People: M, N, O, P, Q, R, S, and T
Arrangements: Circular and square
- The person who is 20 years old is sitting third to the right of M.
(As it is a circular arrangement, we can randomly place M and then accordingly place the person who is 20 years old.)
- O is sitting third to the left of S, who is one of the immediate neighbours of M.
(Implies, S is either to the left of M or to the right of him.)
- Either T or N is sitting opposite to O who is 6 years older than the person sitting opposite to him.
(If we place S to the immediate left of M, then O would be opposite to M. Which is not true, implies S is to the immediate right of M and O is second to the left of M.)
- Q is sitting third to the right of P, whose age is numerically 25% more than that of the person who is to his immediate left.
(There is only one way for this to be possible i.e. if Q is to the immediate left of M and P opposite to M.
Also, the person sitting to the immediate left of P is 20 years old, implies P is 25 years old.)
- R is sitting second to the right of T and third to the left of the person who is 7 years younger than the person sitting opposite to him.
(If T is sitting opposite to O then we cannot place R second to the right of T, as P is already there. So, T is to the immediate left of P and R is to the immediate right of R (as it is the only possibility.)
It also implies, R is third to the left of M which further implies M is 18 years old (25 – 7 = 18).)
- Q is 4 years older than T but three years younger than the person who is to his immediate left.
(Clearly, T is 20 years old implies, Q is 24 years old.
O is to the immediate left of Q, implies O is 27 years old.
Also, as N is 6 years younger than O, implies N is 21 years old.)
- The average age of R, S, and M is 21 years and the age of S is twice the age of R.
(Implies total age of R, S, and M is 63 years. Which means the total age of R and S is 45 years (as M is 18 years old.)
Also, S = 2R
And, R + S = 45
Implies, R = 15 years and S = 30 years)
Square arrangement:
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People whose age is an even number are sitting at the edges and the people whose age is an odd number are sitting at the corners.
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The youngest person is facing either north or north-east.
(R is the youngest person and his age is 15 years which is odd. Implies, R is facing north-east.)
- The oldest person is facing either south direction or north-west.
(S is the oldest person and he is 30 years old, which is an even number. Implies, he is sitting on the edge facing south.)
- The person who is three years younger than S is facing south-east.
(O is three years younger than S as O is 27 years old. Hence, he is facing south-east.)
- Q is one of the immediate neighbours of O.
(Implies, Q is to the immediate left of O.)
- N and P are the immediate neighbours of M.
(Age of N and P are 21 and 25 years old respectively. Implies they are at the corners which further implies M is facing west.
Age of T is 20 years, which is even. Hence T is facing north as it is the only position left for him.)
P and N are the immediate neighbours of T in the circular arrangement and their ages are 25 and 21 respectively. Hence, their average age is 23.
