LIC AAO Prelims Memory Based Paper Shift 2 (Held on: 17 Feb 2023) (Previous Year Paper)

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

Months - January to August 

1) G was born in a month that has 31 days but not in the month of May. 

2) There is a gap of one month between G and A.

3. A born somewhere after G.

4. B was born in the month which has the least number of days.

 

5. There is a gap of two months between A and H.

6. E was born immediately after C.

7. Number of persons born before E is one more than the number of person born after E.

(This will eliminate Case 2)

 

8. F born before D.

 

Hence, three persons were born before C.

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

Months - January to August 

1) G was born in a month that has 31 days but not in the month of May. 

2) There is a gap of one month between G and A.

3. A born somewhere after G.

4. B was born in the month which has the least number of days.

 

5. There is a gap of two months between A and H.

6. E was born immediately after C.

7. Number of persons born before E is one more than the number of person born after E.

(This will eliminate Case 2)

 

8. F born before D.

 

Hence, G was born in the month of January.

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

Months - January to August 

1) G was born in a month that has 31 days but not in the month of May. 

2) There is a gap of one month between G and A.

3. A born somewhere after G.

4. B was born in the month which has the least number of days.

 

5. There is a gap of two months between A and H.

6. E was born immediately after C.

7. Number of persons born before E is one more than the number of person born after E.

(This will eliminate Case 2)

 

8. F born before D.

 

Hence, C and H were born in the month which has 30 days.

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

Months - January to August 

1) G was born in a month that has 31 days but not in the month of May. 

2) There is a gap of one month between G and A.

3. A born somewhere after G.

4. B was born in the month which has the least number of days.

 

5. There is a gap of two months between A and H.

6. E was born immediately after C.

7. Number of persons born before E is one more than the number of person born after E.

(This will eliminate Case 2)

 

8. F born before D.

 

Hence, D was immediately after F..

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

Months - January to August 

1) G was born in a month that has 31 days but not in the month of May. 

2) There is a gap of one month between G and A.

3. A born somewhere after G.

4. B was born in the month which has the least number of days.

 

5. There is a gap of two months between A and H.

6. E was born immediately after C.

7. Number of persons born before E is one more than the number of person born after E.

(This will eliminate Case 2)

 

8. F born before D.

 

Let's check each option:

1) G was born in the month of March. → False

2) There are two persons between A and E. → False

3) E was born immediately before H. → True

4) H was born in the month of July. → False

Hence, E was born immediately before H is true.

Given Statements: M > L = O < K; O < Q ≥ S

On Combining: M > L = O < Q ≥ S; K > L = O < Q ≥ S

Conclusions: 

I. K > Q → False (As K > L = O < Q ≥ S, there is no relation between K and Q because of the opposite sign between K and Q)

II. S > M → False (As M > L = O < Q ≥ S, there is no relation between S and M because of the opposite sign between S and M)

Hence, Neither I nor II follows.

Given statement: P ≤ Q < R = S; P ≥ L < M; N > S

On combining: M > L ≤ P ≤ Q < R = S < N

Conclusion:

I. L < Q → (L ≤ P ≤ Q → L ≤ Q The given conclusion is false)

II. Q = L → (L ≤ P ≤ Q → L ≤ Q The given conclusion is false)

Hence, Either I or II follow.

Point to remember:

1. Both the conclusion should be false.

2. It should be complementary pair.

Given statement: A > B > C < D; E ≥ D; A ≥ Z

On combining: Z ≤ A > B > C < D ≤ E

Conclusion:

I. A > D → False (A > B > C < D, There is no definite path between A and D. So, A > D is false) 

II. C < E → True (C < D ≤ E → C < E is true)

Hence, Only II follow.

Given: 

Eight persons, A, B, C, D, E, F, G and H buy some stuff on different occasions.

1. A buys on the fifth number.

2) Four persons buy between E and F. 

3) Neither E nor F buys first or at the last. 

4) B buys just after D.

5) The number of persons who buy between A and D is equal to the number of persons who buy between A and F.

Here, case 2 will be cancelled.

6) G buys after H but not on the 6th number.

7) C does not buy at the first number.

 

 

 

 

 

 

 

 

 

 

So, the above shown arrangement is the final order of persons buying stuff.

Here, in the options, all persons except B has purchased their stuff on odd place.

Hence, B does not belong to the group.

Given: 

Eight persons, A, B, C, D, E, F, G and H buy some stuff on different occasions.

1. A buys on the fifth number.

2) Four persons buy between E and F. 

3) Neither E nor F buys first or at the last. 

4) B buys just after D.

5) The number of persons who buy between A and D is equal to the number of persons who buy between A and F.

Here, case 2 will be cancelled.

6) G buys after H but not on the 6th number.

7) C does not buy at the first number.

 

 

 

 

 

 

 

 

 

 

So, the above shown arrangement is the final order of persons buying stuff.

 

 

 

 

 

 

 

 

 

 

Hence, had they bought their stuff in reverse alphabetical order, 2 of them would have bought at the same rank as they have bought in actual case.

Given: 

Eight persons, A, B, C, D, E, F, G and H buy some stuff on different occasions.

1. A buys on the fifth number.

2) Four persons buy between E and F. 

3) Neither E nor F buys first or at the last. 

4) B buys just after D.

5) The number of persons who buy between A and D is equal to the number of persons who buy between A and F.

Here, case 2 will be cancelled.

6) G buys after H but not on the 6th number.

7) C does not buy at the first number.

 

 

 

 

 

 

 

 

 

 

So, the above shown arrangement is the final order of persons buying stuff.

I. E buys stuff at the second number. : True

II. C buys stuff just after A. : True

III. One person buys stuff between D and A. : True

Hence, I, II & III are true.

Given: 

Eight persons, A, B, C, D, E, F, G and H buy some stuff on different occasions.

1. A buys on the fifth number.

2) Four persons buy between E and F. 

3) Neither E nor F buys first or at the last. 

4) B buys just after D.

5) The number of persons who buy between A and D is equal to the number of persons who buy between A and F.

Here, case 2 will be cancelled.

6) G buys after H but not on the 6th number.

7) C does not buy at the first number.

 

 

 

 

 

 

 

 

 

 

So, the above shown arrangement is the final order of persons buying stuff.

I. E buys stuff just before B. : False(E buys stuff just before D)

II. Three persons buy stuff between F and B. : False( Only two persons buy stuff between F and B.)

III. G buys in the last. : True

Hence, I & II does not follow.

Given: 

Eight persons, A, B, C, D, E, F, G and H buy some stuff on different occasions.

1. A buys on the fifth number.

2) Four persons buy between E and F. 

3) Neither E nor F buys first or at the last. 

4) B buys just after D.

5) The number of persons who buy between A and D is equal to the number of persons who buy between A and F.

Here, case 2 will be cancelled.

6) G buys after H but not on the 6th number.

7) C does not buy at the first number.

 

 

 

 

 

 

 

 

 

 

So, the above shown arrangement is the final order of persons buying stuff.

Hence, A buys stuff on 5th number.

Given Word:- PROBLEMATIC

According to alphabetical order, all the consonants are replaced by the previous letter, and all the vowels are replaced by the next letter according to the English alphabetical series.

 

2. Eliminate all the vowels and the letters which are repeated in the new alphabets - 

The vowels are A and O and the letter B is repeated twice so eliminate it.

3. All the letters are arranged in ascending order from left to right -

FJKLPQS.

The letter which is fifth from the right end is K.

Hence, the correct answer is K.

Given Word:- TROPHOGENIST

The second letter is 'R', the third letter is 'O', the fifth letter is 'H' and the ninth letter is 'N' from the left end.

Meaningful four-letter English words can be formed is -

1) HORN which means the device in a vehicle that gives a loud warning sound.

Thus, only one such word can be formed.

Hence, the correct answer is One.

From the given statements,

1. I sits 3rd to the left of N. As both I and N faces north direction hence I sits third to the left of N.

2. One person sits between I and J. We get 2 possibilities now – Case 1 and Case 2.  In case 1 , J sits on the left of I while in case 2 J sits on the right of I.

 

3. H sits 4th to the left of J. Hence in case 1 and case 2, H sits on the left side of J.

4. Two persons sit between N and S. Hence in both the cases, S sits on the right side of N because on the left side I is placed so there is no place remaining for S in the given condition.

5. S sits immediate left of O. Hence O placed on the right of S.

6)There are four persons sitting between O and W, who sits third from the extreme right end. Hence W sits on the right side of O in both the cases.

7. At least 15 persons are sitting between H and W. Now Case 2 is ruled out now because in case 2, less than 15 persons are sit between H and W.

8. One person sits between W and V. As W sits on the corner so V sits on the left side of W.

9. G sits 2nd from one of the ends. One person sits between G and H. So here we have to place G on the left side because H is already placed there and we have to satisfy the condition of one person between H and G. Hence H sits on the right of G.

So, the final arrangement-

Hence, 24 persons are sitting in the given row.

From the given statements,

1. I sits 3rd to the left of N. As both I and N faces north direction hence I sits third to the left of N.

2. One person sits between I and J. We get 2 possibilities now – Case 1 and Case 2.  In case 1 , J sits on the left of I while in case 2 J sits on the right of I.

 

3. H sits 4th to the left of J. Hence in case 1 and case 2, H sits on the left side of J.

4. Two persons sit between N and S. Hence in both the cases, S sits on the right side of N because on the left side I is placed so there is no place remaining for S in the given condition.

5. S sits immediate left of O. Hence O placed on the right of S.

6. There are four persons sitting between O and W, who sits third from the extreme right end. Hence W sits on the right side of O in both the cases.

7. At least 15 persons are sitting between H and W. Now Case 2 is ruled out now because in case 2, less than 15 persons are sit between H and W.

8. One person sits between W and V. As W sits on the corner so V sits on the left side of W.

9. G sits 2nd from one of the ends. One person sits between G and H. So here we have to place G on the left side because H is already placed there and we have to satisfy the condition of one person between H and G. Hence H sits on the right of G.

So, the final arrangement-

Hence, J sits fifth to the left of N.

From the given statements,

1. I sits 3rd to the left of N. As both I and N faces north direction hence I sits third to the left of N.

2. One person sits between I and J. We get 2 possibilities now – Case 1 and Case 2.  In case 1 , J sits on the left of I while in case 2 J sits on the right of I.

 

3. H sits 4th to the left of J. Hence in case 1 and case 2, H sits on the left side of J.

4. Two persons sit between N and S. Hence in both the cases, S sits on the right side of N because on the left side I is placed so there is no place remaining for S in the given condition.

5. S sits immediate left of O. Hence O placed on the right of S.

6. There are four persons sitting between O and W, who sits third from the extreme right end. Hence W sits on the right side of O in both the cases.

7. At least 15 persons are sitting between H and W. Now Case 2 is ruled out now because in case 2, less than 15 persons are sit between H and W.

8. One person sits between W and V. As W sits on the corner so V sits on the left side of W.

9. G sits 2nd from one of the ends. One person sits between G and H. So here we have to place G on the left side because H is already placed there and we have to satisfy the condition of one person between H and G. Hence H sits on the right of G.

So, the final arrangement-

Hence, five persons are sitting between H and I.

From the given statements,

1. I sits 3rd to the left of N. As both I and N faces north direction hence I sits third to the left of N.

2. One person sits between I and J. We get 2 possibilities now – Case 1 and Case 2.  In case 1 , J sits on the left of I while in case 2 J sits on the right of I.

 

3. H sits 4th to the left of J. Hence in case 1 and case 2, H sits on the left side of J.

4. Two persons sit between N and S. Hence in both the cases, S sits on the right side of N because on the left side I is placed so there is no place remaining for S in the given condition.

5. S sits immediate left of O. Hence O placed on the right of S.

6)There are four persons sitting between O and W, who sits third from the extreme right end. Hence W sits on the right side of O in both the cases.

7. At least 15 persons are sitting between H and W. Now Case 2 is ruled out now because in case 2, less than 15 persons are sit between H and W.

8. One person sits between W and V. As W sits on the corner so V sits on the left side of W.

9. G sits 2nd from one of the ends. One person sits between G and H. So here we have to place G on the left side because H is already placed there and we have to satisfy the condition of one person between H and G. Hence H sits on the right of G.

So, the final arrangement-

Hence, seven persons are sitting on the left of J.

From the given statements,

1. I sits 3rd to the left of N. As both I and N faces north direction hence I sits third to the left of N.

2. One person sits between I and J. We get 2 possibilities now – Case 1 and Case 2.  In case 1 , J sits on the left of I while in case 2 J sits on the right of I.

 

3. H sits 4th to the left of J. Hence in case 1 and case 2, H sits on the left side of J.

4. Two persons sit between N and S. Hence in both the cases, S sits on the right side of N because on the left side I is placed so there is no place remaining for S in the given condition.

5. S sits immediate left of O. Hence O placed on the right of S.

6. There are four persons sitting between O and W, who sits third from the extreme right end. Hence W sits on the right side of O in both the cases.

7. At least 15 persons are sitting between H and W. Now Case 2 is ruled out now because in case 2, less than 15 persons are sit between H and W.

8. One person sits between W and V. As W sits on the corner so V sits on the left side of W.

9. G sits 2nd from one of the ends. One person sits between G and H. So here we have to place G on the left side because H is already placed there and we have to satisfy the condition of one person between H and G. Hence H sits on the right of G.

So, the final arrangement-

Hence, V sits seventh to the right of N.

With the dat given, we can draw a family tree diagram as shown below.

1. P is the only son-in-law of R.
2. L is the daughter of S.

 So, L is the wife of P.

3. Q is the daughter of P.
4. S is the grand father of Q.

 So, R is the grand mother of Q.

Hence, L is the mother of Q.

Hence, Mother is the answer.

According to the given information, we have the following diagram:

Clearly, R is to the South-east direction with respect to X.

Hence, South-east is the correct answer.

According to the given information, we have the following diagram:

Distance TV = ${ \sqrt{TR^2+VR^2}}$

= ${ \sqrt{12^2+14^2}}$

= ${ \sqrt{144+196}}$

= ${ \sqrt{340}}$

= ${ 2\sqrt{85}}$

Hence, ${ 2\sqrt{85}} m$ is the correct answer.

According to the given information, we have the following diagram:

Clearly, all the given options except "R and T", the first shop is in the South-west direction with respect to the second shop.

Hence, R and T is the correct answer.

Floor: 1, 2, 3, 4, 5

Flat: 1, 2

Persons: A, B, C, D, E, F, G, H, I and J

1. Three floors are there between the F and B, which is living in the odd flat.

 

 

 

 

 

 

 

 

2. Two floors are between B and I, which is living left of person A.

3. D living on the same floor as B.

 

 

 

 

 

 

 

 

4. C lives North West of D and south west of A. (Case 1 and 2 get eliminated)

5. Two floors are there between J and C and both are at same in same flat number (This eliminate case 4)

6. E lives on the north west of H.

 

 

 

 

 

 

 

 

G lives on the third floor of flat 2.

Hence, E lives to the immediate left of the person who lives on third floor.

Floor: 1, 2, 3, 4, 5

Flat: 1, 2

Persons: A, B, C, D, E, F, G, H, I and J

1. Three floors are there between the F and B, which is living in the odd flat.

 

 

 

 

 

 

 

 

2. Two floors are between B and I, which is living left of person A.

3. D living on the same floor as B.

 

 

 

 

 

 

 

 

4. C lives North West of D and south west of A. (Case 1 and 2 get eliminated)

5. Two floors are there between J and C and both are at same in same flat number (This eliminate case 4)

6. E lives on the north west of H.

 

 

 

 

 

 

 

 

All the above except C - D are the persons who live on the same floor number.

Hence, C - D does not belong to the group.

Floor: 1, 2, 3, 4, 5

Flat: 1, 2

Persons: A, B, C, D, E, F, G, H, I and J

1. Three floors are there between the F and B, which is living in the odd flat.

 

 

 

 

 

 

 

 

2. Two floors are between B and I, which is living left of person A.

3. D living on the same floor as B.

 

 

 

 

 

 

 

 

4. C lives North West of D and southwest of A. (Case 1 and 2 get eliminated)

5. Two floors are there between J and C and both are at same in same flat number (This eliminate case 4)

6. E lives on the northwest of H.

 

 

 

 

 

 

 

 

Hence, D lives in the south east of C.

Floor: 1, 2, 3, 4, 5

Flat: 1, 2

Persons: A, B, C, D, E, F, G, H, I and J

1. Three floors are there between the F and B, which is living in the odd flat.

 

 

 

 

 

 

 

 

2. Two floors are between B and I, which is living left of person A.

3. D living on the same floor as B.

 

 

 

 

 

 

 

 

4. C lives North West of D and southwest of A. (Case 1 and 2 get eliminated)

5. Two floors are there between J and C and both are at same in same flat number (This eliminate case 4)

6. E lives on the northwest of H.

 

 

 

 

 

 

 

 

Hence, B lives in Flat 1 is the correct answer.

Floor: 1, 2, 3, 4, 5

Flat: 1, 2

Persons: A, B, C, D, E, F, G, H, I and J

1. Three floors are there between the F and B, which is living in the odd flat.

 

 

 

 

 

 

 

 

2. Two floors are between B and I, which is living left of person A.

3. D living on the same floor as B.

 

 

 

 

 

 

 

 

4. C lives North West of D and southwest of A. (Case 1 and 2 get eliminated)

5. Two floors are there between J and C and both are at same in same flat number (This eliminate case 4)

6. E lives on the northwest of H.

 

 

 

 

 

 

 

 

Hence, The number of floors above G is the same as the number of floors below E.

The required pairs in the given number are:

In Forward Direction -  (1, 5), (6, 8)

In Backward Direction - (2, 6) 

Thus, there are three such pairs that have as many digits between them in the number (both forward and backward direction) as they have between them in the numerical series.

Hence, the correct answer is Three.

Given:   L, M, N, O, P, and Q are facing north and A, B, C, D, E, and F are facing south.

1. E is facing O who is sitting third to the right of Q. i.e. E is facing O and O is sitting third to the right of Q

2. D is sitting to the immediate right of the person who is facing Q. 

(The second statement implies that at least one person is sitting to the left of Q.)

3. B, who is not an immediate neighbour of D, is sitting on one of the extreme ends. At most we can place one people to the right of D because Six people sit in a row But B is not neighbour of D . So, B will sit extreme left end.

4. P is facing the person who is sitting to the immediate right of C.

5) M is an immediate neighbour of P

6. F is not an immediate neighbour of D.

(Implies, F must be sitting second to the left of D and it further implies that A must be sitting between F and D as it is the only seat left to be filled.)

7. L is not facing D.

(Implies, L must be facing B because it is the only other option for L. Also, N must be facing D as it is the only seat left for N and in first row only one seat left for A.)

Clearly, E is sitting to the immediate left of C and O is sitting opposite E.

Hence, the correct answer is "O".

Given:   L, M, N, O, P, and Q are facing north and A, B, C, D, E, and F are facing south.

1. E is facing O who is sitting third to the right of Q. i.e. E is facing O and O is sitting third to the right of Q

2. D is sitting to the immediate right of the person who is facing Q. 

(The second statement implies that at least one person is sitting to the left of Q.)

3. B, who is not an immediate neighbour of D, is sitting on one of the extreme ends. At most we can place one people to the right of D because Six people sit in a row But B is not neighbour of D . So, B will sit extreme left end.

4. P is facing the person who is sitting to the immediate right of C.

5) M is an immediate neighbour of P

6. F is not an immediate neighbour of D.

(Implies, F must be sitting second to the left of D and it further implies that A must be sitting between F and D as it is the only seat left to be filled.)

7. L is not facing D.

(Implies, L must be facing B because it is the only other option for L. Also, N must be facing D as it is the only seat left for N and in first row only one seat left for A.)

Clearly, only one person is sitting between N and P.

Hence, the correct answer is "one".

Given:   L, M, N, O, P, and Q are facing north and A, B, C, D, E, and F are facing south.

1. E is facing O who is sitting third to the right of Q. i.e. E is facing O and O is sitting third to the right of Q.

2. D is sitting to the immediate right of the person who is facing Q. 

(The second statement implies that at least one person is sitting to the left of Q.)

3. B, who is not an immediate neighbour of D, is sitting on one of the extreme ends. At most we can place one people to the right of D because Six people sit in a row But B is not neighbour of D . So, B will sit extreme left end.

4. P is facing the person who is sitting to the immediate right of C.

5) M is an immediate neighbour of P

6. F is not an immediate neighbour of D.

(Implies, F must be sitting second to the left of D and it further implies that A must be sitting between F and D as it is the only seat left to be filled.)

7. L is not facing D.

(Implies, L must be facing B because it is the only other option for L. Also, N must be facing D as it is the only seat left for N and in first row only one seat left for A.)

Except for Q, all are sitting on extreme ends.

Hence, the correct answer is "Q"

Given:   L, M, N, O, P, and Q are facing north and A, B, C, D, E, and F are facing south.

1. E is facing O who is sitting third to the right of Q. i.e. E is facing O and O is sitting third to the right of Q

2. D is sitting to the immediate right of the person who is facing Q. 

(The second statement implies that at least one person is sitting to the left of Q.)

3. B, who is not an immediate neighbour of D, is sitting on one of the extreme ends. At most we can place one people to the right of D because Six people sit in a row But B is not neighbour of D . So, B will sit extreme left end.

4. P is facing the person who is sitting to the immediate right of C.

5) M is an immediate neighbour of P

6. F is not an immediate neighbour of D.

(Implies, F must be sitting second to the left of D and it further implies that A must be sitting between F and D as it is the only seat left to be filled.)

7. L is not facing D.

(Implies, L must be facing B because it is the only other option for L. Also, N must be facing D as it is the only seat left for N and in first row only one seat left for A.)

Clearly, Q is sitting opposite A.

Hence, the correct answer is "Q".

Given:   L, M, N, O, P, and Q are facing north and A, B, C, D, E, and F are facing south.

1. E is facing O who is sitting third to the right of Q. i.e. E is facing O and O is sitting third to the right of Q

2. D is sitting to the immediate right of the person who is facing Q. 

(The second statement implies that at least one person is sitting to the left of Q.)

3. B, who is not an immediate neighbour of D, is sitting on one of the extreme ends. At most we can place one people to the right of D because Six people sit in a row But B is not neighbour of D . So, B will sit extreme left end.

4. P is facing the person who is sitting to the immediate right of C.

5) M is an immediate neighbour of P

6. F is not an immediate neighbour of D.

(Implies, F must be sitting second to the left of D and it further implies that A must be sitting between F and D as it is the only seat left to be filled.)

7. L is not facing D.

(Implies, L must be facing B because it is the only other option for L. Also, N must be facing D as it is the only seat left for N and in first row only one seat left for A.)

Clearly, L is sitting opposite B.

Hence, the correct answer is "BL".

Solution :

 The series follows the following pattern :

⇒ 3 × 6 + 1 = 19

⇒ 4 × 7+ 2 = 30

⇒ 5 × 8 + 3 = 43

⇒ 6 × 9+ 4 = 58

⇒ 7 × 10 + 5 = 75

⇒ 8 × 11 + 6 = 94

⇒ The next term in the series will be 94.

 Hence 94 is the correct answer.

Solution :

 The series follows the following pattern :

 ⇒ 42 + 4 = 46

 ⇒ 46 + 12 = 58

 ⇒ 58 + 20 = 78

 ⇒ 78 + 28 = 106

 ⇒ 106 + 36 = 142

 ⇒ The next term in the series will be 142.

 Hence 142 is the correct answer.

Solution :

The series follows the following pattern :

⇒9 + 3² = 18

⇒18 + 3³ = 45

⇒45 + 3⁴ = 126

⇒126 + 3⁵ = 369

⇒369 + 3⁶ = 1098

⇒The next term in the series will be 9

Hence 9 is the correct answer.

Solution :

The series follows the following pattern :

⇒12² - 1 = 143

⇒13² + 1 = 170

⇒14² - 1 = 195

⇒15² + 1 = 226

⇒16² - 1 = 255

⇒17² + 1 = 290

⇒The next term in the series will be 195.

Hence 195 is the correct answer.

Solution :

 The series follows the following pattern :

⇒ 7 × 1 - 2 = 5

⇒ 5 × 2 - 4 = 6

⇒ 6 × 3 - 6 = 12

⇒ 12 × 4 - 8 = 40

⇒ 40 × 5 - 10 = 190

⇒ 190 × 6 - 12 = 1128

⇒ The next term in the series will be 1128.

Hence 1128 is the correct answer.

Given:

Profit of Prashant = 25%

Profit of Satish = 25%

Profit of Yash = 20%

CP for Shivansh = Rs. 53,250

Formula:

Selling price = (100 + Profit%)/100 × Cost Price

Calculation:

Let the cost at which Prashant bought the laptop be x

According to question,

x × 125/100 × 125/100 × 120/100 = 53250

⇒ x × 5/4 × 5/4 × 6/5 = 53,250

⇒ x = 53250 × 8/15 = Rs. 28,400

∴ Price at which Prashant bought the laptop = Rs. 28400

Given:

Time to go 120 km upstream and come back to the starting point = 8 hours

The speed of the stream is 25% of the speed of the boat in still water

Formula Used:

Downstream Speed = Speed of boat + Speed of stream 

Upstream Speed = Speed of boat - Speed of stream

Calculation:

Let the speed of the boat in still water be x km/h.

So, the speed of stream = x × 25/100 = (x/4) km/h

The upstream speed of boat = x – (x/4) = (3x/4) km/h

The downstream speed of boat = x + (x/4) = (5x/4) km/h

According to the question:

[120/ (3x/4)] + [120/ (5x/4)] = 8

⇒ (480/3x) + (480/5x) = 8

⇒ 480[(5 + 3) /15x] = 8

⇒ 15x = 480

⇒ x = 32

⇒ The upstream speed of the boat = 32 × 3/4 = 24 km/h

⇒ The downstream speed of the boat = 32 × 5/4 = 40 km/h

∴ The required difference = 40 – 24 = 16 km/h

Given:

Pipes A, B, and C together can fill a tank in 12 hours.

Pipes A and B together can fill the same tank in 24 hours.

Pipe D can empty this tank in 48 hours.

Formula Used:

Efficiency = Total work/Total time

Calculation:

Let's assume the capacity of the tank = 48 units (LCM of 12, 24, and 48)

So in 1 hour A, B, and C together can fill = 48/12

⇒ 4 unit 

In 1 hour A, and B together can fill = 48/24

⇒ 2 unit

Then in 1 hour C can fill = 4 - 2

⇒ 2 unit 

Pipe D can empty this tank in 48 hours

So in 1 hour D can empty = 48/48

⇒ 1 unit 

For 8 hours all pipes are opened so they will fill = (4 -1) × 8

⇒ 24 unit

Remaining capacity of tank = 48 - 24

⇒ 24 unit

Now only C and D are open so they will take = 24/(2-1)

⇒ 24 hours 

∴ Total time taken = 8 + 24 = 32 hours

Given:

A alone can complete whole work = 22 days

B alone can complete whole work = 26 days

They work together for 5 days

Concept used:

Work efficiency = Total work/Total working time

Total time = Total work/ Work efficiency

Per hour work = 1/Total time 

Calculation:

Total work = LCM of 22 and 26 = 286 unit

Efficiency of A = 286/22 = 13 days

Efficiency of B = 286/26 = 11 days

Work done by A and B together in 1 day = 13 + 11

⇒ 24 unit

Hence Work done by A and B together in 5 day = 5 x 24

⇒ 120 unit

Remaining work = 286 - 120

⇒ 166 unit

When A left the work then remaining work done by B alone.

Days for completing the remaining work = 166/11

⇒ $15\frac{1}{11}$ days.

Total days for complete the work = 5 + $15\frac{1}{11}$ = $20\frac{1}{11}$ days

∴ Total days for complete the work is $20\frac{1}{11}$ days.

Given:

Ratio of A and B = 3 : 5

Ratio of B and C = 10 : 13

C's Profit at the end of year = 17628

Calculation:

A : B = 3 : 5

B : C = 10 : 13

A : B : C = 6 : 10 : 13

According to the question, we get

⇒ (13 × x)/(6 + 10 + 13) = 17628

⇒13x/29 = 17628

⇒ x = 39324

∴ Total profit earned by all is Rs. 39324.

Calculation:

Student playing all 3 type of sports = (10 / 100) × 300 = 30

∴ Students playing only football = 2 × 30 = 60

Number of student playing only tennis = Number of students playing football and tennis both = (2 / 30) × 300 = 20

We know, 20% = 1 / 5

Let the number of students playing football and cricket both = 5x

According to question, number of students playing cricket and tennis both = 4x

And, Students playing only cricket = 8x

∴ 8x + 4x + 5x = 300 – (30 + 60 + 20 + 20)

⇒ 17x = 170

⇒ x = 10

∴ Number of students playing football and cricket both = 5x = 5 × 10 = 50

Number of student playing cricket and tennis both = 4x = 4 × 10 = 40

Number of Student playing only cricket = 8x = 8 × 10 = 80

25% of 80 = (1 / 4) × 80 = 20

∴ Number of student playing all 3 sports will be = 30 + 20 = 50

Calculation:

Student playing all 3 type of sports = (10 / 100) × 300 = 30

∴ Students playing only football = 2 × 30 = 60

Number of student playing only tennis = Number of students playing football and tennis both = (2 / 30) × 300 = 20

We know, 20% = 1 / 5

Let the number of students playing football and cricket both = 5x

According to question, number of students playing cricket and tennis both = 4x

And, Students playing only cricket = 8x

∴ 8x + 4x + 5x = 300 – (30 + 60 + 20 + 20)

⇒ 17x = 170

⇒ x = 10

∴ Number of students playing football and cricket both = 5x = 5 × 10 = 50

Number of student playing cricket and tennis both = 4x = 4 × 10 = 40

Number of Student playing only cricket = 8x = 8 × 10 = 80

Student playing only basketball and only football together = 80 + 60 = 140

Students playing all of the 3 sports = 30

∴ Required ratio = 140 : 30

⇒ 14 : 3

Calculation:

Student playing all 3 type of sports = (10 / 100) × 300 = 30

∴ Students playing only football = 2 × 30 = 60

Number of student playing only tennis = Number of students playing football and tennis both = (2 / 30) × 300 = 20

We know, 20% = 1 / 5

Let the number of students playing football and cricket both = 5x

According to question, number of students playing cricket and tennis both = 4x

And, Students playing only cricket = 8x

∴ 8x + 4x + 5x = 300 – (30 + 60 + 20 + 20)

⇒ 17x = 170

⇒ x = 10

∴ Number of students playing football and cricket both = 5x = 5 × 10 = 50

Number of student playing cricket and tennis both = 4x = 4 × 10 = 40

Number of Student playing only cricket = 8x = 8 × 10 = 80

∴ Number of students playing atleast 2 games = 50 + 30 + 20 + 40 = 140

Calculation:

Student playing all 3 type of sports = (10 / 100) × 300 = 30

∴ Students playing only football = 2 × 30 = 60

Number of student playing only tennis = Number of students playing football and tennis both = (2 / 30) × 300 = 20

We know, 20% = 1 / 5

Let the number of students playing football and cricket both = 5x

According to question, number of students playing cricket and tennis both = 4x

And, Students playing only cricket = 8x

∴ 8x + 4x + 5x = 300 – (30 + 60 + 20 + 20)

⇒ 17x = 170

⇒ x = 10

∴ Number of students playing football and cricket both = 5x = 5 × 10 = 50

Number of student playing cricket and tennis both = 4x = 4 × 10 = 40

Number of Student playing only cricket = 8x = 8 × 10 = 80

Number of student playing only one game = 80 + 20 + 60 = 160

∴ Average = 160 / 3 = 53.33

Calculation:

Student playing all 3 type of sports = (10 / 100) × 300 = 30

∴ Students playing only football = 2 × 30 = 60

Number of student playing only tennis = Number of students playing football and tennis both = (2 / 30) × 300 = 20

We know, 20% = 1 / 5

Let the number of students playing football and cricket both = 5x

According to question, number of students playing cricket and tennis both = 4x

And, Students playing only cricket = 8x

∴ 8x + 4x + 5x = 300 – (30 + 60 + 20 + 20)

⇒ 17x = 170

⇒ x = 10

∴ Number of students playing football and cricket both = 5x = 5 × 10 = 50

Number of student playing cricket and tennis both = 4x = 4 × 10 = 40

Number of Student playing only cricket = 8x = 8 × 10 = 80

∴ Required percentage = $\frac{{60 - 50}}{{50}} \times 100 = \frac{{10}}{{50}} \times 100 = 20\%$

Calculation:

I. x2 - 15x + 56 = 0

⇒ x2 - 7x - 8x + 56 = 0

⇒ x (x - 7) - 8 (x - 7) = 0

⇒ (x - 7) (x - 8) = 0

⇒ x = 7, 8

II. y2 - 21y + 80 = 0

⇒ y2 - 16y - 5y + 80 = 0

⇒ y (y - 16) - 5 (y - 16) = 0

⇒ (y - 16) (y - 5) = 0

⇒ y = 16, 5

Comparison between x and y (via Tabulation):

<br>

∴ x = y or relationship between x and y cannot be established.

Calculation:

I. x2 - 10x + 9 = 0

⇒ x² – 9x – x + 9 = 0

⇒ x(x – 9) – 1(x – 9)= 0

⇒ (x – 9)(x – 1) = 0

⇒ x = 9, 1

II. y2 – 18y + 81 = 0

⇒ y² – 9y – 9y + 81 = 0

⇒ y(y – 9) – 9(y – 9) =0

⇒ (y – 9)(y – 9) = 0

⇒ y = 9, 9

<br>

When we compared the values of ‘x’ and ‘y’ in the table above, we found that there is TWO relations between X and Y i.e. < and =. So, a relation between x and y is “x ≤ y”.

∴ After comparison, all the values of x and y the relation is “x ≤ y”.

Given:

I. 5x² + 6x - 27 = 0

II. y² + 5y - 14 = 0

Calculation:

From I,

5x² + 6x - 27 = 0

⇒ 5x² + 15x - 9x - 27 = 0

⇒ 5x(x + 3) - 9(x + 3) = 0

⇒ (x + 3)(5x - 9) = 0

Taking,

⇒ (x + 3) = 0 or  (5x - 9) = 0

⇒ x = -3 or (9/5)

From II,

y² + 5y - 14 = 0

⇒ y² + 7y - 2y - 14 = 0

⇒ y(y + 7) - 2(y + 7) = 0

⇒ (y + 7)(y - 2) = 0

Taking,

⇒ (y - 2) = 0 or (y + 7) = 0

⇒ y = 2 or -7

Comparison between x and y (via Tabulation):

<br>

∴ x = y or relation between x and y can not be established.

Given:

I. x² - 7x + 10 = 0

II. y² - 29y + 54 = 0

Calculation:

I. x² - 7x + 10 = 0

⇒ x² - 5x - 2x + 10 = 0

⇒ x(x - 5) - 2(x - 5) = 0

⇒ (x - 5)(x - 2) = 0

⇒ x = 5, 2

II. y² - 29y + 54 = 0

⇒ y² - 27y - 2y + 54 = 0

⇒ y(y - 27) - 2(y - 27) = 0

⇒ (y - 27)(y - 2) = 0

⇒ y = 27, 2

 

∴ No relation in x and y or x = y

Calculation:

I. x2 + 19x + 34 = 0

⇒ x2 + 17x + 2x+ 34 = 0

⇒ x(x + 17) + 2(x + 17) = 0

⇒ (x + 17) (x + 2) = 0

∴ x = -17, -2

II. y2 + 21y + 54 = 0

⇒ y2 + 18x + 3x + 54= 0

⇒ y(y + 18) + 3(x + 18) = 0

⇒ (y + 18) (y + 3) = 0

∴ y = -18, -3

Comparison between x and y (via Tabulation):

<br>

∴ x = y or the relationship between x and y cannot be established.

Number of boys in class A = 80

Number of girls in class C = 85

Ratio of number of boys in class A and girls in class B = 80 : 85 = 16 :17

∴ the required ratio = 16 : 17

Number of boys in class C = 60

Number of girls in class C = 85

Total number of boys and girl in class C= 60 + 85 = 145

Number of boys in class D = 55

Number of girls in class D = 75

Total number of boys and girls in class D = 55 + 75 = 130

Difference between number of boys and girls in class C and in class D = 145 – 130 = 15

∴ the required difference = 15

Number of boys in class A = 80

Number of boys in class C = 60

Percent of boys Class A is more than boys in class C = (20/60 )× 100 = 1/3 = 33.33%

Total numbers of boys in Class A and C = 80 + 60 = 140

Total numbers of girls in class C and D= 85 + 75 = 160

Total numbers of boys in Class A and C and girls in class C and D = 140 + 160 = 300

Average = 300 / 4 = 75

∴ the required average = 75

Number of boys in class A = 80

Number of boys in class C= 60

Total number of boys in class A and C = 80 + 60 = 140

Number of girl in class B = 70

Number of girl in class D = 75

Total number of girl in class B and D= 70 + 75 = 145

Ratio of Total number of boys in class A and C : Total number of girls in Class B and D = 140 : 145 = 28 : 29

∴ the required ratio = 28 : 29

Given:

Total number of people = 160

People who like tennis = 100

People who like both tennis and cricket = 20

Concept used:

Venn Diagram

Calculation:

The number of students who like only tennis = 100 – 20 = 80

The number of students who like only cricket = 160 – (100) = 60

According to the question,

Required ratio = 60 : 80 = 3 : 4

∴ The ratio between the people who like only cricket and the number of people who like only tennis is 3 : 4.

Given:

The ratio in the distributed amount of Ravi, Rahul and Raj = 8 : 5 : 7

Calculation

Let the Ratio of money distributed among Ravi, Rahul and Raj = 8x : 5x : 7x

Ratio of Rahul and Raj = 5x + 7x = 12x

Difference between the ratio of Ravi and Rahul = 12x – 8x = 4x

According to question,

4x = 1000

⇒ 1x = 250

Then share of Ravi = 8x = 250 × 8 = 2000

Share of Raj = 7x = 250 × 7 = 1750

Difference between shares of Ravi and Raj = 2000 – 1750

∴ Difference between shares of Ravi and Raj = 250 Ans.

Given:

In the first case:

Radha's expenditure = 20% of her income.

In the second case:

The income for next month = increased by 20%,

The amount of savings remains the same,

Calculation:

In the first case:

Let the income of Radha = ₹100

The expenditure of Radha = 20% of ₹100 = ₹20

The saving of Radha = ₹100 - ₹20 = ₹80

In the second case:

The increased income of Radha = (100% of 20%) of ₹100 = ₹120

The saving of Radha = ₹80

The expenditure of Radha = ₹120 - ₹80 = ₹40

The required percentage increase = $\frac{₹40-₹20}{₹20}$ × 100 = 100%

∴ The percentage increase in expenditure of Radha is 100%.

Alternate Method

Given:

In the first case:

Radha's expenditure = 20% of her income.

In the second case:

The income for next month = increased by 20%,

The amount of savings remains the same,

Calculation:

According to the question,

The expenditure of Radha = ₹120 - ₹80 = ₹40

The required percentage increase = $\frac{₹40-₹20}{₹20}$ × 100 = 100%

∴ The percentage increase in expenditure of Radha is 100%.

Given:

Let quantity of milk and water in the original mixture be 3a litres and 7a litres respectively.

Calculation:

The quantity of milk in new mixture = (3a + 10) litres

The quantity of water in new mixture = (7a + 6) litres

Then,

⇒ (5a + 10) : (7a + 6) = 5 : 6

⇒ 30a + 60 = 35a - 30

⇒ 5a = 30

⇒ a = 6

The quantity of milk in new mixture = 5 × 6 + 10 = 40 litres

The quantity of water in new mixture = 7 × 6 + 6 = 48 litres

∴ Required difference = 48 - 40 = 8 litres.

Shortcut Trick

Ratio of A : B is 7 : 8 (Present) and 8 : 9 (After 6 years).

Change in ratio units for both is 8 − 7 = 1 unit and 9 − 8 = 1 unit.

Since the time gap is 6 years, 1 unit → 6 years.

A's present age = 7 units × 6 = 42 years.

C's present age = 42 + 10 = 52 years.

∴ The correct answer is 52 years.

Alternate Method

Given: Present age ratio A : B = 7 : 8. After 6 years, ratio A : B = 8 : 9. C = A + 10.

Calculation:

⇒ Let present ages of A and B be 7x and 8x.

⇒ (7x + 6) ÷ (8x + 6) = 8 ÷ 9

⇒ 9 × (7x + 6) = 8 × (8x + 6)

⇒ 63x + 54 = 64x + 48

⇒ 64x − 63x = 54 − 48

⇒ x = 6

⇒ A's present age = 7 × 6 = 42 years

⇒ C's present age = 42 + 10 = 52 years

∴ The correct answer is 52 years.

Additional Information

Age Difference Property

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

Ratio Balancing Method

If the difference in ratio parts is not equal, multiply the ratios by the difference of the other ratio to balance them before solving.

Linear Equation in Ages

For any 'n' years after/before, add/subtract 'n' to the current age variables to form the equation: (Ax + n) / (Bx + n) = New Ratio.

From the given table, we get:

Total number of males, who applied for Hotel reservations in all hotels together = (308 + 132 + 363 + 336 + 324) = 1463

Total number of females, who applied for Hotel reservations in all hotels together = (132 + 198 + 121 + 336 + 216) = 1003

Required percentage = (1463/1003 x 100) = 145. 28%

Hence, the correct answer is option 4.

From the given table, we get:

 200 males applied for hotel reservations in Hotel F.

Number of females, who applied for Hotel reservations in Hotel F = 25% of 132 = 33

So, total number of persons, who applied for Hotel reservations in Hotel F = (200 + 33) = 233

Hence, the correct answer is option 3.

From the given table, we get:

 

Total number of females, who applied for Hotel reservations in Hotel C = 121

Total number of males, who applied for Hotel reservations in Hotel E = 324

Required percentage = 121/324 x 100 = 37.34%

Hence, the correct answer is option 5.

From the given table, we get:

Total number of males, who applied for Hotel reservations in Hotel A = 308

Total number of males, who applied for Hotel reservations in Hotel B = 132

Total number of males, who applied for Hotel reservations in Hotel C = 363

Total number of males, who applied for Hotel reservations in Hotel D = 336

Total number of males, who applied for Hotel reservations in Hotel E = 324

Required sum (308 + 132 + 363 + 336 + 324) = 1463

Hence, the correct answer is option 2.

From the given table, we get:

Total number of males, who applied for Hotel reservations in Hotel B and C together = (132 + 363) = 495

Total number of females, who applied for Hotel reservations in Hotel E and D together = (336 + 216) = 552

Required difference = (552 - 495) = 57, Less

Hence, the correct answer is option 1.

The correct answer is Important.

Key Points

• The given passage is about Banking fraud.
• The underlined word serious means demanding or characterized by careful consideration or application.
• In option 3, Important means of great significance or value.
• So, '​Important' is the most appropriate word for the blank.

Additional Information

• Let us see the meanings of the other words: 
• Trivial - of very little importance or value
• Unimportant - lacking in importance or significance.
• Superficial -  all about the surface of appearances.
• Uncommitted - not committed to a cause, activity, etc.

The correct answer is Desirable**.**

Key Points

• The given passage is about Banking fraud.
• The given word regrettable means things that make you feel sorry.
• In option 5, Desirable means wished for as being an attractive, useful, or necessary course of action or worth having or wanting; pleasing, excellent, or fine.
• So, '​Desirable' is the most appropriate antonym.

Additional Information

• Let us see the meanings of the other words: 
• Undesirable - Not wanted
• Sorry - feeling sad or distressed through sympathy with someone else's misfortune.
• Disappointing - something not as good or as large as you hoped it would be.
• Unfortunate - having or marked by bad fortune; unlucky.

The correct answer is it affects public faith.

Key Points

• The given passage is about Banking fraud.
• Let us refer to the line from the passage, "It is a very sensitive issue as it affects the public faith on which the whole Banking system is predominantly based".
• From the given passage we get to know bank frauds concerns all citizens so it becomes a very sensitive issue because the whole banking system is based on the public.
• So, if citizens face fraud, it will adversely affect the whole Banking system.
• So, '​'it affects public faith' is the correct option.

The correct answer is Cheques.

Key Points

• The given passage is about Banking fraud.
• Let us refer to the line from the passage, "Cheques are a major area where frauds are committed by putting counterfeit signature on the cheque".
• From the given passage we get to know the most common type of fraud that occurs is in cheques.
• Anyone can forge a fake signature on any cheque and commit fraud.
• So, '​​Cheques​' is the correct option.

The correct answer is debatable.

Key Points

• The given passage is about Banking fraud.
• The given word negotiable (adjective) means something you can talk it over until you reach an agreement.
• In option 4, debatable (adjective) means open to discussion or argument.
• So, '​debatable' is the most appropriate synonym.

Additional Information

• Let us see the meanings of the other words: 
• mismanage - to handle something badly.
• misconduct - unacceptable or improper behaviour, especially by an employee or professional person.
• quash - to suppress or extinguish summarily and completely
• inflexible - incapable of change

The correct answer is One should do their work with ethics.

Key Points

• The given passage is about Banking fraud.
• Let us refer to the line from the passage, "Those who do business in the country should do their work with ethics otherwise its consequences can be serious".
• From the given passage we get to know that bank management is sometimes ignorant about the scams happening under them. Anyone who does business must do it with ethics as it would lead to an ideal environment.
• Businesses not done ethically will have to face their consequences.
• So, '​​One should do their work with ethics​' is the correct option.

The correct answer is No voice raised against the scams.

Key Points

• The given passage is about Banking fraud.
• Let us refer to the line from the passage, "Finance Minister Arun Jaitley says that if there are scams happening in many branches of the same bank and no voice is raised then it is a matter of concern".
• From the given passage we get to know that it becomes a big worry it scams are happening in many branches of the same bank. It becomes a huge matter of worry when these scams are not voiced out.
• So, '​No voice raised against the scams' is the correct option.

The correct answer is There is nothing left in this world except hatred and despair.

<br>

Key Points

• "Except" in a sentence denotes exception. The placement of all the parts of speech in the sentence **"There is nothing left in this world except hatred and despair." is absolutely correct.

• The corrected form of the other sentences are:

• | Option | Grammatical mistake | Corrected sentence | | --- | --- | --- | | 2 | The preposition 'to' will replace 'on' in the sentence. | I am coming to town this week. | | 3 | Be verb "is" will replace "are" in the sentence. "No one" always takes a singular verb. | No one is perfect in this world. | | 4 | "Back" is superfluous as "return" itself means to give back. | Please return my money. |

• Therefore, the correct answer is: There is nothing left in this world except hatred and despair.