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
- A, B, C, D and E are sitting on a bench. A and B are sitting next to each other and so are C and D. D is sitting at the extreme left end of the bench and A is sitting at the centre. E is sitting next to B. In which position is A sitting?
- Eight soldiers A, B, C, D, E, F, G and H are sitting in a row facing towards north (not necessarily in the same order). D sits third to the right of A and second to the left of C. Only three soldiers sit between D and E. Only two solders sit between E and F. F sits second to the left of B. A is the neighbour of G. H sits to the right of D. How many soldiers are sitting between H and G?
- Seven judges, A, B, C, D, E, F and G, are sitting in a row of seven seats on the jury panel. C is sitting to the immediate left of A. D is sitting to the immediate right of B and to the immediate left of F. E is sitting on the last seat from the left of the row. C is sitting to right of G and to left of D.
Who is sitting on the fifth position from the left? - Seven friends S1, S2, S3, S4, S5, S6 and S7 are sitting in a row facing towards north (not necessarily in the same order). S4 does not sit at any of the extreme ends. Only three friends sit between S5 and S7. Only two friends sit between S3 and S5. Both S5 and S7 do not sit at any of the extreme ends. S2 sits in the middle of the row.
Who are the neighbours of S2? - Six persons M1, M2, M3, M4, M5 and M6 are sitting in a row facing towards north (not necessarily in the same order). Only three persons sit between M2 and M3. M3 is sitting to the immediate left of M5. Only three persons sit between M1 and M5. M4 sits to the immediate left of M6 and is to the right of M3.
How many persons are sitting between M3 and M6? - Seven persons P, Q, R, S, A, B and D are sitting one above the other on a ladder (not necessarily in the same order). B sits neither at the top nor at the bottom. Only four persons sit between P and R. S sits immediately above A. Only one person sits between R and D. D sits below S. B sits above Q.
Three of the following are similar in a certain way based on their seating arrangement and form a group, which of the following does not belong to that group? - A team of five members is sitting in a row facing towards the north. C is to the left of A and to the right of E. B is to the left of D and to the right of A. Who is sitting in the middle?
- P, Q, R, S, T and U are sitting in a row facing towards the north (not necessarily in the same order). P sits second to the left of S and third to the right of U. Only two persons sit between R and Q. Q is not neighbour of S. Who sits to the immediate left of P?
- 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? - Five boys are sitting on a bench in a hair salon.
(i) P is sitting next to Q.
(ii) S is sitting on the left end of the bench.
(iii) T is sitting next to R.
(iv) T is not sitting with P
(v) P is on the third position from the right.
Where is R sitting?
Important Questions from Linear Arrangement
Seven people, A, B, C, D, E, F and G, are sitting in a straight row facing the north. Only two people sit to the left of C. Only two people sit between A and B. B sits to the left of A. E is an immediate neighbour of A to the right. Only one person sits to the right of D. F is not an immediate neighbour of B. Who sits at the centre?
P, Q, R and S are sitting on a bench and facing in the same direction. P sits next to Q but not next to R. S, who is sitting on the extreme right, does not sit next to either Q or R. How many of them each have two neighbors?
Five friends Ram, Priya, Raunak, Aditya and Shyam are sitting in a row facing north. Raunak is to the right of Shyam and Priya is to the left of Shyam but to the right of Rama. Raunak is to the left of Aditya. Who is fourth from the left end?
Six people P, Q, R, S, T and U sit in a row, not necessarily in the same order. If two persons sit in between P and Q, and two persons sit in between T and U, then how many persons sit in between R and S?
Six persons P, Q, R, S, T and U are sitting in a row facing north (not necessarily in the same order). Q sits fourth to the right of S. One person sits between P and Q. Three persons sit between R and T. R sits immediate left of P. How many persons sit between T and U?
