Consider a group comprising of 4 students- A, B, C and D, who along with other students stand in a row. A and B stand in sixth and seventh positions, respectively from the left. C and D stand in the fourth and fifth positions, respectively from the right. When B and C exchange their positions, then B will be 15th from the left.

With reference to the information given above, which of the following statements are correct?

(A) D's position from the left is 16th.
(B) A's position from the right is 13th.
(C) C's position from the right is 12th, after exchange.
(D) If A and D also exchange their positions between themselves, then D's position from the left is 6th.

Choose the correct answer from the options given below:

(B), (C) and (D) only

The correct answer is Option (4) → (B), (C) and (D) only

1. Analyzing the Initial Positions

• A: 6th from the left.
• B: 7th from the left.
• C: 4th from the right.
• D: 5th from the right.

2. Finding Total Students

When B and C exchange positions, the new position of B is 15th from the left.

Since B is now in the spot originally occupied by C (which was 4th from the right), we can calculate the total number of students ($T$):

$T = (\text{Position from Left}) + (\text{Position from Right}) - 1$

$T = 15 + 4 - 1 = 18 \text{ students total}$

3. Evaluating the Statements

Now that we know there are 18 students, we can find any position from the left using the formula: $\text{Left} = (\text{Total} + 1) - \text{Right}$.

(A) D's position from the left is 16th: D is 5th from the right. $\text{Left} = (18 + 1) - 5 = 14\text{th}$. Statement (A) is Incorrect.

(B) A's position from the right is 13th: A is 6th from the left. $\text{Right} = (18 + 1) - 6 = 13\text{th}$. Statement (B) is Correct.

(C) C's position from the right is 12th, after exchange: After exchange, C moves to B's old spot, which was 7th from the left. $\text{Right} = (18 + 1) - 7 = 12\text{th}$. Statement (C) is Correct.

(D) If A and D exchange, D's position from the left is 6th: A is currently 6th from the left. If D takes A's spot, D will be 6th from the left. Statement (D) is Correct.

Conclusion

Statements (B), (C), and (D) are correct.