Logic Puzzle: Seating Arrangement and Ages
This problem requires determining the seating positions and ages of six individuals based on given clues to find the sum of ages for A and B.
1. Assigning Ages Based on Clues
The ages are successive multiples of 3. Given that D has the maximum age of 18 years, the ages from left to right must be:
- Position 1: $3$
- Position 2: $6$
- Position 3: $9$
- Position 4: $12$
- Position 5: $15$
- Position 6: $18$
Since D has the maximum age (18 years), D is located at the rightmost position ($P_6$).
2. Determining Relative Positions
Analyze the positional clues:
- 'A is immediate left of E' implies the arrangement $AE$.
- 'B is second to the right of A' means B is at position $A+2$. Combined with $AE$, this forms a block $AEB$.
- 'C sits to the left of E' implies $C$ is somewhere before $E$.
- 'Only three persons sit between C and F'.
3. Deriving the Final Arrangement
Consider the possible placements for the $AEB$ block:
- Attempt 1: $A E B$ in positions $P_1, P_2, P_3$. The row starts $A \ E \ B \ \_ \ \_ \ D$.
- Ages: $A=3, E=6, B=9, D=18$.
- The clue '$C$ sits to the left of $E$' cannot be satisfied as $P_1$ (left of $E$ at $P_2$) is occupied by $A$. This case fails.
- Attempt 2: $A E B$ in positions $P_2, P_3, P_4$. The row is $\_ \ A \ E \ B \ \_ \ D$.
- Ages: $D=18$ (at $P_6$). The remaining positions $P_1$ and $P_5$ are for $C$ and $F$.
- $E$ is at $P_3$. '$C$ sits to the left of $E$' implies $C$ must be at $P_1$.
- The arrangement becomes $C \ A \ E \ B \ P_5 \ D$. $P_5$ must be $F$.
- Row: $C \ A \ E \ B \ F \ D$.
- Check '3 persons between C and F': $C$ is at $P_1$, $F$ is at $P_5$. The persons $A, E, B$ (at $P_2, P_3, P_4$) are between them. This condition is met. This is the correct arrangement.
- Attempt 3: $A E B$ in positions $P_3, P_4, P_5$. The row is $\_ \ \_ \ A \ E \ B \ D$.
- Ages: $A=9, E=12, B=15, D=18$.
- $P_1$ and $P_2$ are for $C$ and $F$. The maximum number of persons between $C$ and $F$ is 1 (if they are at $P_1, P_2$). This violates the condition of 3 persons between them. This case fails.
The confirmed arrangement is $C \ A \ E \ B \ F \ D$ with ages $3, 6, 9, 12, 15, 18$ respectively.
4. Calculating the Total Age of A and B
In the confirmed arrangement:
- A is at Position 2, Age(A) = $6$ years.
- B is at Position 4, Age(B) = $12$ years.
The total age of A and B is Age(A) + Age(B) = $6 + 12 = 18$ years.
Similar Questions
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- Study the given information carefully and answer the question that follows.
Eight persons A, B, C, D, E, F, G and H are sitting in a row facing the north but not necessarily in the same order. Three persons are sitting between D and F. G is sitting to the immediate left of D. Only one person is sitting between E and B. E is not sitting at any of the extreme ends. More than three persons are sitting between H and A. A is sitting to the left of H. Either H or A is sitting at one of the ends. Neither D nor F is sitting at any of the extreme ends. E and B are not the immediate neighbours of G and D. E is sitting to the right of B.
How many persons are sitting between H and C?
Important Questions from Linear Arrangement
M, N, L, O, Q and H are sitting in a row. Q and H are in the centre. M and N are at the ends. L is sitting to the immediate left of N. Who is to the right of M?
Five friends, Shruti, Shreya, Anup, Ankit and Kiran, are sitting in a row facing towards the south. Shruti is between Shreya and Anup. Kiran and Shreya are sitting at the extreme ends of the west and east, respectively. Who is sitting in the middle?
Five students are standing in a line. Suman is standing next to Pranav but not next to Deena. Kumar is standing next to Raju, who is standing on the extreme left, and Deena is not standing next to Kumar.
Who is standing in the middle?Eight friends, A, B, C, D, E, F, G and H, are sitting in a straight line, all facing the north. F is sitting between D and G. B is sitting between H and A. E is third to the left of G. G is sitting at one of the corners. H is third to the left of C. Who is sitting between A and E?
Five students are sitting in a row. Akbar is to the left of the person sitting in the middle, but to the right of Sekar. Prakash is to the right of Deva, and Ram is to the right of Prakash. Ram is second from the person sitting in the middle. Who is the person sitting in the middle?
