article 'the' is used, we must go for a singular noun.

So, the correct option is option 3. 

The complete sentence will be: I think that the rose is the sweetest of all flowers.

Since the last part of the sentence uses 'lost' which is a verb in its past form, the verb that will fill the blank will also be in its past form.

Given' and 'taken' are rejected as they are verbs in their past perfect form and are also contextually incorrect. 'Left' is also rejected as it is contextually incorrect.

Hence we must use 'got' in the blank.

Hence the correct answer is option 3.

The complete sentence is: Reputation was the one thing that she got without merit and lost without fault.

The error lies in part 2.

The sentence uses the form' to be close', which is incorrect.

Since the sentence uses the form 'to be' before 'close', the correct form here must be the verb form 'closed' meaning 'not open'.

Therefore, the correct answer is option 2.

The corrected sentence is: The aforementioned position was to be closed for the candidates possessing a score of 160 or lower.

The error lies in part 1.

The sentence uses the form 'have engulfed', which is incorrect here.

The correct form here should be either 'has' or 'had', since the 'mist' is singular and so the corresponding auxiliary verb form must also be singular.

Therefore, the correct answer is option 1.

Te corrected sentence will be: The cold mist has engulfed the entire town as if reclaimed in its own parallel dimension.

The error lies in part 3.

The sentence uses the form 'could never hoped', which is incorrect. 

The correct form here should be the simple present tense form of the verb, viz, 'hope', as the modal verb 'could' already expresses the tense and ability of the verb.

Therefore, the correct answer is option 3.

The corrected sentence will be: Try hard as he might, Alvira knew her brother could never hope to regain his health.

The error lies in part 1.

The sentence uses the form 'little does' one know, which is incorrect here.

As the sentence uses the past tense verb 'was', the correct form here should be 'little did' the King know.

'Little did/does one know' is a way of expressing the ignorance of a person about something.

Therefore, the correct answer is option 1.

The corrected sentence is: Little did the King know that an evil plan was already being hatched in his palace at that moment.

The error lies in part 4.

The sentence uses the preposition 'to' after the verb form 'to be proven', which, given the context of the sentence is unnecessary. It should be 'to be proven disastrous' and not 'to be proven to disastrous'.

Note here that both past participle forms 'proved' and 'proven' are correct.

Therefore, the correct answer is option 4.

The corrected sentence will be: He was aware that the oath he had taken was soon to be proven disastrous.

The error lies in part 1.

The sentence uses the form 'had they seen us', which is used to show a possibility of something happening, which means this conjunction 'had' is used synonymously with the conditional conjunction 'if'.

Whenever we use the conjunction 'had', there is no need to use the auxiliary verb again in the sentence. i.e. 'had they seen us' (which means if they had seen us) is correct and not 'had they had seen us'. The second 'had' is redundant here. 

Therefore, the correct answer is option 1.

The corrected sentence is*: Had they seen us misappropriate their belongings they would have been enraged.*

The error lies in part 3.

The sentence uses the adjective form 'inevitable', which is incorrect here. As the sentence is referring to the storm following the man, the correct form here should be the adverb 'inevitably'.

Inevitable means something that is sure to happen. For e.g. All men find that death is an inevitable enemy.

Therefore, the correct answer is option 3.

The corrected sentence is: The raging storm followed the man, inevitably swallowing up everything in its path.

The correct answer is 4- the error lies in the 4^th part of the sentence.

Key Points

We must remember it as a rule of thumb that ''seldom if ever'' and ''seldom or never'' are the correct expressions. ''Seldom if never'' is wrong.

So the correct option is 4. 

The corrected sentence is: The actual legal responsibilities may vary between jurisdictions and are seldom if ever clear. 

Additional Information

• Seldom if ever: this expression is used as a more forceful way to say 'seldom' or 'rarely'
• Seldom or never: this expression is used to mean 'very rarely'

The error is in part 2 of the sentence.

Here ''had Rekha'' and ''if Rekha had'' means the same thing. So this formation is correct. What's wrong is the use of 'may' which is in the present tense. We need to use the past tense. So we must use ''might'' instead of ''may.'' 

So, option 2 is correct. 

The corrected sentence is: Had Rekha not discouraged me I might have sung a song or two at your wedding.

The error here is in part 1 of the sentence.

We can see the formation of ''would have+V3'' in the later part of the sentence, which demands that the dependent clause or the first part of the sentence be in the past perfect tense. Now 'we had'' gives us the illusion that the sentence is already in past perfect, but actually, it is not.

Note that, here ''had'' is used as the main verb'' which means ''possess.'' So, to make it past perfect we must use the helping verb ''had''. 

So, option 1 is correct. 

The corrected sentence is: If we had had players like Ronaldo in our team, we would have qualified for the FIFA World Cup long ago.

The first sentence in the paragraph should always introduce a new topic. Out of all the given sentences, only C is independent as it gives the main subject, which is Daisy. Hence C is the first sentence.

The second sentence is B as it talks about what Daisy would like to do, that is, going home. This is followed by A as it talks about why she can't go home.

Next is D as the ‘she’ refers to Daisy's boss who is mentioned in A.

Next comes E which talks about how everyone else had left and how Daisy feels alone.

So, the correct sequence is CBADE.

Hence the correct answer is option 2.

The ordered paragraph is:  It had been a long tiring week for Daisy. All she wanted to do was go home and snuggle in her bed with a hot mug of cocoa. But she was brutally snapped out of her daydreams when the boss asked her to work for some more hours after the closing time. She was angry at her for asking her to stay back. It was a Friday so everyone else had gone back home, and she felt so alone and tired and frustrated.

The first sentence in the paragraph should always introduce a new topic. Out of all the given sentences, only C is independent as it gives the main subject, which is Daisy. Hence C is the first sentence.

The second sentence is B as it talks about what Daisy would like to do, that is, going home. This is followed by A as it talks about why she can't go home.

Next is D as the ‘she’ refers to Daisy's boss who is mentioned in A.

Next comes E which talks about how everyone else had left which is followed by F which supports the previous statement by saying how Daisy feels alone.

So, the correct sequence is CBADE.

Hence the correct answer is option 2.

The ordered paragraph is:  It had been a long tiring week for Daisy. All she wanted to do was go home and snuggle in her bed with a hot mug of cocoa. But she was brutally snapped out of her daydreams when the boss asked her to work for some more hours after the closing time. She was angry at her for asking her to stay back. It was a Friday so everyone else had gone back home, and she felt so alone and tired and frustrated.

The first sentence in the paragraph should always introduce a new topic. Out of all the given sentences, only C is independent as it gives the main subject, which is Daisy. Hence C is the first sentence.

The second sentence is B as it talks about what Daisy would like to do, that is, going home. This is followed by A as it talks about why she can't go home.

Next is D as the ‘she’ refers to Daisy's boss who is mentioned in A.

Next comes E which talks about how everyone else had left which is followed by F which supports the previous statement by saying how Daisy feels alone.

So, the correct sequence is CBADE.

Hence the correct answer is option 1. 

The ordered paragraph is:  It had been a long tiring week for Daisy. All she wanted to do was go home and snuggle in her bed with a hot mug of cocoa. But she was brutally snapped out of her daydreams when the boss asked her to work for some more hours after the closing time. She was angry at her for asking her to stay back. It was a Friday so everyone else had gone back home, and she felt so alone and tired and frustrated.

The first sentence in the paragraph should always introduce a new topic. Out of all the given sentences, only C is independent as it gives the main subject, which is Daisy. Hence C is the first sentence.

The second sentence is B as it talks about what Daisy would like to do, that is, going home. This is followed by A as it talks about why she can't go home.

Next is D as the ‘she’ refers to Daisy's boss who is mentioned in A.

Next comes E which talks about how everyone else had left which is followed by F which supports the previous statement by saying how Daisy feels alone.

So, the correct sequence is CBADE.

Hence the correct answer is option 4.

The ordered paragraph is:  It had been a long tiring week for Daisy. All she wanted to do was go home and snuggle in her bed with a hot mug of cocoa. But she was brutally snapped out of her daydreams when the boss asked her to work for some more hours after the closing time. She was angry at her for asking her to stay back. It was a Friday so everyone else had gone back home, and she felt so alone and tired and frustrated.

The first sentence in the paragraph should always introduce a new topic. Out of all the given sentences, only C is independent as it gives the main subject, which is Daisy. Hence C is the first sentence.

The second sentence is B as it talks about what Daisy would like to do, that is going home. This is followed by A as it talks about why she can't go home.

Next is D as the ‘she’ refers to Daisy's boss who is mentioned in A.

Next comes E which talks about how everyone else had left which is followed by F which supports the previous statement by saying how Daisy feels alone.

So, the correct sequence is CBADE.

Hence the correct answer is option 3.

The ordered paragraph is:  It had been a long tiring week for Daisy. All she wanted to do was go home and snuggle in her bed with a hot mug of cocoa. But she was brutally snapped out of her daydreams when the boss asked her to work for some more hours after the closing time. She was angry at her for asking her to stay back. It was a Friday so everyone else had gone back home, and she felt so alone and tired and frustrated.

All the words in the given statement are spelled correctly. 

The correct answer is option 5. No error.

The correct answer is Option 2 i.e. 'Campany'

Key Points

• The word 'campany' has been incorrectly spelled in the sentence.
• The correct spelling of the word is 'company'.
• Company is a business organization selling goods or services.
• All the other words have been correctly spelled.

Given expression is,

⇒ 34500 ÷ 460 ÷ 25 =?

⇒ 75 ÷ 25 =?

⇒ 3 =?

Hence the answer is 3

Follow BODMAS rule to solve this question, as per the order given below,

Step-1- Parts of an equation enclosed in 'Brackets' must be solved first, and in the bracket, the BODMAS rule must be followed,

Step-2- Any mathematical 'Of' or 'Exponent' must be solved next,

Step-3-Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step-4-Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Now, given expression:

⇒ 199 + 5³ ÷ 4 × 4² =?

⇒ 199 + 125 ÷ 4 × 4² = ?

⇒ 199 + 125 × 4 = ?

⇒ ? = 199 + 500

⇒ ? = 699

Follow BODMAS rule to solve this question, as per the order given below,

**Step-1-**Parts of an equation enclosed in 'Brackets' must be solved first,

**Step-2-**Any mathematical 'Of' or 'Exponent' must be solved next,

**Step-3-**Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

**Step-4-**Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Now, the given expression:

196 + 42 × 11 – 171

= 196 + 462 – 171

= 487

Follow BODMAS rule to solve this question, as per the order given below,

Step - 1 - Parts of an equation enclosed in the ‘BRACKETS’ must be solved first

Step - 2 - Any mathematical ‘OF’ or ‘EXPONEMTS’ must be solved next

Step - 3 - Next the part of the equation that contains ‘DIVISION; and ‘MULTIPLICATION’ are calculated

Step - 4 - Last but not least, the parts of the equation that contains ‘ADDITION’ and ‘SUBTRACTION’ should be calculated

Now, the given expression:

⇒ $2\frac{1}{9} \times 2\frac{2}{{19}} \div 6\frac{2}{3} = ? -1\frac{1}{2}$

⇒ $\frac{{19}}{9} \times \frac{{40}}{{19}} \div \frac{{20}}{3} = ? -\frac{3}{2}$

⇒ $\frac{{19}}{9} \times \frac{{40}}{{19}} \times \frac{3}{{20}} = ? -\frac{3}{2}$

⇒ $\frac{2}{3} = ? - \frac{3}{2}$

⇒ $\frac{2}{3} + \frac{3}{2} = ?$

⇒ $? = \frac{{13}}{6} = 2\frac{1}{6}$

Hence, the required answer is $2\frac{1}{6}$.

Follow BODMAS rule to solve this question, as per the order given below,

Step-1- Parts of an equation enclosed in 'Brackets' must be solved first, and in the bracket,

Step-2- Any mathematical 'Of' or 'Exponent' must be solved next,

Step-3- Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step-4- Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Given expression is,

\begin{array}{l} 15; + ;\left{ {\left( {2\frac{4}{7}; \times ;5\frac{4}{2}} \right); \div ;\left( {6\frac{2}{9}; \times ;2\frac{4}{7}} \right)} \right}; = ;?\ \Rightarrow {\rm{;}}15; + ;\left{ {\left( {\frac{{18}}{7}; \times ;\frac{{14}}{2}} \right); \div ;\left( {\frac{{56}}{9}; \times ;\frac{{18}}{7}} \right)} \right}; = ;?\ \Rightarrow {\rm{;}}15; + ;\left( {\frac{{18}}{{16}}} \right); = ;?\ \Rightarrow {\rm{;}}15; + ;\frac{9}{8}; = ;?\ \Rightarrow {\rm{;}}?; = ;\frac{{120; + ;9}}{8}; = ;\frac{{129}}{8} \end{array}  

⇒ ? = 129/8

Follow BODMAS rule to solve this question, as per the order given below,

Step - 1. Parts of an equation enclosed in 'Brackets' must be solved first,

Step - 2. Any mathematical 'Of' or 'Exponent' must be solved next,

Step - 3. Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step - 4. Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Given expression:

Following the order, we first attempt to solve the part in the brackets: (x + 1289).

We observe that this cannot be simplified any further. Hence we move on to “Of”.

We have,

25% of (x + 1289) = $\frac{{25}}{{100}} \times \left( {x; + ;1289} \right); = ;\frac{{x; + ;1289}}{4}$

Next, we add ⇒ $46; + ;\frac{{x; + ;1289}}{4}$

Equating it to the RHS, we have

$\begin{array}{l} 46; + ;\frac{{x; + ;1289}}{4}; = ;1340\ \Rightarrow \frac{{x; + ;1289}}{4}; = ;1294 \end{array}$

⇒ x + 1289 = 5176

⇒ x = 3887

Follow BODMAS rule to solve this question, as per the order given below,

Step - 1. Parts of an equation enclosed in 'Brackets' must be solved first,

Step - 2. Any mathematical 'Of' or 'Exponent' must be solved next,

Step - 3. Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step - 4. Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Given expression:

We have, 36% of 450 + ?% of 350 = 463

⇒ 162 + 7/2 × ? = 463

⇒ 7/2 × ? = 301

⇒ ? = 301 × 2/7 = 86

Applying the BODMAS Rule, the priority of operations is Bracket of

• Division
• Multiple
• Addition
• Subtraction

Rearranging the given problem,

⇒ (15 × 184) + 27 – 59 = ? + (156/12)

⇒ (15 × 184) + 27 – 59 = ? + 13

⇒ 2760 + 27 – 59 = ? + 13

⇒ 2760 + 27 – 59 – 13 = ?

⇒ 2760 + 27 – (59 + 13) = ?

⇒ 2760 + 27 – 72 = ?

⇒ (2760 + 27) – 72 = ?

⇒ 2787 – 72 = ?

∴ ? = 2715

To Follow BODMAS Rule

Step-1- Parts of an equation enclosed in 'Brackets' must be solved first, and in the bracket, the BODMAS rule must be followed,

Step-2- Any mathematical 'Of' or 'Exponent' must be solved next,

Step-3-Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step-4-Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Given expression is,

3780 ÷ 14 × 15 + 340 = ?

⇒ 270 × 15 + 340 = ?

⇒ 4050 + 340 = ?

⇒ ? = 4390

Follow BODMAS rule to solve this question, as per the order given below,

**Step-1-**Parts of an equation enclosed in 'Brackets' must be solved first,

**Step-2-**Any mathematical 'Of' or 'Exponent' must be solved next,

**Step-3-**Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

**Step-4-**Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Now, the given expression,

55 + 8 × 0.75 – 12 = ?

⇒ ? = 55 + 6 – 12

⇒ ? = 49

As per the given data,

From I)

⇒ x² - 7x + 12 = 0

⇒ x² - 3x - 4x +12 = 0

⇒ x (x - 3) - 4 (x - 3) = 0

⇒ (x - 4)(x - 3) = 0

∴ x = 4 and x = 3

From II)

⇒ y² + y - 30 = 0

⇒ y² + 6y - 5y -30 = 0

⇒ y (y + 6) - 5 (y + 6) = 0

⇒ (y - 5)(y + 6) = 0

∴ y = 5 and y = -6

When x = 4 and y = 5, then x < y

 x = 4 and y = -6, then x > y

 x = 3 and y = 5, then x < y

 x = 3 and y = -6, then x > y

∴ from the above, we can say relationship cannot be determined

As per the given data,

From I)

⇒ 2x² + 15x + 13 = 0

⇒ 2x² + 2x + 13x + 13 = 0

⇒ 2x (x + 1) + 13 (x + 1) = 0

⇒ (2x + 13)(x + 1) = 0

∴ x = -13/2 and x = -1

From II)

⇒ y² - 7y +12 = 0

⇒ y² - 3y - 4y + 12 = 0

⇒ y (y - 3) - 4 (y -3) = 0

⇒ (y - 4)(y - 3) = 0

∴ y = 4 and y = 3

When x = -13/2 and y = 4, then x < y

 x = -13/2 and y = 3, then x < y

 x = -1 and y = 4, then x < y

 x = -1 and y = 3, then x < y

∴ From the above, we can say x < y

As per the given data,

From I)

⇒ x² – 16x + 63 = 0

⇒ x² - 7y - 9y + 63 = 0

⇒ x (x - 7) -9 (x - 7) = 0

⇒ (x - 9)(x - 7) = 0

∴ x = 9 and 7

From II)

⇒ y² - 44y + 84 = 0

⇒ y² - 42y - 2y + 84 = 0

⇒ y (y - 42) - 2 (y - 42) = 0

⇒ (y - 2)(y - 42) = 0

∴ y = 2 and y = 42

When x = 9 and y = 2, then x > y

 x = 9 and y = 42, then x < y

 x = 7 and y = 2, then x > y

 x = 7 and y = 42, then x < y

∴ From the above we can say, Relationship cannot be determined

From the given data,

⇒ x² + 16x + 48 = 0

⇒ x² + 12x + 4x + 48 = 0

⇒ x (x + 12) + 4 (x + 12) = 0

⇒ (x + 4) (x + 12) = 0

∴ x = - 4 and x = - 12

Also given that y² + 21y + 38 = 0

⇒ y² + 19 y + 2y + 38 = 0

⇒ y (y + 19) + 2 (y + 19) = 0

⇒ (y + 2) (y + 19) = 0

⇒ y = - 2 and y = - 19

∴ When x = - 4 and y = - 2, then x < y

x = - 4 and y = - 19, then x > y

x = - 12 and y = - 2, then x < y

x = - 12 and y = - 19, then x > y

∴ Relationship cannot be determined

From equation 1:

⇒ x² + 2x + x + 2 = 0

⇒ (x + 2)(x + 1) = 0

∴ x = −2 or x = −1

From equation 2:

⇒ y² + 4y − y − 4 = 0

⇒ (y − 1)(y + 4) = 0

∴ y = 1 or y = −4

When x = −1, y = 1 then x < y

When x = −1, y = −4 then x > y

When x = −2, y = 1 then x < y

When x = −2, y = −4 then x > y

∴ No relation is obtained between x and y

Total books read by Mridul and Sachin in both the years = 170 + 80 = 250

Total books read by Vishnu and Praveen in both the years = 90 + 130 = 220

Difference = 250 – 220 = 30 More

Total books read by Vishnu in both the years = 90

Total books read by Mridul in both the years = 170

Total books read by Sachin in both the years = 80

Total books read by Praveen in both the years = 130

Total = 90 + 170 + 80 + 130 = 470

Number of books read by Praveen in 2015 = 70

Number of books read by Mridul in 2015 = 80

∴ Required Percentage = (80 – 70 / 80) × 100 = 12.5%

Number of books read by Vishnu in 2016= 40

Number of books read by Mridul in 2016 = 90

Number of books read by Sachin in 2016= 50

Number of books read by Praveen in 2016= 60

Total Number of books read by all of them in 2016= 40 + 90 + 50 + 60 = 240

∴ Required Average = 240/4 = 60

Number of books read by Vishnu in 2015 = 50

Number of books read by Mridul in 2015 = 80

Number of books read by Vishnu and Mridul in 2015 = 50 + 80 = 130

Number of books read by Sachin in 2015 = 30

Number of books read by Praveen in 2015 = 70

Number of books read by Sachin and Praveen in 2015 = 30 + 70 = 100

∴ Required ratio = 130 ∶ 100 = 13 ∶ 10

Shortcut Trick

Ratio of shares Abhishek : Pritha = 5 : 7

Difference in ratio parts = 7 − 5 = 2 units

Given, 2 units = ₹2000 → 1 unit = ₹1000

Abhishek’s share (5 units) = 5 × ₹1000 = ₹5000

∴ The correct answer is ₹5000.

Alternate Method

Given:

Ratio of distribution = 5 : 7

Difference in amounts = ₹2000

Calculations:

⇒ Let Abhishek’s share be 5x and Pritha’s share be 7x.

⇒ According to the question, 7x − 5x = 2000

⇒ 2x = 2000

⇒ x = 2000 ÷ 2 = 1000

⇒ Abhishek’s share = 5x = 5 × 1000

⇒ Abhishek’s share = ₹5000

∴ The correct answer is ₹5000.

Additional Information

Ratio and Proportion

A ratio compares two quantities. If A:B is the ratio and the total amount is T, then A's share = [A / (A+B)] × T.

Difference in Ratios

When the difference between two shares is given, the value of one unit is calculated as (Actual Difference) ÷ (Difference in Ratio Parts).

Shortcut Trick

Relative Speed in same direction = 72 − 54 = 18 km/hr.

Convert to m/s: 18 × (5/18) = 5 m/s.

Time to cross = Distance ÷ Relative Speed = 32 ÷ 5 = 6.4 seconds.

∴ The correct answer is 6.4 sec.

Alternate Method

Given:

Speed of White Car (S₁) = 72 km/hr

Speed of Black Car (S₂) = 54 km/hr

Initial Distance (D) = 32 m

Formula Used:

Relative Speed (Same Direction) = S₁ − S₂

Time = Distance ÷ Relative Speed

Calculations:

⇒ Relative Speed = 72 − 54 = 18 km/hr

⇒ Conversion to m/s = 18 × (5/18) = 5 m/s

⇒ Time required = 32 ÷ 5

⇒ Time = 6.4 seconds

∴ The correct answer is 6.4 sec.

Additional Information

Relative Speed Concepts

When two objects move in the same direction, relative speed is (S₁ − S₂). When moving in opposite directions, it is (S₁ + S₂).

Unit Conversion

To convert km/hr to m/s, multiply by 5/18. To convert m/s to km/hr, multiply by 18/5.

Overtaking Time

The time taken to overtake depends only on the gap distance and the difference in speeds between the two vehicles.

Shortcut Trick

Use the ratio formula: MP ÷ CP = (100 + Profit%) ÷ (100 − Discount%).

MP ÷ CP = (100 + 20) ÷ (100 − 25) = 120 ÷ 75.

Simplified Ratio: MP : CP = 8 : 5.

Marked up value = 8 − 5 = 3 units.

Markup percentage = (3 ÷ 5) × 100 = 60%.

∴ The correct answer is 60%.

Alternate Method

Given: Profit = 20%, Discount = 25%.

Formulas: SP = CP × (100 + Profit%) ÷ 100 | SP = MP × (100 − Discount%) ÷ 100 | Markup% = (MP − CP) ÷ CP × 100.

⇒ Let Cost Price (CP) be 100.

⇒ To gain 20%, Selling Price (SP) = 100 + 20 = 120.

⇒ Since SP is obtained after 25% discount on Marked Price (MP), SP = 75% of MP.

⇒ 120 = (75 ÷ 100) × MP ⇒ MP = (120 × 100) ÷ 75 = 160.

⇒ Markup = MP − CP = 160 − 100 = 60.

⇒ Markup% = (60 ÷ 100) × 100 = 60%.

∴ The correct answer is 60%.

Additional Information

Relation between MP and CP

The ratio of Marked Price to Cost Price is always (100 + Profit%) / (100 − Discount%). If there is a loss, use (100 − Loss%).

Marked Price & Discount

Discount is always calculated on the Marked Price (MP), whereas Profit or Loss is calculated on the Cost Price (CP).

Shortcut Trick

Speed downstream (u) = 9 + 3 = 12 km/hr

Speed upstream (v) = 9 − 3 = 6 km/hr

Ratio of Speed (Down : Up) = 12 : 6 = 2 : 1

Ratio of Time (Down : Up) = 1 : 2 (since Distance is constant)

Difference in time ratio = 2 − 1 = 1 unit → 6 hours

Time taken downstream = 1 × 6 = 6 hours | Distance = 12 × 6 = 72 km

Total distance covered (Up + Down) = 72 + 72 = 144 km.

∴ The correct answer is 144 km.

Alternate Method

Given: Speed of boat (x) = 9 km/hr, Speed of stream (y) = 3 km/hr, Time difference = 6 hours.

Formula Used: Distance (D) = [ (u × v) ÷ (u − v) ] × Time Difference

⇒ Downstream Speed (u) = 9 + 3 = 12 km/hr

⇒ Upstream Speed (v) = 9 − 3 = 6 km/hr

⇒ One-way Distance (D) = [ (12 × 6) ÷ (12 − 6) ] × 6

⇒ D = [ 72 ÷ 6 ] × 6 = 72 km

⇒ Total Distance = Upstream Distance + Downstream Distance = 72 + 72

⇒ Total Distance = 144 km

∴ The correct answer is 144 km.

Additional Information

Relative Speed in Streams

Downstream speed (u) = x + y; Upstream speed (v) = x − y, where x is boat speed in still water and y is stream speed.

Still Water Speed Formula

Speed of boat in still water (x) = (u + v) ÷ 2 and Speed of stream (y) = (u − v) ÷ 2.

Average Speed of Boat

For a round trip (Upstream and Downstream), Average Speed = (u × v) ÷ x = (x² − y²) ÷ x.

Shortcut Trick

Let A's present age be 7x and B's age 4 years ago be 8x.

Current ages: A = 7x, B = 8x + 4.

Ages after 8 years: (7x + 8) / (8x + 4 + 8) = 9 / 11.

Solving for x: 77x + 88 = 72x + 108 → 5x = 20 → x = 4.

B's present age = 8(4) + 4 = 32 + 4 = 36 years.

∴ The correct answer is 36 years.

Alternate Method

Given: Ratio of A : (B − 4) = 7 : 8 and (A + 8) : (B + 8) = 9 : 11.

Calculations:

⇒ Let A = 7x and B − 4 = 8x → B = 8x + 4.

⇒ After 8 years, A's age = 7x + 8.

⇒ After 8 years, B's age = (8x + 4) + 8 = 8x + 12.

⇒ (7x + 8) / (8x + 12) = 9 / 11

⇒ 11(7x + 8) = 9(8x + 12)

⇒ 77x + 88 = 72x + 108

⇒ 5x = 20

⇒ x = 4

⇒ B's present age = 8x + 4 = 8(4) + 4 = 36 years.

∴ The correct answer is 36 years.

Additional Information

Ratio Method for Ages

When comparing ages at different points in time, ensure all parts of the ratio refer to the same timeframe or define variables clearly relative to the present age.

Age Difference Constant

The difference between the ages of two people remains constant throughout their lives, which can often be used to balance ratios quickly.

Shortcut Trick

Remaining mixture = 40 − 20 = 20 liters.

In remaining mixture, water = (1 / 5) × 20 = 4 liters.

Final water = Initial water in remaining + Added water = 4 + 10 = 14 liters.

∴ The correct answer is 14 liters.

Alternate Method

Given: Total mixture = 40 liters, Ratio (M:W) = 4:1, Removed = 20 liters, Added water = 10 liters.

⇒ Remaining Mixture = 40 − 20 = 20 liters.

⇒ Ratio in remaining mixture remains 4 : 1.

⇒ Quantity of water in 20 liters = [1 / (4+1)] × 20

⇒ Quantity of water = (1 / 5) × 20 = 4 liters.

⇒ Final quantity of water = 4 + 10 = 14 liters.

∴ The correct answer is 14 liters.

Additional Information

Ratio Invariance

When a portion of a homogeneous mixture is removed, the ratio of components in the remaining part and the removed part remains the same as the initial ratio.

Mixture Alligation

To find final concentrations after adding pure components, treat pure water as 100% water (or 0% milk) and apply the weighted average formula.

Shortcut Trick

Ratio of Profit = Ratio of (Capital × Time).

Ratio A : B : C = (5 × 12) : (6 × 12) : (3 × 6) = 60 : 72 : 18 = 10 : 12 : 3.

Given A share (10 units) = Rs. 2400 ⇒ 1 unit = Rs. 240.

C share (3 units) = 3 × 240 = Rs. 720.

∴ The correct answer is Rs. 720.

Alternate Method

Given: Capital ratio A : B = 5 : 6. C joins after 6 months with half of B capital. Duration = 1 year.

Formulas: Profit = Capital × Time | Profit Share_A : Profit Share_B : Profit Share_C = (C_a × T_a) : (C_b × T_b) : (C_c × T_c)

⇒ Let capital of A and B be 5x and 6x respectively.

⇒ Capital of C = 6x ÷ 2 = 3x.

⇒ Time periods: T_a = 12 months, T_b = 12 months, T_c = 6 months.

⇒ Profit ratio = (5x × 12) : (6x × 12) : (3x × 6) = 60x : 72x : 18x.

⇒ Simplifying the ratio = 10 : 12 : 3.

⇒ A share = 10 units = 2400 ⇒ 1 unit = 240.

⇒ C share = 3 units = 3 × 240 = 720.

∴ The correct answer is Rs. 720.

Additional Information

Partnership Basics

In a simple partnership, profits are shared in the ratio of investments if the time period is the same. In a compound partnership, profits are shared in the ratio of the product of capital and time.

Investment Calculation

If the profit ratio and time ratio are known, the capital ratio can be found using: Capital = Profit ÷ Time.

Shortcut Trick

Let the Principal (P) be 100 units.

First year CI = 20% of 100 = 20 units.

Second year CI = First year CI + Interest on First year CI = 20 + (20% of 20) = 24 units.

Difference = 24 − 20 = 4 units → ₹1200.

1 unit = ₹300 ∴ 100 units = 100 × 300 = ₹30000.

∴ The correct answer is ₹30000.

Alternate Method

Given: Rate (R) = 20%, Difference between 2^nd year CI and 1^st year CI = ₹1200.

Formula Used: CI for 1^st year = PR/100; CI for 2^nd year = P(R/100)(1 + R/100).

⇒ CI₁ = P × (20/100) = 0.2P

⇒ CI₂ = P × (20/100) × (1 + 20/100) = 0.2P × 1.2 = 0.24P

⇒ Difference = 0.24P − 0.2P = 0.04P

⇒ 0.04P = 1200

⇒ P = 1200 ÷ 0.04 = 120000 ÷ 4

⇒ P = 30000

∴ The correct answer is ₹30000.

Additional Information

CI for Particular Year

The difference between the CI of two consecutive years (e.g., 2^nd year and 1^st year) is simply the interest calculated on the previous year's interest: Diff = CI₁ × R/100.

Difference for 2 Years

The difference between CI and SI for 2 years is given by the formula D = P(R/100)².

Effective Rate Method

For a rate R%, the 1^st year interest is R% of P and the 2^nd year interest is [R + (R²/100)]% of P. The difference is (R²/100)% of P.

Shortcut Trick

Initial average = 25 years, New average = 25 + 3 = 28 years.

Total increase = (Initial persons × Increase in average) + (New persons × New average)

Sum of 3 new persons = (18 × 3) + (3 × 28) = 54 + 84 = 138 years.

Average of 3 new persons = 138 ÷ 3 = 46 years.

∴ The correct answer is 46 years.

Alternate Method

Given: Initial persons = 18, Initial average = 25 years. New persons added = 3. New average = 25 + 3 = 28 years.

Formula Used: Total Sum = Average × Number of people

⇒ Total age of 18 people = 18 × 25 = 450 years.

⇒ Total people after addition = 18 + 3 = 21 people.

⇒ Total age of 21 people = 21 × 28 = 588 years.

⇒ Sum of ages of 3 new persons = 588 − 450 = 138 years.

⇒ Average of 3 new persons = 138 ÷ 3 = 46 years.

∴ The correct answer is 46 years.

Additional Information

Weighted Average Formula

When two groups are combined, the resulting average is (n₁x₁ + n₂x₂) ÷ (n₁ + n₂).

Net Deviation Method

The sum of deviations from the average is always zero. New sum = (Change in average × Total final members) + (Old average × New members).

Shortcut Trick

Ratio of length and breadth = 2 : 3

Area ratio parts = 2 × 3 = 6 units²

6 units² = 96 cm² ⇒ 1 unit² = 16 ⇒ 1 unit = 4 cm

Perimeter = 2 × (2 + 3) units = 10 units = 10 × 4 = 40 cm

∴ The correct answer is 40 cm.

Alternate Method

Given: Ratio of Length (L) to Breadth (B) = 2 : 3

Formula Used: Area = L × B; Perimeter = 2(L + B)

⇒ Let Length = 2x and Breadth = 3x

⇒ Area = 2x × 3x = 96

⇒ 6x² = 96

⇒ x² = 16

⇒ x = 4 cm

⇒ Length = 2 × 4 = 8 cm and Breadth = 3 × 4 = 12 cm

⇒ Perimeter = 2(8 + 12) = 2(20) = 40 cm

∴ The correct answer is 40 cm.

Additional Information

Properties of Rectangle

A rectangle is a quadrilateral where opposite sides are equal and all internal angles are 90°.

Diagonal of Rectangle

The diagonal (d) can be calculated using the Pythagorean theorem: d = √(L² + B²).

Area and Perimeter relationship

For a fixed perimeter, a square (where L=B) has the maximum possible area among all rectangles.

2.5 × 2 = 5

⇒ 5 × 3 = 15

⇒ 15 × 4 = 60

⇒ 60 × 5 = 300

⇒ 300 × 6 = 1800

4 × 1 – 1 = 3

⇒ 3 × 2 – 2 = 4

⇒ 4 × 3 – 3 = 9

⇒ 9 × 4 – 4 = 32

⇒ 32 × 5 – 5 = 155

343 = 7³

729 = 9³

1331 = 11³

2197 = 13³

3375 = 15³

100

100 × 1.5 = 150

150 × 2 = 300

300 × 2.5 = 750

750 × 3 = 2250

The series follows the following pattern:

55 - 5 = 50

50 - 10 = 40

40 - 15 = 25

25 - 20 = 5

5 - 25 = -20

Given,

i) Only two people sit between P and R.

From the above statement we have two cases i.e. Case 1 and Case 2;

ii) S sits immediate right of R.

iii) Three people sit between S and T.

From the above statement, Case-2 is eliminated because there is no place for T.

iv) Two people sit between V and U.

v) Q sits second to the left of U.

vi) W sits immediate left of V.

S sits third to the left of U.

Hence, Third to left is the correct answer.

Given,

i) Only two people sit between P and R.

From the above statement we have two cases i.e. Case 1 and Case 2;

ii) S sits immediate right of R.

iii) Three people sit between S and T.

From the above statement, Case-2 is eliminated because there is no place for T.

iv) Two people sit between V and U.

v) Q sits second to the left of U.

vi) W sits immediate left of V.

Q sits fourth to the right of W.

Hence, Q is the correct answer.

Given,

i) Only two people sit between P and R.

From the above statement we have two cases i.e. Case 1 and Case 2;

ii) S sits immediate right of R.

iii) Three people sit between S and T.

From the above statement, Case-2 is eliminated because there is no place for T.

iv) Two people sit between V and U.

v) Q sits second to the left of U.

vi) W sits immediate left of V.

T sits second to the left of V

Hence, T is the correct answer.

Given,

i) Only two people sit between P and R.

From the above statement we have two cases i.e. Case 1 and Case 2;

ii) S sits immediate right of R.

iii) Three people sit between S and T.

From the above statement, Case-2 is eliminated because there is no place for T.

iv) Two people sit between V and U.

v) Q sits second to the left of U.

vi) W sits immediate left of V.

All of have 1 person between them except VW.

Hence, VW is the correct answer.

Distance between F and E = √(6² + 8²) = √(36 + 64) = √100 = 10 m

Hence, 10m is the correct answer. 82−−−−−−√√62−−√62−−√62

36+64−−−−−−−

Clearly, F is not in a straight line.

Hence, F is the correct answer.

Clearly, from the above diagram, we can say D is North-west of A.

Hence, North-west is the correct answer.

1. A is sitting in third place form the right end. 

2. There are 2 people between A and C. 

3. There is one person between C and D. 

4. E is to the second left of D. 

5. H is to the fifth right of C. 

6. A is exactly sitting between B and F who is to the right of A. 

7. G is to the second left of J who is to the second left of I.

Hence, E and H are sitting at the extreme ends.

1. A is sitting in third place form the right end. 

2. There are 2 people between A and C. 

3. There is one person between C and D. 

4. E is to the second left of D. 

5. H is to the fifth right of C. 

6. A is exactly sitting between B and F who is to the right of A. 

7. G is to the second left of J who is to the second left of I.

Hence, D is sitting seven to the left of H.

1. A is sitting in third place form the right end. 

2. There are 2 people between A and C. 

3. There is one person between C and D. 

4. E is to the second left of D. 

5. H is to the fifth right of C. 

6. A is exactly sitting between B and F who is to the right of A. 

7. G is to the second left of J who is to the second left of I.

Hence, there are 3 persons are sitting between C and F.

1. A is sitting in third place form the right end. 

2. There are 2 people between A and C. 

3. There is one person between C and D. 

4. E is to the second left of D. 

5. H is to the fifth right of C. 

6. A is exactly sitting between B and F who is to the right of A. 

7. G is to the second left of J who is to the second left of I.

Hence, the statement given only in option 2 is correct.

1. A is sitting in third place form the right end.

2. There are 2 people between A and C.

3. There is one person between C and D.

4. E is to the second left of D.

5. H is to the fifth right of C.

6. A is exactly sitting between B and F who is to the right of A.

7. G is to the second left of J who is to the second left of I.

Hence, J is exactly sitting between G and I.

The least possible diagram for the given statements is as follows

Conclusions:

I. Very few fans are grey → True (It is definitely true)

II. No fan is grey → False (It is definitely false)

Hence, only I follows.

The possible diagrams of the statements are,

I. Some cats are plates → False

II. No van is cat → True

III. Some plates are vans → True

Hence, only II and III follow.

The least possible Venn diagram for the given statements is as follows,

Conclusions:

I. Some figs are mangoes → True (as shown is figure)

II. Some skies are bats → False (it is possible but not definite)

III. Some skies being mangoes is a possibility → True

Hence, only I and III follow.

The least possible Venn diagram for the given statements is as follows

Conclusions:

I. No cap is a boat → False, as no cap is map.

II. Some boats being phones is a possibility→ True (it is possible but not definite)

Hence, only conclusion II follows.

Persons: Row 1 – A, B, C, D, E.

Row 2 – L, M, N, O, P.

Directions: North and South

B sits second to the right of D who is sitting in the middle of the row.

The person facing B sits to the immediate left of N.

L sits second to the right of N.

Only two persons sit between L and P.

E is not an immediate neighbour of D.

O does not face E.

C is not facing N.

Hence, O sits exactly in the middle of the row is true.

Persons: Row 1 – A, B, C, D, E.

Row 2 – L, M, N, O, P.

Directions: North and South

B sits second to the right of D who is sitting in the middle of the row.

The person facing B sits to the immediate left of N.

L sits second to the right of N.

Only two persons sit between L and P.

E is not an immediate neighbour of D.

O does not face E.

C is not facing N.

Hence, N is facing A.

Persons: Row 1 – A, B, C, D, E.

Row 2 – L, M, N, O, P.

Directions: North and South

B sits second to the right of D who is sitting in the middle of the row.

The person facing B sits to the immediate left of N.

L sits second to the right of N.

Only two persons sit between L and P.

E is not an immediate neighbour of D.

O does not face E.

C is not facing N.

Hence, E is facing M.

Persons: Row 1 – A, B, C, D, E.

Row 2 – L, M, N, O, P.

Directions: North and South

B sits second to the right of D who is sitting in the middle of the row.

The person facing B sits to the immediate left of N.

L sits second to the right of N.

Only two persons sit between L and P.

E is not an immediate neighbour of D.

O does not face E.

C is not facing N.

Except, 'PO' all others are neighbours of each other.

Hence, 'PO' is the odd one.

Persons: Row 1 – A, B, C, D, E.

Row 2 – L, M, N, O, P.

Directions: North and South

B sits second to the right of D who is sitting in the middle of the row.

The person facing B sits to the immediate left of N.

L sits second to the right of N.

Only two persons sit between L and P.

E is not an immediate neighbour of D.

O does not face E.

C is not facing N.

Hence, C is third to the left of B.

1. Immediately preceded by means immediately before or to come just before.
2. Immediately followed by means immediately after or to come just after. 3. Here, G @ I will not followed this condition and I is a vowel not consonant.

Given series:

Left Side # 6 B G @ I L 7 3 H A % © D F K E 8 J Q 1 * V T U 2 $ W Right Side

1. Symbols which are immediately followed by a consonant but not preceded by another symbol:

Condition to be checked:

Not symbol → Symbol → Consonant

6 B G @ I L 7 3 H A % © D F K E 8 J Q 1 * V T U 2 $ W

Here there are 2 Symbols which is immediately followed by a consonant but not preceded by another symbol: 1 * V, 2 $ W.

Hence, there are 2 symbols which is immediately followed by a consonant but not preceded by another symbol$.

Given series:

Left Side # 6 B G @ I L 7 3 H A % © D F K E 8 J Q 1 * V T U 2 $ W Right Side

Here the group is formed in which second element is to the immediate left of the first element, and the third element is immediate right of the first element.

Left Side # 6 B G @ I L 7 3 H A % © D F K E 8 J Q 1 *** V T** U 2 $ W Right Side

Hence, I L @ does not belong to the group.

Given series:

Left Side # 6 B G @ I L 7 3 H A % © D F K E 8 J Q 1 * V T U 2 $ W Right Side

1. If all the numbers are dropped:

B G @ I L H A % © D F K E J Q * V T U $ W

2. Fifth to the left of eleventh from the left.

As, Left – Left = Left

11^th from the left – 5^th from the left = 6^th from the left

Clearly, 6^th from the left is L.

Then, letter/ Symbol that is fifth to the left of eleventh from the left is ‘L’.