Question

8 people A - H are sitting in line facing north.
I. D sits immediate to the right of A.
II. E sits at the left end.
III. C sits 3\(^{rd}\) to the left of D.
IV. B sits immediate right of E.
V. H, B & G sits together with H in middle.
VI. F sits immediately left of A.
Which of the following is the correct arrangement?

• A. EBHGCEAD
• B. EAHDB GFC
• C. ACGDHBFC
• D. EBHGCFAD

Hint:

In linear arrangement problems, start with the most definite clues, like positions at the ends. Then, look for blocks of people who sit together and try to fit these blocks into the arrangement.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
We need to determine the linear seating arrangement of 8 people (A to H) based on a set of given clues. All are facing North.
Step 2: Detailed Explanation:
Let's break down and combine the clues step-by-step. The 8 positions are:
_ _ _ _ _ _ _ _

Clue II: E sits at the left end.
E _ _ _ _ _ _ _

Clue IV: B sits immediate right of E.
E B _ _ _ _ _ _

Clue V: H, B & G sits together with H in the middle. This means the block is B H G. Since we already placed B, H and G must be to its right.
E B H G _ _ _ _

Clue I & VI: D sits immediate to the right of A (AD), and F sits immediately left of A (FA). Combining these, we get a block of three people: F A D.

Now we have the group E B H G and the group F A D. We have one person left, C. We have 4 empty seats: E B H G \underline{\hspace{0.5cm}} \underline{\hspace{0.5cm}} \underline{\hspace{0.5cm}} \underline{\hspace{0.5cm}}. The FAD block and C must fit here.

Clue III: C sits 3\(^{rd}\) to the left of D. This means there are two people between C and D (C _ _ D).

Let's try to place the F A D block at the end of the line:
E B H G _ F A D
The only person left is C, so C must be in the 5th position.
E B H G C F A D

Let's verify this arrangement with Clue III. C is in the 5th position and D is in the 8th position. C is indeed 3rd to the left of D. All conditions are satisfied.
Step 3: Final Answer:
The final correct arrangement is E B H G C F A D. This matches option (D).