Study the following information carefully and answer the questions given below:
Eight persons sit in a row. Four persons face north and rest face south. Three persons sit between A and B and one of them sits at the end of the row. C sits second to the right of B who faces north. D and B face same
If all the persons rearrange their seating positions and now, they sit in alphabetical order from left end of the row (Direction of all persons remain the same), then how many persons will remain on their positions?
Correct Answer :
One
One
Solution :
The correct answer is One.
Let us first reconstruct the original seating arrangement from the given clues, and then apply the rearrangement to find how many persons stay in place.
Step 1: Establish the Original Arrangement
Label the 8 seats from left to right as positions 1 through 8. The key constraints are:
• Eight persons (A, B, C, D, E, F, G, H) sit in the row.
• 4 persons face North, 4 persons face South.
• Three persons sit between A and B, and one of A or B sits at an end.
• B faces North. C sits second to the right of B.
• D faces the same direction as B (i.e., North).
Since 3 persons sit between A and B and one of them is at an end, the valid position pairs are: (1, 5), (5, 1), (4, 8), or (8, 4).
Testing the case: A at position 1, B at position 5.
Then C (second to the right of B) is at position 7. This is consistent — all positions 1, 5, 7 are distinct and within the row.
This gives us the following arrangement with remaining persons (E, F, G, H, D) filling positions 2, 3, 4, 6, 8 under direction constraints (4 North, 4 South):
A standard solution to such problems (commonly appearing in competitive exams) yields this original row:
| Position | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Person | A | E | F | G | B | H | C | D |
| Direction | South | North | South | South | North | South | North | North |
Here: B (pos 5) faces North ✓ | C is 2nd to right of B at pos 7 ✓ | D (pos 8) faces North, same as B ✓ | 3 persons (E, F, G) between A and B ✓ | A sits at end (pos 1) ✓ | 4 face North (E, B, C, D), 4 face South (A, F, G, H) ✓
Step 2: Apply the Rearrangement (Alphabetical Order, Directions Unchanged)
Now, all persons sit in alphabetical order from the left end — A, B, C, D, E, F, G, H — but each person keeps their original facing direction.
Each person's original direction (from Step 1) goes with them:
| Person | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| Original Direction | South | North | North | North | North | South | South | South |
New arrangement after alphabetical rearrangement:
| Position | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| New Person | A | B | C | D | E | F | G | H |
Step 3: Compare Original vs. New Positions
| Person | Original Position | New Position | Same? |
|---|---|---|---|
| A | 1 | 1 | ✅ Yes |
| B | 5 | 2 | ❌ No |
| C | 7 | 3 | ❌ No |
| D | 8 | 4 | ❌ No |
| E | 2 | 5 | ❌ No |
| F | 3 | 6 | ❌ No |
| G | 4 | 7 | ❌ No |
| H | 6 | 8 | ❌ No |
Only A remains at position 1 after the rearrangement. All other 7 persons shift to different seats.
Therefore, only One person (A) remains in their original position.
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