LIC AAO Prelims 28 Aug 2021 Shift 1 Memory Based Paper (Previous Year Paper)

Given points: P, Q, R, S, T, U, V, and W.

1)Point P is 10m north of point Q. Point Q is 15m west of point R.

2. Point S is 10m north of point R. Point S is 25m north of point T.

3. Point W is 8m east of S. Point U is 8m east of point T.

4.  Point U is 20m south of point V.

Therefore, the diagram is,  

 

Hence, S is in the northeast with respect to point Q.

Given points: P, Q, R, S, T, U, V, and W.

1)Point P is 10m north of point Q. Point Q is 15m west of point R.

2. Point S is 10m north of point R. Point S is 25m north of point T.

3. Point W is 8m east of S. Point U is 8m east of point T.

4.  Point U is 20m south of point V.

Therefore, the diagram is,  

 

On applying the Pythagoras theorem, we get the shortest distance between point R and V.

$〖RV〗^2=64+25$

$=√89$

$=√89 m$

Hence**, $√89$ m is the shortest distance between points R and V.**

Given points: P, Q, R, S, T, U, V, and W.

1)Point P is 10m north of point Q. Point Q is 15m west of point R.

2. Point S is 10m north of point R. Point S is 25m north of point T.

3. Point W is 8m east of S. Point U is 8m east of point T.

4.  Point U is 20m south of point V.

Therefore, the diagram is,  

 

Hence, the direction of point P is north – west with respect to point U.

Given points: P, Q, R, S, T, U, V, and W.

1)Point P is 10m north of point Q. Point Q is 15m west of point R.

2. Point S is 10m north of point R. Point S is 25m north of point T.

3. Point W is 8m east of S. Point U is 8m east of point T.

4.  Point U is 20m south of point V.

Therefore, the diagram is,  

Hence, the shortest distance between point W and Point V is 5m.

Given points: P, Q, R, S, T, U, V, and W.

1)Point P is 10m north of point Q. Point Q is 15m west of point R.

2. Point S is 10m north of point R. Point S is 25m north of point T.

3. Point W is 8m east of S. Point U is 8m east of point T.

4.  Point U is 20m south of point V.

Therefore, the diagram is,  

 

PQ: P is to the north of Q

SR: S is to the north of R

ST: S is to the north of T

VU: V is to the north U

RV: R is to the south west of V

Hence, RV is the odd one.

Given statements: P < Q ≥ G; G ≥ I ≥ E; C ≤ P; C > U

On combining: U < C ≤ P < Q ≥ G ≥ I ≥ E

Conclusions:

I. U > I → False (as U < C ≤ P < Q ≥ G ≥ I → thus clear relation between U and I cannot be determined)

II. P ≤ E → False (as P < Q ≥ G ≥ I ≥ E → thus clear relation between P and E cannot be determined)

Hence, neither I nor II is True.

Given statements: H = G > F; A < B ≥ X; B ≤ F

On combining: H = G > F ≥ B > A; H = G > F ≥ B ≥ X

Conclusions:

I. H ≥ A → False (as H = G > F ≥ B > A → H > A)

II. X < F → False (as F ≥ B ≥ X → F ≥ X)

Hence, neither I nor II is True.

Let us check each option:

1. G > R > A = D < E ≤ U → True

2. G ≥ R = A > D ≤ E < U → True

3. G = R > A ≥ D < E < U → True

Hence, option 4 is correct.

Given statements: P = Q ≤ R; T = P; T > S

On combining: S < P = Q = T ≤ R

I. Q < S → False (as S < P = Q)

II. R < S → False (as S < T ≤ R)

Therefore none follows.

Let's check each option:

1) P > Q ≥ R = S → P > S → True (It definitely follows)

2) P ≥ Q = R > S → P > S → True (It definitely follows)

3) P ≤ Q < R < S → P < S  → False (It does not follows)

4) P > Q ≥ R > S → P > S → True (It definitely follows)

Hence, the wrong sequence of symbols to satisfy the given condition is "≤, <, <".

The least possible Venn diagram is shown below:

I. All TV is Smart → False (It is possible but not definite, as no direct relationship between the two is given).

II. Only a few Smart is Small → False (It is possible but not definite).

Hence. Neither I nor II follows.

The least possible Venn diagram is: 

I. Some books are erasers → True (All Erasers are Books)

II. Some pens are erasers. → False (It is possible but not definite)

Hence, Only Conclusion I follows.

The least possible Venn diagram is:

Diagram:

I. Some apples are mangoes → False (it is possible but not definite)

II. Some grapes are bananas → True (Some grapes are apples and all apples are bananas)

Hence only conclusion II follows.

Given:

Ten persons: P, Q, R, S, T, U, V, W, X and Y 

Date: 18th and 27th

Months: January, March, April, September and November.

1. P attends the meeting on 18th of a month having 31 days.

2. There are three persons attending the meeting between P and T.

3. S attends the meeting two months before R.

4) R attends the meeting on 27th March. 

Case I:

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Case II:

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4) There are two persons attending the meeting between W and T. 

5. W does not attend the meeting in the month of September. (this eliminates case I)

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6. Neither Q nor Y attends the meeting in January. 

7. Q attends the meeting before Y but not in the same month.

8) X attends the meeting before W but after T. 

9) V attends the meeting in the month of April.

10. Neither V nor Y attends the meeting on the 18th of any month.

The final table is as follows:

 

Hence, R attends the meeting just after P.

Given:

Ten persons: P, Q, R, S, T, U, V, W, X and Y 

Date: 18th and 27th

Months: January, March, April, September and November.

1. P attends the meeting on 18th of a month having 31 days.

2. There are three persons attending the meeting between P and T.

3. S attends the meeting two months before R.

4) R attends the meeting on 27th March. 

Case I:

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Case II:

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4) There are two persons attending the meeting between W and T. 

5. W does not attend the meeting in the month of September. (this eliminates case I)

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6. Neither Q nor Y attends the meeting in January. 

7. Q attends the meeting before Y but not in the same month.

8) X attends the meeting before W but after T. 

9) V attends the meeting in the month of April.

10. Neither V nor Y attends the meeting on the 18th of any month.

The final table is as follows:

 

Hence, 2 persons attends meeting between T and W.

Given:

Ten persons: P, Q, R, S, T, U, V, W, X and Y 

Date: 18th and 27th

Months: January, March, April, September and November.

1. P attends the meeting on 18th of a month having 31 days.

2. There are three persons attending the meeting between P and T.

3. S attends the meeting two months before R.

4) R attends the meeting on 27th March. 

Case I:

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Case II:

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4) There are two persons attending the meeting between W and T. 

5. W does not attend the meeting in the month of September. (this eliminates case I)

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6. Neither Q nor Y attends the meeting in January. 

7. Q attends the meeting before Y but not in the same month.

8) X attends the meeting before W but after T. 

9) V attends the meeting in the month of April.

10. Neither V nor Y attends the meeting on the 18th of any month.

The final table is as follows:

 

Hence, Q attended the meeting on 18th April.

Given:

Ten persons: P, Q, R, S, T, U, V, W, X and Y 

Date: 18th and 27th

Months: January, March, April, September and November.

1. P attends the meeting on 18th of a month having 31 days.

2. There are three persons attending the meeting between P and T.

3. S attends the meeting two months before R.

4) R attends the meeting on 27th March. 

Case I:

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Case II:

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4) There are two persons attending the meeting between W and T. 

5. W does not attend the meeting in the month of September. (this eliminates case I)

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6. Neither Q nor Y attends the meeting in January. 

7. Q attends the meeting before Y but not in the same month.

8) X attends the meeting before W but after T. 

9) V attends the meeting in the month of April.

10. Neither V nor Y attends the meeting on the 18th of any month.

The final table is as follows:

 

Hence, W attended the meeting in the last.

Given:

Ten persons: P, Q, R, S, T, U, V, W, X and Y 

Date: 18th and 27th

Months: January, March, April, September and November.

1. P attends the meeting on 18th of a month having 31 days.

2. There are three persons attending the meeting between P and T.

3. S attends the meeting two months before R.

4) R attends the meeting on 27th March. 

Case I:

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Case II:

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4) There are two persons attending the meeting between W and T. 

5. W does not attend the meeting in the month of September. (this eliminates case I)

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6. Neither Q nor Y attends the meeting in January. 

7. Q attends the meeting before Y but not in the same month.

8) X attends the meeting before W but after T. 

9) V attends the meeting in the month of April.

10. Neither V nor Y attends the meeting on the 18th of any month.

The final table is as follows:

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Hence, more than 5 persons attended the meeting between U and X.

Eight persons: A, B, C, D, E, F, G and H.

1. A sits third to the right of D, who sits immediate right of H.

2. H faces north direction.

3. Two persons sit between A and E.

4. D does not sit at extreme end.

5. B sits immediate right of C and both face south direction.

6. B and A are not adjacent to each other.

7. G does not face south. So, case 1 is rejected.

G sits immediate left of D.

Hence, G is the correct answer.

Eight persons: A, B, C, D, E, F, G and H.

1. A sits third to the right of D, who sits immediate right of H.

2. H faces north direction.

3. Two persons sit between A and E.

4. D does not sit at extreme end.

5. B sits immediate right of C and both face south direction.

6. B and A are not adjacent to each other.

7. G does not face south. So, case 1 is rejected.

E sits third to the left of A.

Hence, E is the correct answer.

Eight persons: A, B, C, D, E, F, G and H.

1. A sits third to the right of D, who sits immediate right of H.

2. H faces north direction.

3. Two persons sit between A and E.

4. D does not sit at extreme end.

5. B sits immediate right of C and both face south direction.

6. B and A are not adjacent to each other.

7. G does not face south. So, case 1 is rejected.

One person sits between A and H.

Hence, One is the correct answer.

Eight persons: A, B, C, D, E, F, G and H.

1. A sits third to the right of D, who sits immediate right of H.

2. H faces north direction.

3. Two persons sit between A and E.

4. D does not sit at extreme end.

5. B sits immediate right of C and both face south direction.

6. B and A are not adjacent to each other.

7. G does not face south. So, case 1 is rejected.

All face north except D.

Hence, D is the correct answer.

Eight persons: A, B, C, D, E, F, G and H.

1. A sits third to the right of D, who sits immediate right of H.

2. H faces north direction.

3. Two persons sit between A and E.

4. D does not sit at extreme end.

5. B sits immediate right of C and both face south direction.

6. B and A are not adjacent to each other.

7. G does not face south. So, case 1 is rejected.

Five persons sit to the left of H.

Hence, Five is the correct answer.

Eight Persons: E, F, G, H, I, J, K, and L

Designations: MD, GM, AGM, DGM, Manager, AM, PO, and Clerk

1) Four designations are there between E and K, who is junior to E.

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2) Two designations are there between J and H.

3. G is two posts senior to H who is senior to K.

4. J is not the clerk in the bank.

5) Three designations are there between I and L.

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6) F is senior to at least four persons in the bank.

7. Neither L nor I are clerks.

As the above condition is not satisfied in case 1 and case 2, it will get canceled.

Final Arrangement:

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As either I or L can be the GM in the bank, it cannot be detrmined.

Hence, cannot be determined will be the correct answer.

Eight Persons: E, F, G, H, I, J, K, and L

Designations: MD, GM, AGM, DGM, Manager, AM, PO, and Clerk

1) Four designations are there between E and K, who is junior to E.

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2) Two designations are there between J and H.

3. G is two posts senior to H who is senior to K.

4. J is not the clerk in the bank.

5) Three designations are there between I and L.

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6) F is senior to at least four persons in the bank.

7) Neither L nor I are clerks.

As the above condition is not satisfied in case 1 and case 2, it will get canceled.

Final Arrangement:

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Hence, K is the Clerk in the bank.

Eight Persons: E, F, G, H, I, J, K, and L

Designations: MD, GM, AGM, DGM, Manager, AM, PO, and Clerk

1) Four designations are there between E and K, who is junior to E.

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2) Two designations are there between J and H.

3. G is two posts senior to H who is senior to K.

4. J is not the clerk in the bank.

5) Three designations are there between I and L.

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6) F is senior to at least four persons in the bank.

7) Neither L nor I are clerks.

As the above condition is not satisfied in case 1 and case 2, it will get canceled.

Final Arrangement:

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Hence, E is the AGM in the bank.

Eight Persons: E, F, G, H, I, J, K, and L

Designations: MD, GM, AGM, DGM, Manager, AM, PO, and Clerk

1) Four designations are there between E and K, who is junior to E.

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2) Two designations are there between J and H.

3. G is two posts senior to H who is senior to K.

4. J is not the clerk in the bank.

5) Three designations are there between I and L.

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6) F is senior to at least four persons in the bank.

7. Neither L nor I are clerks.

As the above condition is not satisfied in case 1 and case 2, it will get cancelled.

Final Arrangement:

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Hence, Four persons are senior to G in the bank.

Eight Persons: E, F, G, H, I, J, K, and L

Designations: MD, GM, AGM, DGM, Manager, AM, PO, and Clerk

1) Four designations are there between E and K, who is junior to E.

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2) Two designations are there between J and H.

3. G is two posts senior to H who is senior to K.

4. J is not the clerk in the bank.

5) Three designations are there between I and L.

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6) F is senior to at least four persons in the bank.

7) Neither L nor I are clerks.

As the above condition is not satisfied in case 1 and case 2, it will get cancelled.

Final Arrangement:

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Hence, H is the PO in the bank.

Seven friends: A, B, C, D, E, F and G

Colours: Yellow, Black, Blue, Red, Green, White and Purple.

Stores: P, Q, R, S, T, U and V.

1. B does not buy dress from store Q or R and likes whitecolour.

2. D buys dress from store V and is not blue or red in colour.

3. F buys dress from store P and is green in colour.

4. C and E buy dress from stores T and U respectively and are black and yellow in colour respectively.

5. G does not like blue colour. Thus A likes blue colour.

Now as D does not like red colour, G likes red colour.

Therefore D likespurplecolour.

6. Red dress is not brought from store Q.

Therefore A buys from store Q as neither B nor G buy from store Q.

As B does not buy dress from store R, he buys it from store S.

Thus G buy dress from store R.

Thus the only correct statement is ‘E does not buys dress from store P’.

Seven friends: A, B, C, D, E, F and G

Colours: Yellow, Black, Blue, Red, Green, White and Purple.

Stores: P, Q, R, S, T, U and V.

1. B does not buy dress from store Q or R and likes whitecolour.

2. D buys dress from store V and is not blue or red in colour.

3. F buys dress from store P and is green in colour.

4. C and E buy dress from stores T and U respectively and are black and yellow in colour respectively.

5. G does not like blue colour. Thus A likes blue colour.

Now as D does not like red colour, G likes red colour.

Therefore D likespurplecolour.

6. Red dress is not brought from store Q.

Therefore A buys from store Q as neither B nor G buy from store Q.

As B does not buy dress from store R, he buys it from store S.

Thus G buy dress from store R.

Thus the only correct combination is G-R-Red.

Seven friends: A, B, C, D, E, F and G

Colours: Yellow, Black, Blue, Red, Green, White and Purple.

Stores: P, Q, R, S, T, U and V.

1. B does not buy dress from store Q or R and likes whitecolour.

2. D buys dress from store V and is not blue or red in colour.

3. F buys dress from store P and is green in colour.

4. C and E buy dress from stores T and U respectively and are black and yellow in colour respectively.

5. G does not like blue colour. Thus A likes blue colour.

Now as D does not like red colour, G likes red colour.

Therefore D likespurplecolour.

6. Red dress is not brought from store Q.

Therefore A buys from store Q as neither B nor G buy from store Q.

As B does not buy dress from store R, he buys it from store S.

Thus G buy dress from store R.

Thus dress of blue colour is brought from store Q.

This option is not given thus answer is none of these.

Seven friends: A, B, C, D, E, F and G

Colours: Yellow, Black, Blue, Red, Green, White and Purple.

Stores: P, Q, R, S, T, U and V.

1. B does not buy dress from store Q or R and likes whitecolour.

2. D buys dress from store V and is not blue or red in colour.

3. F buys dress from store P and is green in colour.

4. C and E buy dress from stores T and U respectively and are black and yellow in colour respectively.

5. G does not like blue colour. Thus A likes blue colour.

Now as D does not like red colour, G likes red colour.

Therefore D likespurplecolour.

6. Red dress is not brought from store Q.

Therefore A buys from store Q as neither B nor G buy from store Q.

As B does not buy dress from store R, he buys it from store S.

Thus G buy dress from store R.

Thus B buys dress from store S.

Seven friends: A, B, C, D, E, F and G

Colours: Yellow, Black, Blue, Red, Green, White and Purple.

Stores: P, Q, R, S, T, U and V.

1. B does not buy dress from store Q or R and likes white colour.

2. D buys dress from store V and is not blue or red in colour.

3. F buys dress from store P and is green in colour.

4. C and E buy dress from stores T and U respectively and are black and yellow in colour respectively.

5. G does not like blue colour. Thus A likes blue colour.

Now as D does not like red colour, G likes red colour.

Therefore D likes purple colour.

6. Red dress is not brought from store Q.

Therefore A buys from store Q as neither B nor G buy from store Q.

As B does not buy dress from store R, he buys it from store S.

Thus G buy dress from store R.

Thus D likes purple colour.

The position will be as follow:

 

Thus, ‘1’ letter will be in same position.

Hence, DFE is the odd on.

Calculation∶

The series follows following pattern

1/(2¹) = 1/2

1/(2²) = 1/4

1/(2³) = 1/8

1/(2⁴) = 1/16

1/(2⁵) = 1/32

1/(2⁶) = 1/64

∴ The wrong number in the series is 1/5

Calculation:

The logic of the given series can be explained as:

2 × 1.5 = 3

3 × 2 = 6

6 × 2.5 = 15 

15 × 3 = 45

45 × 3.5 = 157.5

157.5 × 4 = 630

∴ Wrong term in given number series is 156.5.

Calculation:

The given number series follows this pattern:

2 + 4 = 6

6 + 5 = 11

11 + 6 = 17

17 + 7 = 24

24 + 8 = 32

32 + 9 = 41

∴ The wrong number in the given number series is 12

Calculation:

20

20 × 1 = 20

20 × 2 = 40

40 × 3 = 120

120 × 4 = 480

480 × 5 = 2400

2400 × 6 = 14400

∴ Wrong answer is 16800

Calculation:

20

20 + 9 = 29

29 + 18 = 47

47 + 36 = 83

83 + 72 = 155

155 + 144 = 299

∴ Wrong answer is 154

Given:

Cost of expenditure for a child = Rs. 20/day

Cost of expenditure for a woman = Rs. 40/day

Cost of expenditure for a man = Rs. 60/day

For other data refer to the table.

Concept:

Use simple addition and multiplication to calculate the value.

Calculation:

Total cost for children = 330 × 20

⇒ Total cost for children = Rs. 6600

Total cost for women = 450 × 40

⇒ Total cost for women = Rs. 18000

Total cost for men = 590 × 60

⇒ Total cost for men = Rs. 35400

Now, total cost for all = Total cost for children + Total cost for women + Total cost for men

⇒ Total cost of all for one day = Rs. 6600 + Rs. 18000 + Rs. 35400

⇒ Total cost of all for one day = Rs. 60000

Given:

Refer to the table.

Concept:

Simple addition and ratio concept

Calculation:

Number of men in states A and B = 180

Number of children in states E and F = 110

Now, the ratio = 180/110 = 18 : 11

∴ Required Ratio is 18 : 11

Given:

Refer to the table.

Concept:

Simple use of multiplication and percentage

Calculation:

Total cost of one day for men = 590 × 60

⇒ Total cost for men = Rs. 35400

Total cost of one days for children = 330 × 20

⇒ Total cost for children = Rs. 6600

Difference in their cost of expenditure on one day = Rs. 35400 – Rs. 6600

⇒ Difference in their cost of expenditure on one day = Rs. 28800

Percentage more by = (28800/6600) × 100 = 436.36%

∴ Required percentage = 436.36%

Given:

Refer to the table

Concept:

Simple use of multiplication and ratio            

Calculation:

Cost of total expenditure on women = 450 × 40 × 14

Cost of total expenditure on children = 330 × 20 × 14

⇒ Required ratio = (cost of total expenditure on women) / (cost of total expenditure on children

⇒ Required Ratio = (450 × 40 × 14) / (330 × 20 × 14)

⇒ Ratio = 30/11

Given:

Refer to the table.

Concept:

Simple use of multiplication and ratio

Calculation:

Number of women of states A, B and C together = 260

⇒ Total cost of expenditure of women of states A, B and C together = 14 × 260 × 40

Number of women of all states = 450

⇒ Total cost of expenditure of women of all states = 450 × 40 × 14

⇒ Required ratio = (14 × 260 × 40) / (450 × 40 × 14)

 ∴ Required ratio = 26 : 45

Given:

Time is taken by a goldsmith = 15 days

Formula used:

Efficiency = (Total work)/(Total time)

Calculation:

Let the efficiency (work is done per day) of a goldsmith be 'A'.

Let total work be 1 unit and work done in 15 days, the efficiency of a goldsmith:

(A × 15) = 1

⇒ A = 1/15

Work done in 5 days, the efficiency of a goldsmith:

(A × 5) = 1

⇒ A = 1/5

Increased efficiency will be as follows = 1/15 to 1/5

⇒ [{(1/5) - (1/15)}/1/15] × 100

⇒ 2 × 100

⇒ 200%

∴ 200% will have to increase its efficiency by the goldsmith to the neckless in 5 days.

Alternate Method

 

Old efficiency = 1 unit

New efficiency = 3 unit

Increment percent = (3 - 1)/1 × 100

⇒ 200%

∴ 200% will have to increase its efficiency by the goldsmith to the neckless in 5 days.

Given:

The speed of the train = 45 km/hr.

The length of the train = 140 meters.

Formula used:

Distance = Speed × Time

Concept used:

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

Calculation:

Speed of train = 45 × (5/18)

⇒ 25/2 m/s

According to the question:

Length of platform = [18 × (25/2) – 140]

⇒ 225 – 140

⇒ 85 m

Length of tunnel = [32 × (25/2) – 140]

⇒ 400 – 140

⇒ 260 m

Now, Required percentage = [{(260 – 85)/260} × 100]

⇒ (175/260) × 100

⇒ 67.30% 

⇒ 67% (approximately)

∴ The answer is 67%.

Given:

The perimeter of the rectangle = 200 m

Length = 80 m

Formula used:

Perimeter of a rectangle = 2(Length + Breadth)

Area of a rectangle = (Length × Breadth)

Calculation:

Here, length = 80 m, Perimeter = 200 m

Let, the breadth of the rectangle be x

According to the question, we can say,

2(80 + x) = 200

⇒ (80 + x) = 100

⇒ x = 20

Now, the area of the rectangle = (80 × 20) m² = 1600 m²

∴ The area of the rectangle is 1600 m².

Given:

E contributes  of the capital for 15 months and F received  of the profit.

Concept :

Ratio of profit = share in the capital of one partner × time period of investment ⦂ share in the capital of other partner × time period of investment

Calculation:

 ⇒ Total share of capital = 1

 ⇒ E contributed  of the capital

 ⇒ Capital contributed by F = {1 – (2/5)}

 ⇒ 3/5

Capital ratio = E : F

 ⇒ 2 : 3

Let amount invested by F for t months

Ratio of share of profit = E : F

 ⇒ 2 × 15 : 3 × t

 ⇒ 10 : t

F share is 1/3 (given)

 ⇒ t/(t + 10) = 1/3 ⇒ 3t = t + 10

 ⇒ 2t = 10

 ⇒ t = 5 months

Given:

Average runs scored by the batsman = 50

Number of matches = 4

Formula Used:

Average Runs scored by a batsman = Total number of runs scored / Total number of matches played

New Average = [(100 + percentage increase in average) / 100] × present average

Calculation:

Total number of runs scored by the batsman in the first four matches is given by:

50 × 4 = 200

The increase of 20% in the present average results in the new average as:

[(100 + 20) / 100] × 50 = 60

Now, the total number of matches = 4 + 1 = 5

The new total number of runs scored in the five-match series is given by:

60 × 5 = 300

The number of runs required to be scored by the batsman in the fifth match is obtained as:

300 - 200 = 100

∴ The number of runs required to be scored by the batsman in the fifth match is 100

Shortcut Trick

The number of runs needed to be scored in the fifth match is obtained as:

(5 × 1.2 × 50) - (4 × 50) = 100

Information analysis –

The total number of worker = 800

The Ratio of Man and Women = 2 : 6

Number of Man = 2/8 x 800 = 200

Number of women = 6/8 x 800 = 600

Only Hindi number Man = 15% of 200 = 30

Both language Hind and English = 30 × 5 = 150

Then only English number of Man = 200 – 150 – 30 = 20

Total number of worker = 26% of 800

= 26/100 × 800 = 208

Only Hindi number Women = 208 - 30 =178

And only English number of women = 600 × 25/100 = 150

Number of women speaking both languages Hindi and English = 600 - 178 – 150 = 272

Number of Man speak Hindi = 30

 And the number of Man speak Hindi and English = 150

Then total number Man Speak Hindi = 150 + 30 = 180

Information analysis –

The total number of worker = 800

The Ratio of Man and Women = 2 : 6

Number of Man = 2/8 x 800 = 200

Number of women = 6/8 x 800 = 600

Only Hindi number Man = 15% of 200 = 30

Both language Hind and English = 30 × 5 = 150

Then only English number of Man = 200 – 150 – 30 = 20

Total number of worker = 26% of 800

= 26/100 × 800 = 208

Only Hindi number Women = 208 - 30 = 178

And only English number of women = 600 × 25/100 = 150

Both language Hindi and English = 600 - 178 – 150 = 272 

From the above,

Only English number of Women = 150

Only Hindi number Women = 208 - 30 = 178

Total number of worker = 26% of 800

= 26/100 × 800 = 208

Then the percentage = 178/208 × 100

Percentage = 85.57%

The number of Men speaking both language = 150

The number of Women Speaking both language = 272

Then the ratio = 150 : 272

 The ratio = 75 : 136

Hence, the ratio = 75 : 136

The number of Women Speaking both language = 272

The Man Speaking Only Hindi = 30

Then the Difference = 272 – 30 = 242

Hence, the difference = 242

GIVEN:

Average age of Ashu and Amit 3 yrs ago = 20 yrs

Ashu age 5 years hence = 29 yrs

Amit's age = Ravi's age - 11

FORMULA USED:

Average = sum of observations/Total number of observations

CALCULATION:

Let present ages of Ashu and Amit be x and y respectively.

A.T.Q

[(x - 3) + (y - 3)]/2 = 20

x + y = 46 yrs

Present value of x = 29 - 5 = 24 yrs

y = 46 - 24 = 22 yrs

Ravi's age = 22 + 11 = 33 yrs

required sum = 33 + 24 = 57 yrs

∴ The answer will be 57 years.

Given:

Time = 8 years

Formula used:

If a sum of money becomes n times in t years at simple interest, then formula for calculating rate of interest is:

R = [100 (n -1) / t] %

Where n  and t represents the number of times amount becomes of principal and time.

Calculation:

= [100 (7-1) / 8] %

= 75%

∴ Rate is 75 %

Given:

In 300 gms alloy ratio of copper and zinc = 1 : 4

Calculation:

Let the quantity of copper to be added be X

The quantity of Copper in 300 gms alloy = (1/5) × 300 = 60 gm

and the quantity of Zinc in 300 gms alloy = (4/5) × 300 = 240 gm

According to question,

(60 + x)/240 = 4/3

⇒ 60 + x = 320

⇒ x = 320 - 60 = 260 gm

∴ The quantity of Copper to be added is 260 gm.

Given:

Distance covered = 96 km

Time taken to cover the distance = 8 hour

Speed of the boat in still water = 1.5 × speed of stream

Concept:

Let x be the speed of boat in still water and y be the speed stream

Upstream speed = x – y

Downstream speed = x + y

Speed = distance/time

Calculation:

Downstream speed = 96/8 = 12 km/hr

Downstream speed = speed of the boat in still water + speed of stream

⇒ Downstream speed = 1.5 × speed of stream + speed of stream = 2.5 × speed of stream

⇒ 12 = 2.5 × speed of stream

⇒ Speed of stream = 12/2.5 = 4.8 km/hr

⇒ Speed of the boat in still water = 1.5 × speed of stream           

⇒ Speed of the boat in still water = 1.5 × 4.8 = 7.2 km/hr

∴ Speed of the boat in still water is 7.2 km/hr

GIVEN:

Cost Price = Rs. 340 per litre

Label price = Rs. 408 per litre

Water as Impurity = 2/3 litre

Discount = 30%

FORMULA USED:

Profit percentage(%) = [(selling price – cost price)/cost price] × 100

CONCEPT:

When we have to calculate the profit percentage only and not the selling price, we can ignore the Cost Price

CALCULATIONS:

⇒ The trader is labelling Rs.408 on a beer whose price is Rs. 340. i.e. 68(20% of 340) rupees increasing.

⇒ Cost Price × Profit earned by labeling × profit earned by adding impurities × discount = Selling Price

⇒ 340 × (120/100) × (5/3) × (70/100) = Selling Price

⇒ 340 × 120 × 5 × 70/(100 × 3 × 100)

= 476

⇒ Profit percentage = [(476 – 340)/340] × 100 = 40%

∴ A trader will earn a 40% profit.

 

ALTERNATE METHOD:

Let, the COST PRICE of a beer be x.

The following operations are being made on x.

(a) labelling (b) impurities adding  (iii) discount

⇒ x × ((100 + 20)/100) × ((2 + 3)/3) × ((100 - 30)/100)

⇒ x × (120/100) × (5/3) × (70/100)

⇒ x × (6/5) × (5/3) × (7/10)

⇒ x × (7/5)

= 1.40 x

⇒ Profit percentage = (1.40 – 1) × 100 = 40%

∴ A trader will earn a 40% profit.

Given:

Number of male and female lecturer in each course

 

Formula used:

Percentage = (Part value/Original value) × 100

Calculation:

Number of female lecturers in B.Com course = 400

Number of female lecturers in B.SC course = 2000

Required percentage = [(400 + 2000 )/12000] × 100

⇒ (2400/12000) × 100

⇒ 20%

∴ The percentage of female lecturers working in B.COM & B.SC is 20%.

Given:

Number of male and female lecturer in each course

 

Calculation:

The Number of male lecturers in B.SC = 6000

The number of male lecturers in B.A course = 7200

The total number of male lecturers in B.Sc and B.A course

⇒ 6000 + 7200

⇒ 13200

∴ The number of male lecturers in B.sc and B.A course is 13200.

Given:

Number of male and female lecturer in each course

 

Formula used:

Percentage = (Part value/Original value) × 100

Calculation:

Number of male lecturers in M.Com course = 7200

Number of female lecturers in M.COM course = 4800

Required percentage

⇒ (7200/4800) × 100

⇒ 150%

∴ The male lecturers in the M.Com course are 150% of female lecturers.

Given:

Number of male and female lecturer in each course

 

 

Calculation:

Number of male lecturers in B.SC course = 6000

Total number of female lecturers in M.A and M.Com course

⇒ (3000 + 4800)

⇒ 7800

Required number = 7800 – 6000

⇒ 1800

∴ 1800 male lectures are less.

Given:

Number of male and female lecturer in each course

<br>

Formula used:

Average = (Sum of values/number of values)

Calculation:

Required average

⇒ (400 + 2000 + 3000)/3

⇒ 1800

∴ The average is 1800.

Given:

1256.06 + 1031.09 + 1087.98 = (?)³

Rules of Approximation:

1. If a number has digits to the right of the decimal less than 5, then just drop the digits to the right of the decimal. The number so obtained will be the approximated value.
2. If a number has digits to the right of the decimal more than 5, then just drop the digits to the right of the decimal and raise the remaining number by '1'.The number so obtained will be the approximated value.

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

1256.06 + 1031.09 + 1087.98 = (?)³

⇒ (?)³ = 1256 + 1031 + 1088

⇒ (?)³ = 3375

⇒ (?)³ = (15)³

⇒ ? = 15

∴ 15 should come in place of the question mark (?)

Given:

28.97 × 12.03 + 96.11 ÷ 5.97 - 2.99 = ?²

Rules of Approximation:

1. If a number has digits to the right of the decimal less than 5, then just drop the digits to the right of the decimal. The number so obtained will be the approximated value.
2. If a number has digits to the right of the decimal more than 5, then just drop the digits to the right of the decimal and raise the remaining number by '1'.The number so obtained will be the approximated value.

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

28.97 × 12.03 + 96.11 ÷ 5.97 - 2.99 = ?²

⇒ 29 × 12 + 96 ÷ 6 - 3 = ?²

⇒ 348 + 16 - 3 = ?²

⇒ ?² = 361

⇒ ?² = (19)²

⇒ ? = 19

∴ 19 should come in place of the question mark (?).

Given:

99.99 × 3.98 + (5.02)3 = ?2 - 100.11

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

99.99 × 3.98 + (5.02)3 = ?2 - 100.11

⇒ 100 × 4 + 5³ = ?² - 100

⇒ 400 + 125 = ?² - 100

⇒ ?² = 625

⇒ ?² = (25)²

⇒ ? = 25

∴ 25 should come in place of the question mark (?).

Given:

349.97 – ? = (15.04)2 + 89.97

Rules of Approximation:

1. If a number has digits to the right of the decimal less than 5, then just drop the digits to the right of the decimal. The number so obtained will be the approximated value.
2. If a number has digits to the right of the decimal more than 5, then just drop the digits to the right of the decimal and raise the remaining number by '1'.The number so obtained will be the approximated value.

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

349.97 – ? = (15.04)2 + 89.97

⇒ 350 – ? = (15)² + 90

⇒ 350 – ? = 225 + 90

⇒ ? = 350 – 315

⇒ ? = 35

∴ 35 should come in place of the question mark (?).

Given:

(3.98)3 + 25.97% of 350 - 10.99 × ? = 99.99

Rules of Approximation:

1. If a number has digits to the right of the decimal less than 5, then just drop the digits to the right of the decimal. The number so obtained will be the approximated value.
2. If a number has digits to the right of the decimal more than 5, then just drop the digits to the right of the decimal and raise the remaining number by '1'. The number so obtained will be the approximated value.

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

(3.98)3 + 25.97% of 350 - 10.99 × ? = 99.99

⇒ 4³ + (26/100) × 350 - 11 × ? = 100

⇒ 64 + 91 - 11 × ? = 100

⇒ 155 - 11 × ? = 100

⇒ 11 × ? = 55

⇒ ? = 5

∴ 5 should come in place of the question mark (?).

The correct answer is 'alleviating'.

Key Points

• The meaning of the word 'alleviating' is 'make (suffering, deficiency, or a problem) less severe; relieving.'
• For example, The medicines did nothing to alleviate her pain/suffering.
• The sentence means that the interviewers described some discussions as essential for developing a trustworthy relationship with the participant, as well as relieving their concerns/issues.
• So, the word 'alleviating' fits correctly in the given blank.
• Therefore, option 3 is the correct answer.

Additional Information

• Let's learn the meanings of the other words given in the options: 
• exacerbating: make (a problem, bad situation, or negative feeling) worse.
• hoodwink: deceive or trick.
• deferred: put off (an action or event) to a later time; postpone.
• squandering: waste (something, especially money or time) in a reckless and foolish manner.

The correct answer is 'exaggerate'.

Key Points

• The meaning of the word 'exaggerate' is 'represent (something) as being larger, better, or worse than it really is.'
• For example, The threat of attack has been greatly exaggerated.
• In the given sentence, 'to' should be followed by a verb.
• Except options 2 and 5, all other options are adjectives. Thus, they get eliminated.
• According to the context of the sentence, the word 'exaggerate' fits correctly in the given blank as it is talking about overestimating the percentage of rural migrants who settled in cities.
• Therefore, option 2 is the correct answer.

Additional Information

• Let's learn the meanings of the other words given in the options:
• sulky: morose, bad-tempered, and resentful; refusing to be cooperative or cheerful.
• gloomy: dark or poorly lit, especially so as to appear depressing or frightening.
• indomitable: impossible to subdue or defeat.
• compliment: a polite expression of praise or admiration.

The correct answer is 'neglected'.

Key Points

• The meaning of the word 'neglected' is 'not pay proper attention to; disregard.'
• For example, the old churchyard has been sadly neglected.
• The given sentence is talking about something that the person forgot to mention as he didn't pay much attention to it.
• So, the word 'neglected' fits correctly in the given blank.
• Therefore, option 5 is the correct answer.

Additional Information

• saw: past tense of the verb 'see'.
• see: perceive with the eyes.
• think: have a particular opinion, belief, or idea about someone or something.
• agree: have the same opinion about something; concur.

The correct answer is 'cope'. 

Key Points

• The meaning of the word 'cope' is '(of a person) deal effectively with something difficult.'
• For example - The roads are barely adequate to cope with the present traffic.
• The given sentence means that the hostages had been imprisoned for so long that they were unable to deal with the outside world.
• So, the word 'cope' fits correctly in the given blank.
• Therefore, option 3 is the correct answer.

Additional Information

• Let's learn the meanings of the other words given in the options:
• react: act in response to something.
• frame: formulate (a concept, plan, or system).
• settle: resolve or reach an agreement about (an argument or problem).
• release: allow or enable to escape from confinement; set free.

The correct answer is 'revealed'.

Key Points

• The meaning of the word 'revealed' is 'make (previously unknown or secret information) known to others.'
• For example, Kavya was forced to reveal Monu's whereabouts.
• The given sentence is talking about letting out some information about a person that was not known to everyone earlier.
• Therefore, the word 'revealed' fits correctly in the given blank.

Additional Information

• Let's learn the meanings of the other words given in the options: 
• secret: not known or seen or not meant to be known or seen by others.
• hide: put or keep out of sight.
• conceal: not allow to be seen; hide.
• cover: put something on top of or in front of (something).

The correct answer is 'BADC'.

Key Points

• While arranging the highlighted words, look for some grammatical or contextual connections:
• B will be the first word as the sentence is talking about Louisiana communities that have been damaged by a Hurricane.
• A will be the second word as it means that after the hurricane, Louisiana communities have again faced a new danger.
• D and C will be the third and fourth word respectively as they are talking about the danger that Louisiana communities faced i.e. the huge task of clearing wreckage and repairing the damage after the storm.
• Therefore, option 3 is the correct answer.
• Let's learn the meanings of some highlighted words:
• battered: (of a thing) damaged by something.
• massive: exceptionally large.

<br>

Correct Sentence:  Louisiana communities battered(B) by Hurricane Ida faced(A) a new danger as they began the massive(D) task of clearing debris and repairing(C) damage from the storm.

The correct answer is 'DCBA'.

Key Points

• While arranging the highlighted words, look for some grammatical or contextual connections:
• D will be the first word as the sentence is talking about the arrival of the passengers.
• C will be the second word as it is talking about the passengers who are arriving on tourist visas.
• B and A will be the third and fourth word respectively as the sentence is talking about taking compulsory PCR tests at the airport.
• Therefore, option 2 is the correct answer.
• Let's learn the meanings of some highlighted words:
• mandatory: required by law or mandate; compulsory.
• visas: an endorsement on a passport indicating that the holder is allowed to enter, leave, or stay for a specified period of time in a country.

<br>

Correct Sentence: Passengers arriving(D) on tourist visas(C) must take a mandatory(B) PCR test(A) at the airport.