SBI Clerk Prelims Memory Based Paper (Held On: 23 June 2018) (Previous Year Paper)

The correct answer is Option 1. 

Key Points

• Let's have a look at the spellings used in the above-given sentence:
• Essay is correctly used and means a description or paragraph written on a topic.
• Various means variety.
• Interesting means engaging.
• Wrighting should be replaced with writing as it conveys the correct meaning and usage.
• Hence, option 1 is the correct answer.

Let's have a look at the spellings used in the above given sentence:

Exciting means stimulating.

Spacious means roomy.

Studies is the third person form of the verb 'to study'.

Clauses should be replaced by classes as it conveys the correct meaning and usage.

Hence, option 3 is the correct answer.

All are correct.

The sentence is logically and grammatically correct. There is no error in the sentence.

In this question, a single sentence has been broken into five different parts and we need to find out the logical sequence. In order to do that, consider the following:

Decide on the opening phrase, first. The first part of the sentence contains the subject, i.e. part D as the sentence is based on the science of television. After this, D is joined with B with help of a conjunction 'and' and further it is joined by a pronoun 'its' which is in part C of the sentence. Thus, option 2 is the correct answer.

Correct Sentence: The science of television is highly sophisticated and based on a delicate system of filming and recording. It's working does not consist in storing or recording an image, it rather catches and reflects an image like a mirror, the image dies as soon as it is seen.

Key Points

• In the given sentence, there seem to be two subjects, i.e. in part B 'he' and in part C 'Shaw'.
• But, 'he' is a pronoun, used to replace the noun.
• Shaw, i.e. part C will thus follow the first part of the sentence.
• Thus, in the sentence, option 1 and 3 could be the answers.
• Now, we need to follow the last part of the sentence which follows the pronoun 'he' and is in continuity, i.e. part D.
• Thus, option 1 is the correct answer.

Correct Sentence: Shaw read the first few lines of the volume and was at once convinced that what he was reading was real poetry. He sent a few copies of the book to well-known poets and awaited their reaction.

In this question, a single sentence has been broken into five different parts and we need to find out the logical sequence. In order to do that, consider the following:

Decide on the opening phrase, first. The first part of the sentence contains the subject, here, part B is the opening part of the sentence. Thus, we will eliminate option 1,4 and 5. The first part will be in continuity with the part E. Now, since the subject is passive, the verb form will be followed by 'by' and the doer. So, part A will be the third part and the doer is contained in part D followed by part C. Thus, option 2 is the correct answer.

Correct Sentence: The child was so spoiled and overpampered by her indulgent parents that she pouted and became sullen when she did not receive all of their attention.

Using the elimination method, we can fairly see that part A is the central theme of the labelled parts, thus option 3 and 4 can be the correct answers.

Now, after part A, option C seems to be in an approximate continuity with the sentence. Thus, option 4 is neglected. Therefore, option 3 is the correct answer.

Correct Sentence: Smoke billowed up between the plants, the rising gale fanned the smoldering fire, everyone now knew there was a fire on board, flames broke out here and there, passengers were told to be ready to quit the ship, most people bore the shock bravely.

Instead of ordering the entire sentence, it is easier to find connections between one or two parts and then eliminating the options. So, in order to make the sentence meaningful, we must begin by finding connections between the words. 

The only interdependent meaning part is option C which begins with an explanation. Therefore, option 1, 3 and 4 can be considered. 

Now, after part C, part A and D are correlating parts and thus, option 4 is eliminated.  There, in between the last two options, option 1 will be correct answer because part E makes sense at the end of the sentence. Thus, option 1 is the correct answer.

Correct Sentence: As my jogging-enthusiast sister was often bothered by the neighborhood dogs, her husband started to accompany her on a bicycle on her daily run with a stick in hand to ward off any attackers.

If we read the whole passage carefully, then we can easily deduce that the author is positive for the things to come in future. He has clearly shown a 'moving forward' attitude. This is prominently depicted by option 3 and hence the answer.

Let's have a look at the meanings - 

Unbroken => Intact

Flat => Horizontal to the Earth's surface

Smooth => Even

Whole => Complete

Smashed => Broken

Thus, option 5 is the correct answer.

Author's opinion is clearly mentioned as he is very optimistic about future. What has happened is past and what is yet to come is future and should be looked forward to. Hence, option 2 is the correct answer. All other options don't convey the required sense.

Let's have a look at the meanings of the words - 

Gloomy=> Dim

Pessimistic => Negative 

Ominous => Threatening

Clearly, option 3 i.e. Positive is the correct answer.

It is evident from the passage what the author is trying to convey and through which tone. When someone talks about future, it's usually in a positive manner. The tone nowhere seems to be sarcastic, threatening, neutral or criticising. Hence, option 4 is the correct answer.

Let us examine the meanings of the above given alternatives:

Asked means to say something in order to obtain an answer or some information.

Confirmed means  a person who firmly establishes a particular habit, belief, or way of life and is unlikely to change his or her ways.

Invited means to make a polite, formal, or friendly request to someone to go somewhere or to do something.

Planned means to decide on and make arrangements for in advance.                      

Surprised means to feel or show surprise.

As in the above sentence, it is clearly indicated that the mother has planned the birthday, invited is the most apt option.

Hence, option 3 is the correct answer.

Let's have a look at the meanings of the given words:

Pounced=> Jump 

Attacked=> Strike; charge

Caught=> to catch

Wept=> to cry

Clearly, option 1 i.e. Pounced is the correct answer.

Let us examine the meanings, of the above given alternatives:

Reasonable means something to be as much as is appropriate or fair.

Moderate means to be average in amount, intensity, quality or degree.

Middling means to be neither very good nor bad.

Massive means to be large and heavy or solid.

Extravagant means lacking restraint in spending money or using resources.

As in the above sentence, it has been clearly stated that no expenses should be spared for the wedding, it is very apt for the filler to be extravagant.

Hence, option 5 is the correct answer.

Correct option- 1

Let's find out meaning of all the options :-

Appealed - A request for support, mercy, aid, etc.

Ordered - A command.

Asked - To put a question; to request for an information of someone or something.

Applied - To put something to use.

Knocked - To strike or hit something.

With respect to the context of the passage, the accused is a person who has committed the crime. So, he must have appealed the judge for his aid.

Thus, correct option is 1 i.e. Appealed. 

The accused appealed to the judge for mercy.

The correct answer is Intelligent

Key Points

Let's find out meaning of all the options:-

• Strong - Having great muscular power
• Pretty - Pleasing; attractive
• Intelligent - Having good mental understanding; Sharp
• Innocent - Someone who has not committed any crime
• Dedicated - Completely committed to something

With respect to the context of the sentence, it says that the person is so intelligent that he cannot be deceived(cheated) easily.

Thus, the correct option is 3 i.e. intelligent.

Intelligence helps you to come out of tricky situations and helps you to understand the ulterior(bad) motive of a cheat.

Thus intelligence and getting deceived are two opposite ideas.

The correct answer is 'Esteem'.

Key Points

• The word "Esteem" means respect or admiration. (सम्मान)
• The sentence talks about how the individual is viewed by his colleagues, which fits well with the meaning of "esteem."
• The other options: "savage," "frugal," "swoon," and "exodus" do not fit the context, as they do not convey the intended meaning of respect or admiration.

​Therefore, the correct answer is 'Option 3'.

Complete Sentence: He is held in high esteem by colleagues in his company.

Additional Information

• Savage (जंगली): means fierce or violent, unrelated to the context of respect.
• Frugal (मितव्ययी): means economical or thrifty, which does not fit the context of high regard.
• Swoon (बेहोश होना): means fainting or being overwhelmed by emotion, which doesn't fit the context of respect or admiration.
• Exodus (प्रस्थान): means a mass departure, which is unrelated to the context of high regard.

The sentence mentions a negative action thus the word here must be a suitable adjective. The meanings of the words are:

Steadfast=> loyal

Meritorious=> deserving reward or praise

Unconscionable=> unscrupulous

Pristine=>  in its original condition; unspoilt

Fortuitous=> Happening by chance

Thus option 3 is the word that fits here.

The correct answer is option (5)

• Here, the concept of "since" with two actions is brought under consideration.
• present perfect continuous(2^nd action) + since + simple past tense(1^st action).
• It means phrase after since will carry simple past tense.
• The point in time after since can also be expressed with a clause containing a verb in the past simple:
• He has been living here since he started school.
• They have been dating since they first met last May.

So, option 5 is the correct answer.

Correct Sentence: "They have been playing in the garden since it began to rain"

Correct option - 5

Key Points

• Here, concept of preposition is brought under consideration. Firstly, verb report takes preposition to with it. So, options 1, 2 & 4 are eliminated. Now, verb affect does not carry any preposition with it. Hence, option 3 is eliminated.
• When we want to convey that we have informed someone about something, we use the form "report to someone". So, "the patient reported to the doctor" is the correct usage.
• The verb "affect" does not require a preposition when a direct object follows it -- in this case, the pronoun "him". Therefore, "the medicine had severely affected him" is correct.
• So, putting it all together, option 5 is the most grammatically and structurally correct sentence.

So, option 5 is the correct answer.

Out of the given sentences, the only correct sentence is 1.

The rule when using 'neither-nor' is to use them after the main verb, and there is no need to use the main verb again and again. So, option 2 is incorrect.

Note that 'but' and 'for' are used differently in this sentence. 'But', which is usually a conjunction, is used as a preposition here. 'For', which is generally used as a preposition is used as a conjunction here, which is an archaic English usage. 'For', here, means 'because'.

The options 3 and 4 use the conjunctions 'than' and 'unless', which change the meaning of the sentence. Also, using 'either-or' in option 5 turns the sentence positive, and hence also changes the meaning. So, none of them, can be grammatically correct.

Therefore, the correct answer is option 1.

Out of the given sentences, the only correct sentence is 2.

To beg is to request someone. Such a verb does not require an additional preposition such as 'to', which means options 1 and 4 are incorrect.

The fish begged the fisherman, so the appropriate verb here becomes 'might', which indicates a possibility and not the simple future tense verb 'will'. So, option 3 is also incorrect.

Option 5 uses the passive form 'have been allowed', which is incorrect, given the context.

None of the other sentences are grammatically sound.

Therefore, the correct answer is option 2.

Out of the given sentences, the only correct sentence is 4.

The sentence uses the conjunction 'lest', which means to avoid the risk of something unpleasant. e.g. She did not speak out loud, lest she disturb anyone.

So, by using 'lest', the sentence means 'you must take care-so that you avoid the risk wherein-you fall.'

This means that the sentences that use a negative verb oughtn't, mustn't etc. are incorrect, as they change the meaning of the sentence. So, options 1 and 2 are incorrect.

Option 3 uses the preposition 'in', which is also incorrect, given the context. Option 5 uses the conjunction 'unless', which means 'except if', which also changes the meaning of the sentence and hence is incorrect. 

Therefore, the correct answer is option 4.

The error is in option 1 as 'illegible' means ' a handwriitng that is hard to read ' and here the word needed is 'eligible' means qualified for or the best person for marriage'

The error is in option 3 as 'allot' means to distribute and here ' a  lot' meaning 'many' is required. 

The error is in option 2 as 'addition' means to add something ; but the word needed here is 'edition' meaning published version of a book.

The error is in option 2 as 'ascent' means to climb high, and the word required here is 'accent' meaning the specific way that a community or citizen of any country speaks.

Here, we need a word to show the prices have risen. The use of 'sore' which means 'painful or aching' is incorrect. The correct word will be 'soar' which means 'high rise'. Thus the correct answer is that there is an error in part 4.

Considering both statements one by one :

Statement 1 Alone:

Given,

Average weight = 52

Statement 2 Alone:

Increase in Weight = 64 + 56 - 44 - 52 = 24

Increased Average = 1.2

⇒ No. of Students = 24/1.2 = 20

∴ if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.

Considering statement I:

SP = 22000

∴ CP = 22000 + 8500

= 30500

$loss\% = \frac{{loss}}{{CP}} \times 100$

$= \frac{{CP - SP}}{{CP}} \times 100$

\begin{array}{*{20}{c}} { = \frac{{30500 - 22000}}{{30500}} \times 100 = \frac{{8500}}{{30500}} \times 100} \end{array}

= 27.86%

Considering statement II:

Let SP = 5x and CP = 4x

It is given that SP = 22000

Hence, 5x = 22000

⇒ x = 22000/5

⇒ x = 4400

⇒ CP = 4x = 17600

Now,

$\begin{array}{l} Profit\% = \frac{{Profit}}{{CP}} \times 100\ = \frac{{SP - CP}}{{CP}} \times 100\ = \frac{{22000 - 17600}}{{17600}} \times 100 = \frac{{4400}}{{17600}} \times 100 \end{array}$

= 25%

∴ If the data either in statement l alone or in statement Il alone is sufficient to answer the question.

Considering the statements one by one :

Statement I

Diameter = Circumference – 90

⇒ 2r = 2πr – 90

⇒ 2πr – 2r = 90

⇒ πr – r = 45

⇒ r = 45/(π – 1)

∴ Area = πr² = π[45/(π – 1)]²

∴ Statement I is alone enough to answer the question.

⇒ Statement II

Perimeter = 77

⇒ 2l + 2b = 77

Also, l = r

There’s no way we can find r since l and b are unknown.

∴ Statement II cannot determine the question

Considering statement I:

Time taken by train to cross a pole of negligible length = 15 sec

This statement is not sufficient to answer as we do not know the speed of the train to place it in the below formula.

Distance = Speed × Time

OR

Length of train = Speed of train × Time

Length cannot be found by using statement A alone.

Considering statement II:

Speed of the train = 60 kmph = $60 \times \frac{{1000}}{{3600}}m/sec = \frac{{50}}{3};m/sec$

Here, we do not know the time. Hence, we cannot find the length of the train.

However, if we take both statements together,

Length of train = Speed of train ×Time

$= \frac{{50}}{3} \times 15$

= 250 m

∴ BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Considering statement I:

No of hours taken by A to do the job = 8 hours

⇒ Fraction of work done by A in 1 hour = $\frac{1}{8}$

Here, details about work done by A alone is not given and not details about B.

∴ Statements I alone is NOT sufficient.

Considering statement II:

No of hours taken by B to do the job = 10 hours

⇒ Fraction of work done by B in 1 hour = $\frac{1}{{10}}$

Here, details about work done by B alone is not given and not details about A.

∴ Statements (B) alone is NOT sufficient.

Considering statement I and II together:

Fraction of work done by both A and B in 1 hour = $\frac{1}{8} + \frac{1}{{10}} = \frac{{5 + 4}}{{40}} = \frac{9}{{40}}$

⇒ No of hours taken by B to do the job = $\frac{{40}}{9} = 4\frac{4}{9}$ hours

∴ BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Shortcut Trick

Ratio of Length (L) and Breadth (B) = 5 : 4

Difference in ratio units = 5 − 4 = 1 unit

Given difference = 10 m ⇒ 1 unit = 10 m

Sum of ratio parts (L + B) = 5 + 4 = 9 units

Perimeter = 2 × (L + B) = 2 × 9 units = 18 units

Perimeter = 18 × 10 = 180 m

∴ The correct answer is 180 m.

Alternate Method

Given:

Ratio of Length (L) to Breadth (B) = 5 : 4

Difference (L − B) = 10 m

Formula Used:

Perimeter of rectangle = 2 × (Length + Breadth)

Calculations:

⇒ Let Length = 5x and Breadth = 4x

⇒ 5x − 4x = 10

⇒ x = 10 m

⇒ Length (L) = 5 × 10 = 50 m

⇒ Breadth (B) = 4 × 10 = 40 m

⇒ Perimeter = 2 × (50 + 40)

⇒ Perimeter = 2 × 90 = 180 m

∴ The correct answer is 180 m.

Additional Information

Area of Rectangle

The total space occupied by the rectangle is given by Area = Length × Breadth.

Diagonal of Rectangle

The distance between opposite corners is calculated using Pythagoras theorem: Diagonal = √(Length² + Breadth²).

Perimeter vs Area Units

Perimeter is a linear measure (m, cm), while Area is a square measure (m², cm²).

Shortcut Trick

Let the highest odd number be x. Then the lowest even number is x + 3.

Three odd numbers: (x − 4), (x − 2), x → Sum = 3x − 6.

Four even numbers: (x + 3), (x + 5), (x + 7), (x + 9) → Sum = 4x + 24.

Difference: (4x + 24) − (3x − 6) = 35 ⇒ x + 30 = 35 ⇒ x = 5.

Sum of even numbers = 4(5) + 24 = 44.

∴ The correct answer is 44.

Alternate Method

Given: Four even numbers starting from x; Three odd numbers ending at y. x = y + 3.

Calculations:

⇒ Sum of Even = x + (x + 2) + (x + 4) + (x + 6) = 4x + 12

⇒ Sum of Odd = y + (y − 2) + (y − 4) = 3y − 6

⇒ (4x + 12) − (3y − 6) = 35

⇒ Substitute y = x − 3: (4x + 12) − [3(x − 3) − 6] = 35

⇒ 4x + 12 − [3x − 9 − 6] = 35

⇒ 4x + 12 − 3x + 15 = 35

⇒ x + 27 = 35 ⇒ x = 8

⇒ Sum of even numbers = 4(8) + 12 = 32 + 12 = 44

∴ The correct answer is 44.

Additional Information

Consecutive Numbers Properties

For consecutive even or odd numbers, the common difference is always 2. The sum of n consecutive numbers is equal to n × Average.

Average of Arithmetic Progression

The average of an Arithmetic Progression (AP) is (First term + Last term) ÷ 2. For an odd number of terms, it is exactly the middle term.

Summation Formula

Sum = (n ÷ 2) × [2a + (n − 1)d], where a is the first term, d is the common difference, and n is the number of terms.

Shortcut Trick

In Compound Interest, the amount grows by a constant multiplying factor over equal time intervals.

Time gap between 3 years and 5 years = 2 years. Ratio of amounts = 9000 ÷ 1000 = 9.

So, the 2-year multiplier is 9. This means for 1 year, the multiplier is √9 = 3.

Amount after 8 years = Amount after 5 years × (1-year multiplier)³ = 9000 × 3³.

Amount after 8 years = 9000 × 27 = 243000.

∴ The correct answer is 243000 rupees.

Alternate Method

Given: Amount after 3 years (A₃) = ₹1000, Amount after 5 years (A₅) = ₹9000.

Formula: A = P(1 + r/100)ⁿ

⇒ A₅ / A₃ = [P(1 + r/100)⁵] / [P(1 + r/100)³] = 9000 / 1000

⇒ (1 + r/100)² = 9

⇒ (1 + r/100) = √9 = 3

⇒ Amount after 8 years (A₈) = A₅ × (1 + r/100)^(8-5)

⇒ A₈ = 9000 × (3)³

⇒ A₈ = 9000 × 27

⇒ A₈ = 243000

∴ The correct answer is 243000 rupees.

Additional Information

Constant Ratio Property

In Compound Interest, the ratio of amounts at equal intervals of time remains constant. If amounts are A₁, A₂, A₃ at times t, 2t, 3t, then A₂/A₁ = A₃/A₂.

Effective Rate of Interest

When interest is compounded more than once a year, the effective rate is higher. Formula: R_eff = [ (1 + r/n)ⁿ − 1 ] × 100.

Difference between CI and SI

For 2 years, Difference = P(r/100)². For 3 years, Difference = P(r/100)² × (3 + r/100).

Shortcut Trick

Net change in Total Expenditure = Value of new month (July) − Value of removed month (January).

Net change = 1500 − 1200 = Rs. 300.

Change in Average = Net change ÷ Number of months = 300 ÷ 6 = Rs. 50.

New Average = Old Average + Change = 4200 + 50 = Rs. 4250.

∴ The correct answer is Rs 4250.

Alternate Method

Given: Average (Jan−June) = Rs. 4200, Jan expenditure = Rs. 1200, July expenditure = Rs. 1500.

Formula: Total = Average × Number of observations

⇒ Total expenditure (Jan−June) = 4200 × 6 = Rs. 25200

⇒ Total (Feb−June) = Total (Jan−June) − Jan = 25200 − 1200 = Rs. 24000

⇒ Total expenditure (Feb−July) = Total (Feb−June) + July = 24000 + 1500 = Rs. 25500

⇒ Average expenditure (Feb−July) = 25500 ÷ 6 = Rs. 4250

∴ The correct answer is Rs 4250.

Additional Information

Average Change Concept

When one value is replaced by another, the New Average = Old Average + (New Value − Old Value) ÷ Total Number.

Weighted Average

Used to find the combined average of two groups: (n₁x₁ + n₂x₂) ÷ (n₁ + n₂).

Shortcut Trick

Let the initial cost price of the item for Rajiv be 100.

The successive transactions are: 17% profit, then 9% profit, and finally 5% loss.

Selling Price to Chetna = 100 × (117 ÷ 100) × (109 ÷ 100) × (95 ÷ 100)

Selling Price to Chetna = 117 × 1.09 × 0.95 = 127.53 × 0.95 = 121.1535 ≈ 121.23

Overall Profit% = 121.23% − 100% = 21.23%

∴ The correct answer is 21.23%.

Alternate Method

Given:

Profit percentage of Rajiv = 17%

Profit percentage of Richa = 9%

Loss percentage of Shivani = 5%

Formula:

Net Percentage Change = a + b + (a × b ÷ 100)

For successive profit/loss, we apply the percentage change formula step-by-step.

⇒ Let the initial Cost Price for Rajiv = 100

⇒ Price paid by Richa = 100 × (117 ÷ 100) = 117

⇒ Price paid by Shivani = 117 × (109 ÷ 100) = 127.53

⇒ Price paid by Chetna = 127.53 × (95 ÷ 100) = 121.1535 ≈ 121.23

⇒ Total profit earned on the item = 121.23% − 100% = 21.23%

∴ The correct answer is 21.23%.

Additional Information

Successive Percentage Changes

When a value is changed by x% and then further changed by y%, the net percentage change is given by: [x + y + (x × y ÷ 100)]%.

Compound Profit Concept

Chain transactions behave identically to compounding interest, where each successive seller's selling price becomes the next buyer's cost price.

Given expression,

1110 + 246 - 10² = ?

1356 - 100 = ?

? = 1256

We know that:

$\sqrt[3]{{343}}$ = 7

The given expression after taking approximate values,

(7)² + √(? – 4) = 91

√(? – 4) = 91 - 49

√(? – 4) = 91 - 49 = 42

Squaring both sides

? - 4 = 1764

? = 1768

Given expression,

$4 - 5 \times \frac{1}{5} + 20 = ? - 16$

4 - 1 + 20 = ? - 16

3 + 20 = ? - 16

23 + 16 = ?

? = 39

√441 - √121 = √?

21 - 11 = √?

10² = ?

? = 100

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,

⇒ [(6.5)^{2 _} (1.2)²] = ?² - 8.19

⇒ (6.5 - 1.2)(6.5 + 1.2) = ?² - 8.19

⇒ 5.3 × 7.7 = ?² - 8.19

⇒ 40.81 = ?² - 8.19

⇒ ?² = 49

⇒ ? = 7

Concept Used:

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

Calculations:

Given expression is,

$\Rightarrow 5\frac{1}{6} - 3\frac{4}{9} + ? = \frac{7}{3} \times 4\frac{1}{6}$

$\Rightarrow {\rm{;}}\frac{{31}}{6} - \frac{{31}}{9} + ? = \frac{7}{3} \times \frac{{25}}{6}$

$\Rightarrow 31\left( {\frac{1}{6} - \frac{1}{9}} \right) + ;? = \left( {\frac{{175}}{{18}}} \right)$

$\Rightarrow {\rm{;}}31(\frac{3}{{54}}) + ? = \frac{{175}}{{18}}$

$\Rightarrow {\rm{;}}\frac{{31}}{{18}} + ? = \frac{{175}}{{18}}$

⇒ ? = 144/18

⇒ ? = 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, 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,

⇒ (81.27)² – (17.01)² = 7.84 × ?

We can write the given values as:

81.27 ≈ 81, 17.01 ≈ 17 and 7.84 ≈ 8

⇒ (81)² – (17)² = 7.84 × ?

⇒ (81 – 17)(81 + 17) = 7.84 × ?

⇒ 64 × 98 = 8 × ?

$\Rightarrow \frac{{64 \times 98}}{8} =:?$

∴ ? = 784

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,

⇒ 81.84 + 145.87 + 15.64 = 90.003 + 35.88 + ?

⇒ 82 + 146 + 16 = 90.003 + 35.88 + ?

⇒ 244 = 90 + 36 + ?

⇒ 244 = 126 + ?

⇒ ? = 244 – 126

∴ ? = 118

Follow the 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:

2.448 + 88 × 0.6 ÷ 14.2

⇒ 2.5 + 88 × 0.6 ÷ 14

⇒ 2.5 + 88 × 0.042

⇒ 2.5 + 3.696

⇒ 6.196 ≈ 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,

⇒ (7.98 % of 7200) ÷ 24 = 11.99 % of ?

$\Rightarrow \left( {\frac{8}{{100}} \times 7200} \right) \div 24 = \frac{{12}}{{100}} \times ?$

$\Rightarrow \frac{{72; \times 8}}{{24}} = \frac{{12}}{{100}} \times ?$

⇒ 24 × 100 = 12 × ?

⇒ ? = (24 × 100)/12

⇒ ? = 200

Shortcut Trick

Profit Ratio = (Capital₁ × Time₁) : (Capital₂ × Time₂)

8 : 7 = (60000 × 12) : (Capital_S × 9)

8 : 7 = 720000 : 9C_S

9C_S × 8 = 720000 × 7 ⇒ C_S = 70000

Difference = 70000 − 60000 = 10000

∴ The correct answer is Rs. 10000.

Alternate Method

Given → Harish Investment = Rs. 60000, Harish Time = 12 months, Sanish Time = 9 months, Profit Ratio = 8 : 7. Formulas: Profit = Investment × Time | Investment = Profit ÷ Time

⇒ Let Sanish investment be x. ⇒ Ratio of investments = (60000 × 12) / (x × 9) = 8 / 7. ⇒ 720000 / 9x = 8 / 7 ⇒ 80000 / x = 8 / 7. ⇒ x = (80000 × 7) ÷ 8 = 70000. ⇒ Sanish invested 70000 − 60000 = 10000 more than Harish.

∴ The correct answer is Rs. 10000.

Additional Information

Partnership Principles

In a partnership, the profit is distributed in the ratio of the product of investment and duration (Time).

Investment Ratio

If profit ratios and time ratios are known, the investment ratio can be calculated as (P1/T1) : (P2/T2).

Shortcut Trick

Total Distance = 5000 km

Total Time = (2000 ÷ 40) + (1500 ÷ 60) + (1500 ÷ 30) = 50 + 25 + 50 = 125 hours

Average Speed = 5000 ÷ 125 = 40 km/hr

∴ The correct answer is 40 km/hr.

Alternate Method

Given:

Total Distance (D) = 5000 km

Part 1: D₁ = 2000 km, S₁ = 40 km/hr

Part 2: D₂ = 1500 km, S₂ = 60 km/hr

Part 3: D₃ = 5000 − (2000 + 1500) = 1500 km, S₃ = 30 km/hr

Formula Used:

Average Speed = Total Distance ÷ Total Time

Time = Distance ÷ Speed

Calculations:

⇒ T₁ = 2000 ÷ 40 = 50 hours

⇒ T₂ = 1500 ÷ 60 = 25 hours

⇒ T₃ = 1500 ÷ 30 = 50 hours

⇒ Total Time = 50 + 25 + 50 = 125 hours

⇒ Average Speed = 5000 ÷ 125 = 40 km/hr

∴ The correct answer is 40 km/hr.

Additional Information

Average Speed Formula

Average speed is always (Total Distance) ÷ (Total Time) and is NOT the arithmetic mean of individual speeds.

Equal Distance Case

If two equal distances are covered at speeds u and v, Average Speed = (2 × u × v) ÷ (u + v).

Unit Conversion

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

Shortcut Trick

Speed of Boat (u) = 8 kmph, Speed of Stream (v) = 2 kmph

Downstream Speed (u+v) = 10 kmph, Upstream Speed (u-v) = 6 kmph

Use Distance Formula: D = [Total Time × (u² − v²)] ÷ (2 × u)

D = [(24/60) × (8² − 2²)] ÷ (2 × 8) = [0.4 × 60] ÷ 16 = 24 ÷ 16 = 1.5 km

∴ The correct answer is 1.5 km.

Alternate Method

Given: Speed in still water (u) = 8 kmph, Speed of river (v) = 2 kmph, Total time = 24 minutes = 24/60 hours = 0.4 hours.

Formula Used: Time = Distance ÷ Speed

⇒ Downstream Speed = 8 + 2 = 10 kmph

⇒ Upstream Speed = 8 − 2 = 6 kmph

⇒ Let the distance be D.

⇒ D/10 + D/6 = 24/60

⇒ (3D + 5D)/30 = 0.4

⇒ 8D = 0.4 × 30

⇒ 8D = 12

⇒ D = 12/8 = 1.5 km

∴ The correct answer is 1.5 km.

Additional Information

Average Speed in Boats

The average speed for a round trip is (u² − v²) / u, which is different from 2xy/(x+y) because the distances are the same but the speeds are u+v and u−v.

Relative Speed in Water

Downstream speed = Speed of boat + Speed of stream. Upstream speed = Speed of boat − Speed of stream.

Speed Conversion

To convert kmph to m/s, multiply by 5/18. To convert minutes to hours, divide by 60.

Shortcut Trick

Ratio (G:D) 5 years ago = 6 : 1 | Ratio 10 years later = 3 : 1

Make the ratio difference (6−1=5 and 3−1=2) same by multiplying by 2 and 5 respectively.

New Ratios: 12 : 2 and 15 : 5. Difference in units = 3 units = 15 years ⇒ 1 unit = 5 years.

Diksha 5 yrs ago = 2 × 5 = 10; GF 5 yrs ago = 12 × 5 = 60. Present ages: 15 and 65.

∴ The correct answer is 3 : 13.

Alternate Method

Let Diksha's age 5 years ago be x and Grandfather's age be 6x.

⇒ Present ages: Diksha = x + 5, Grandfather = 6x + 5.

⇒ Ages 10 years from now: Diksha = x + 15, Grandfather = 6x + 15.

⇒ According to question: 6x + 15 = 3 × (x + 15)

⇒ 6x + 15 = 3x + 45 ⇒ 3x = 30 ⇒ x = 10.

⇒ Present age of Diksha = 10 + 5 = 15 years.

⇒ Present age of Grandfather = 6(10) + 5 = 65 years.

⇒ Ratio = 15 : 65 = 3 : 13.

∴ The correct answer is 3 : 13.

Additional Information

Age Difference Invariance

The difference between the ages of two people remains constant regardless of the number of years passed.

Ratio Balancing Method

To solve age problems quickly, multiply the ratios so that the difference between the terms in each ratio becomes equal.

The pattern of the given series is:

⇒ 3 × 2 - 2 = 4

⇒ 4 × 3 -  3 = 9

⇒ 9 × 4 - 4 = 32

⇒ 32 × 5 - 5 = 155 = ?

⇒ 155 × 6 - 6 = 930 - 6 = 924 

∴ ? = 155

The pattern of the given series is:

⇒ 12 × 1 = 12

⇒ 12 × 3 = 36

⇒ 36 × 5 = 180

⇒ 180 × 7 = 1260 = ?

⇒ 1260 × 9 = 11340

∴ ? = 1260

7.2 - 6 = 1.2

8.7 - 7.2 = 1.5  (1.2 + 0.3) 

10.8 - 8.7 = 2.1  (1.5 + 0.6)

14.1 - 10.8 = 3.3   (2.1 + 1.2)

14.1 + 5.7(3.3 + 2.4) = 19.8  = ?

86 - 16 = 70

149 - 86 = 63

205 - 149 = 56

? = 205 + 49 = 254

The pattern of the given series:

⇒ 1² + 11 = 1 + 11 = 12

⇒ 11² + 21 = 121 + 21 = 142

⇒ 21² + 31 = 441 + 31 = 472

⇒ 31² + 41 = 961 + 41 = 1002

⇒ 41² + 51 = 1681 + 51 = 1732 = ?

Shortcut Trick

Speed of Train A = 72 km/h = 72 × 5/18 = 20 m/s. Length of A = 20 × 72 = 1440 m.

Length of Train B = 1440 − 240 = 1200 m.

Speed of Train B = 60 km/h = 60 × 5/18 = 50/3 m/s.

Time for B = 1200 ÷ (50/3) = 1200 × 3 ÷ 50 = 24 × 3 = 72 seconds.

∴ The correct answer is 72 sec.

Alternate Method

Given: Speed of Train A (S_A) = 72 km/h, Time to cross pole (T_A) = 72 sec, Speed of Train B (S_B) = 60 km/h, Length difference = 240 m.

Formula Used: Length = Speed × Time; Time = Length ÷ Speed; 1 km/h = 5/18 m/s.

⇒ Speed of Train A in m/s = 72 × (5/18) = 20 m/s

⇒ Length of Train A (L_A) = Speed × Time = 20 × 72 = 1440 m

⇒ Length of Train B (L_B) = L_A − 240 = 1440 − 240 = 1200 m

⇒ Speed of Train B in m/s = 60 × (5/18) = 50/3 m/s

⇒ Time taken by Train B (T_B) = L_B ÷ S_B = 1200 ÷ (50/3)

⇒ T_B = 1200 × 3 ÷ 50 = 24 × 3 = 72 sec

∴ The correct answer is 72 sec.

Additional Information

Unit Conversion

To convert speed from km/h to m/s, multiply by 5/18. To convert m/s to km/h, multiply by 18/5.

Train Crossing a Pole

When a train crosses a stationary object of negligible length (pole, man, tree), the distance traveled is equal to the length of the train itself.

Relative Speed

If two trains cross each other in opposite directions, relative speed is S₁ + S₂. In the same direction, it is |S₁ − S₂|.

Total marks obtained by James and Mark are 15 and 24, respectively.

Total marks obtained by Shane = (1 × 3 + 5× 2 + 3 × 5) = 28

Total marks obtained by Ricky = (1 × 5 + 12× 2 + 1 × 5) = 34

⇒ All of them have scored at least 15 marks.

Shane and Ricky have passed as they have answered correctly at least one question of each category.

Mark has not passed as he did not answer correctly any question of 1 mark.

Suppose James answered T questions of 5 marks correctly.

⇒ (2 × 1 + 4 × 2 + T× 5) = 15

⇒ T = (15 - 10)/5 = 1

⇒ James has also passed as he has answered correctly at least one question of each category.

∴ 3 students have passed.

Suppose Mark answered T questions of 2 marks correctly.

⇒ (T × 2 + 2 × 5) = 24

⇒ T = (24 – 10)/2 = 7

∴ Average number of marks scored by four students answering 2 marks questions = 2 × [(5 + 4 + 7 + 12)/4] = 2 × 7 = 14

Suppose James answered T questions of 5 marks correctly.

⇒ (2 × 1 + 4 × 2 + T× 5) = 15

⇒ T = (15 – 10)/5 = 1

⇒ James answered 1 question of 5 marks correctly, while Shane answered 3. Ratio will be 1 : 3.

James correctly answered 4 questions of 2 marks.

Suppose Mark answered T questions of 2 marks correctly.

⇒ (T × 2 + 2× 5) = 24

⇒ T = (24 - 10)/2 = 7

∴ Number of 2 marks questions answered correctly by James and Mark together = 4 + 7 = 11

Total marks obtained by James and Mark are 15 and 24, respectively.

Total marks obtained by Shane = (1 × 3 + 5 × 2 + 3 × 5) = 28

Total marks obtained by Ricky = (1 × 5 + 12 × 2 + 1 × 5) = 34

∴ Ricky obtained maximum marks.

Odd series = 1, 3, 5, 7,

Even series = 2, 4, 6,

Odd Series = 3, 5, 7,

Even series = 2, 4,

Odd Series = 5, 7,

Even Series = 2,

Odd sereis = 7 =?

Word: DYNAMICS 

on Arranging as per dictionary: ACDIMNSY

Only one alphabet whose positions are unchanged is M

Hence, one is the answer.

Given Word: INEVITABLE 

2^nd letter = N; 3^rd letter = E; 6^th letter = T

Letters have given: N, E, T

Possible words: NET, TEN 

Hence, two words can be made, and the answer is Y.

Given Series: M J % 4 T E K I 9 # O A $ Q 3 8 N 5 U 7 W ⋆ B @ D F © 1 Z 6 H

Question series:

J4E   I#A    Q85   7⋆@   ?

Here, ‘J4E’ have J, J + 2 unit = ‘4’, ‘4’ + 2 unit = E

E + 2 unit = I, I + 2 unit = #, # + 2 unit = A ⇒ I#A is 2^nd element

A + 2 unit = Q, Q + 2 unit = ‘8’, ‘8’ + 2 unit = ‘5’ ⇒ Q85 is 3^rd element

‘5’ + 2 unit = 7, ‘7’ + 2 unit = ⋆, ⋆ + 2 unit = @ ⇒ 7⋆@ is 4^th element

For 5^th element: @ + 2 unit = F, F + 2 unit = ‘1’, ‘1’ + 2 unit = ‘6’.

So, F16 is the next term$.

Given Series: M J % 4 T E K I 9 # O A $ Q 3 8 N 5 U 7 W ⋆ B @ D F © 1 Z 6 H

1. I 9 E: I and 9 are consecutive, E = ‘I’ - 2 unit.

2. 7 W 5: 7 and W are consecutive, 5 = ‘7’ - 2 unit.

3. © 1 D: © and 1 are consecutive, D = ‘©’ - 2 unit.

4. Q A 3: Q and A are not consecutive.

5. E K 4: E and K are consecutive, 4 = ‘E’ - 2 unit.

The pattern followed is first two elements are consecutive to each other, third element is - 2 of 1^st element. Hence, (Q A 3) is odd-one out$.

Given Series: M J % 4 T E K I 9 # O A $ Q 3 8 N 5 U 7 W ⋆ B @ D F © 1 Z 6 H

Removing symbols:

(Left End) M J 4 T E K I 9 O A Q 3 8 N 5 U 7 W B D F 1 Z 6 H (Right End)

12^th from left end = 3

4^th to left of ‘3’ = 9.

Hence answer is 9$.

Given Series: M J % 4 T E K I 9 # O A $ Q 3 8 N 5 U 7 W ⋆ B @ D F © 1 Z 6 H

Removing numbers:

(Left End) M J % T E K I # O A $ Q N U W ⋆ B @ D F © Z H (Right End)

⇒ 13^th from the right end = $

⇒ 6^th to right of ‘$’ = B

Hence answer is ‘B’.

Given Series: M J % 4 T E K I 9 # O A $ Q 3 8 N 5 U 7 W ⋆ B @ D F © 1 Z 6 H

Pattern to look for: Number → Symbols → Vowel

Such Symbols: #.

Hence only one such symbol is there$.

Friends: P, Q, R, S, T, U and V are seven friends.

1. U is shorter than only one person.

__ > U > __ > __ > __ > __ > __

2. P is taller than Q and T, but P is not the tallest.

3. S is taller than only V.

(Now leftover is R therefore R is tallest)

R > U > P > Q/T  > Q/T > S > V

Hence, “P” is 3^rd tallest among them.

Using the following notations, we can draw the family tree,

1. M is the only son of X.

2. C is the wife of X.

3. None of the daughters of X is married.

4. S and Y are the daughters of C.

5. C is the daughter of W and R.

6. Q is the grandson of C.

7. D is the mother of X.

As per family diagram D is Mother-in-law of C.

Using the following notations, we can draw the family tree,

1. M is the only son of X.

2. C is the wife of X.

3. None of the daughters of X is married.

4. S and Y are the daughters of C.

5. C is the daughter of W and R.

6. Q is the grandson of C.

7. D is the mother of X.

I) Y is Brother of M. ⇒ False (as Y is sister of M)

II) S is the granddaughter of D. ⇒ True

III) R is Father-in-Law of M.⇒ False (as per family diagram gender of R is not defined therefore R is either father-in-law or mother-in-law of M.)

Thus, only Statement II is definitely correct.

Using the following notations, we can draw the family tree,

1. M is the only son of X.

2. C is the wife of X.

3. None of the daughters of X is married.

4. S and Y are the daughters of C.

5. C is the daughter of W and R.

6. Q is the grandson of C.

7. D is the mother of X.

Hence, S is the aunt of Q.

Based on given information direction diagram can be traced as,

Hence, point F is South - East with respect to point B.

Based on given information direction diagram can be traced as,

Hence, A is 5 meter to the west of F.

Based on given information direction diagram can be traced as,

Hence, point Z is North - West with respect to point E.

Sushmita remembers that her birthday falls between April and October.

Therefore, Sushmita Birthday = May or June or July or August or September.

Zahida remembers that Sushmita’s birthday falls in between April and July.

Therefore, Sushmita Birthday = May or June

Box: S, T, U, V, W, X and Y.

1. There are 4 boxes between T and W.​

2. There are 2 boxes between W and Y.

3. Box U is kept above V.

4. Only one box is between U and V.

5. U is not immediately above Y.

6. U is not the topmost box.

7) As many boxes are between T and V is as between W and S.

Only, box X is left which will be placed between S and Y.

Above arrangement will be the final arrangement.

Hence, none will be kept below V, as V is the bottom-most box.

Box: S, T, U, V, W, X and Y.

1. There are 4 boxes between T and W.

2) There are 2 boxes between W and Y.

3. Box U is kept above V.

4. Only one box is between U and V.

5. U is not immediately above Y.

6. U is not the topmost box.

7) As many boxes are between T and V is as between W and S.

Only, box X is left which will be placed between S and Y.

Above arrangement will be the final arrangement.

As no box is kept between S and X, therefore none is the correct answer.

Box: S, T, U, V, W, X and Y.

1. There are 4 boxes between T and W.

2) There are 2 boxes between W and Y.

3. Box U is kept above V.

4. Only one box is between U and V.

5. U is not immediately above Y.

6. U is not the topmost box.