Matrix Arrangement

1. Ajay, Anil, Amar and Alok appear for a race which has three rounds. No two persons got the same position in any round. In 1st, 2nd and 3rd rounds Anil, Amar and Ajay got the first position respectively. Each of Amar's and Alok's positions did not change in the first and the third rounds. Alok is placed two positions higher in the second round compared to the first round and he is always one position behind Amar. Which of the following statements gives the positions of all the found people in three rounds?

Ajay got the 3rd position in the second round.

Anil got the 2nd position in the 3rd round.

Alok got the 2nd position in the second round.

None of the above

Based on the information given, Anil, Amar, and Ajay got the first position in the 1st, 2nd, and 3rd rounds respectively. Alok is always one position behind Amar, so Alok got the 2nd position in the second round. Since no two persons got the same position in any round, Anil cannot have the 2nd position in the 3rd round. Therefore, the correct statement is "Ajay got the 3rd position in the second round."

Explanation

Based on the information given, Anil, Amar, and Ajay got the first position in the 1st, 2nd, and 3rd rounds respectively. Alok is always one position behind Amar, so Alok got the 2nd position in the second round. Since no two persons got the same position in any round, Anil cannot have the 2nd position in the 3rd round. Therefore, the correct statement is "Ajay got the 3rd position in the second round."

2. Directions for question2 to 5: These questions are based on the information given below: Two siblings – Bunty and Babli – divide 10 fruits equally between them. The fruits are divided such that, each of them has at least one banana and at least one apple. Also, the number of appeals and the number of bananas with Bunty is different from the number of appeals and the number of bananas with Babli. When asked about the details of the fruits with each of them, they came up with the following replies. Bunty:I have more than two bananas. Babli has less than two appeals Babli:Bunty has more than two apples. I have less than two bananas. It is known that, of the statements made by each of them, exactly one is true and the other is false, in any order. If the number of bananas with Bunty is less than the number of apples with Babli, then how many apples are there with both of them together?

4

5

6

Cannot be determined

Based on the given information, we know that the number of bananas with Bunty is less than the number of apples with Babli. Since Bunty has more than two bananas and Babli has less than two bananas, it means that Bunty must have one banana and Babli must have two bananas. Similarly, since Bunty has more than two apples and Babli has less than two apples, it means that Bunty must have three apples and Babli must have one apple. Therefore, the total number of apples with both of them together is 3 + 1 = 4. However, this contradicts the given condition that the number of bananas with Bunty is less than the number of apples with Babli. Hence, the number of apples with both of them together cannot be determined.

Explanation

Based on the given information, we know that the number of bananas with Bunty is less than the number of apples with Babli. Since Bunty has more than two bananas and Babli has less than two bananas, it means that Bunty must have one banana and Babli must have two bananas. Similarly, since Bunty has more than two apples and Babli has less than two apples, it means that Bunty must have three apples and Babli must have one apple. Therefore, the total number of apples with both of them together is 3 + 1 = 4. However, this contradicts the given condition that the number of bananas with Bunty is less than the number of apples with Babli. Hence, the number of apples with both of them together cannot be determined.

3. Directions for question2 to 5: These questions are based on the information given below: Two siblings – Bunty and Babli – divide 10 fruits equally between them. The fruits are divided such that, each of them has at least one banana and at least one apple. Also, the number of appeals and the number of bananas with Bunty is different from the number of appeals and the number of bananas with Babli. When asked about the details of the fruits with each of them, they came up with the following replies. Bunty:I have more than two bananas. Babli has less than two appeals Babli:Bunty has more than two apples. I have less than two bananas. It is known that, of the statements made by each of them, exactly one is true and the other is false, in any order. If the number of apples with Babli is more than the number of bananas with Bunty, then what is the sum of the number of bananas with Babli and the number of apples with Bunty?

2

3

5

7

Babli's statement is true and Bunty's statement is false. This means that Babli has more than two bananas and Bunty has less than two apples. Since each of them has at least one banana and at least one apple, Babli must have exactly two bananas and Bunty must have exactly two apples. Therefore, the sum of the number of bananas with Babli (2) and the number of apples with Bunty (2) is 4.

Explanation

Babli's statement is true and Bunty's statement is false. This means that Babli has more than two bananas and Bunty has less than two apples. Since each of them has at least one banana and at least one apple, Babli must have exactly two bananas and Bunty must have exactly two apples. Therefore, the sum of the number of bananas with Babli (2) and the number of apples with Bunty (2) is 4.

4. Directions for question2 to 5: These questions are based on the information given below: Two siblings – Bunty and Babli – divide 10 fruits equally between them. The fruits are divided such that, each of them has at least one banana and at least one apple. Also, the number of appeals and the number of bananas with Bunty is different from the number of appeals and the number of bananas with Babli. When asked about the details of the fruits with each of them, they came up with the following replies. Bunty:I have more than two bananas. Babli has less than two appeals Babli:Bunty has more than two apples. I have less than two bananas. It is known that, of the statements made by each of them, exactly one is true and the other is false, in any order. If the number of apples with Babli is less than the number of apples with Bunty, then how many bananas are there with both of them together?

4

5

6

Cannot be determined

Based on the given information, we know that both Bunty and Babli have at least one banana and one apple. We also know that the number of apples with Babli is less than the number of apples with Bunty.

If the number of apples with Babli is less, then the statement made by Bunty must be true, which is "I have more than two bananas." This means that Bunty has at least three bananas.

Since the statement made by Babli must be false, we can conclude that Bunty does not have more than two apples. Therefore, Bunty has exactly two apples.

Since each of them has 10 fruits in total, and we know that Bunty has three bananas and two apples, Babli must have 10 - 3 - 2 = 5 fruits, which includes at least one banana and one apple.

Therefore, the total number of bananas with both of them together is 3 + 1 = 4. However, since this option is not available in the answer choices, the correct answer is 6, which cannot be determined based on the given information.

Explanation

Based on the given information, we know that both Bunty and Babli have at least one banana and one apple. We also know that the number of apples with Babli is less than the number of apples with Bunty.

If the number of apples with Babli is less, then the statement made by Bunty must be true, which is "I have more than two bananas." This means that Bunty has at least three bananas.

Since the statement made by Babli must be false, we can conclude that Bunty does not have more than two apples. Therefore, Bunty has exactly two apples.

Since each of them has 10 fruits in total, and we know that Bunty has three bananas and two apples, Babli must have 10 - 3 - 2 = 5 fruits, which includes at least one banana and one apple.

Therefore, the total number of bananas with both of them together is 3 + 1 = 4. However, since this option is not available in the answer choices, the correct answer is 6, which cannot be determined based on the given information.

5. Directions for question2 to 5: These questions are based on the information given below: Two siblings – Bunty and Babli – divide 10 fruits equally between them. The fruits are divided such that, each of them has at least one banana and at least one apple. Also, the number of appeals and the number of bananas with Bunty is different from the number of appeals and the number of bananas with Babli. When asked about the details of the fruits with each of them, they came up with the following replies. Bunty:I have more than two bananas. Babli has less than two appeals Babli:Bunty has more than two apples. I have less than two bananas. It is known that, of the statements made by each of them, exactly one is true and the other is false, in any order. If out of the ten fruits, the number of appeals is less than the number of bananas, then which of the following gives the correct combination of the number of bananas and apples, respectively, with Babli?

1, 4

2, 3

3, 2

None of these

If the number of apples is less than the number of bananas, then according to Bunty's statement, he must have more than two bananas. But according to Babli's statement, she has less than two bananas, which contradicts Bunty's statement. Therefore, the given combination of 2 apples and 3 bananas with Babli is not possible. Hence, the correct combination of the number of bananas and apples with Babli is None of these.

Explanation

If the number of apples is less than the number of bananas, then according to Bunty's statement, he must have more than two bananas. But according to Babli's statement, she has less than two bananas, which contradicts Bunty's statement. Therefore, the given combination of 2 apples and 3 bananas with Babli is not possible. Hence, the correct combination of the number of bananas and apples with Babli is None of these.