Directions : Study the following information carefully to answer the given…
2022
Directions : Study the following information carefully to answer the given questions:
9 persons P, Q, R, S, T, U, V, W and X of different age belong to three different states viz. Assam, Manipur and Tripura but not necessarily in the same order. Not less than two and not more than four persons belong to any state.
Note: If it is given that A and the one who is 12 years old belong to same state then it means A is not 12 years old.
W and the one who is 51 years old belong to same state. Only Q and the one whose age is 18 years belong to same state. P and V belong to different state. W is 7 years younger to V. S is twice older to Q. P and S belong to different state. V who is 61 years old and the one whose age is 64 years belong to same state. S neither belongs to Assam nor Tripura. The one whose age is 35 years belong to Tripura. No one’s age is less than 18 years and more than 68 years. T and the one who is 64 years old belong to the same state. W does not belong to Tripura. U and the one who is 29 years old belong to same state. P is not belonged to Assam. R is 29 years old and 3 years younger to Q. X is the youngest one. P is 2 years older to U. P’s age is not multiple of 5.
What is the sum of the ages of T, P and W?
- A.
134 years
- B.
142 years
- C.
147 years
- D.
98 years
- E.
None of these
Show answer & explanation
Correct answer: B
Concept
This is a constraint-satisfaction (logical reasoning) puzzle. The method is to FIX every age that a clue determines directly or through a relation, then place people into the three states so that every grouping clue holds and each group has 2 to 4 members. A clue of the form "X and the one who is N years old belong to the same state" is binding, and "Only Q and the 18-year-old belong to the same state" additionally fixes that state's size at exactly two.
Step 1 — Pin every age from the relations
Translate each numeric relation into a value:
V = 61 (given).
R = 29 (given), and R is 3 years younger than Q, so Q = 29 + 3 = 32.
S is twice Q, so S = 2 x 32 = 64.
W is 7 years younger than V, so W = 61 - 7 = 54.
The puzzle names people of age 18, 35 and 51; X is the youngest, so X = 18. The 35- and 51-year-olds are among the people still without an age.
P is 2 years older than U, P is not a multiple of 5, and all ages lie between 18 and 68. Testing the open values, U = 35 and P = 37 is the only pair that keeps every age distinct, places the remaining special ages, and keeps P off a multiple of 5; this forces T = 51.
Step 2 — Resulting ages
Person | Age |
|---|---|
X | 18 |
R | 29 |
Q | 32 |
U | 35 |
P | 37 |
T | 51 |
W | 54 |
V | 61 |
S | 64 |
Step 3 — Place the states (consistency check)
S is neither Assam nor Tripura, so S is in Manipur. "T and the 64-year-old (S) share a state" and "V(61) and the 64-year-old share a state" put T and V in Manipur too; W shares with the 51-year-old (T), so W is in Manipur — a group of 4 (S, T, V, W). "Only Q and the 18-year-old (X) share a state" makes Assam a group of exactly two: Q and X. The remaining people P, R and U form Tripura (size 3): U sits with the 29-year-old (R), the 35-year-old (U) is in Tripura as required, and P is neither Assam nor in S's/V's state, so P belongs in Tripura. Every grouping clue is satisfied and each group size is between 2 and 4.
Step 4 — Answer
Required sum = age of T + age of P + age of W = 51 + 37 + 54 = 142 years.
Cross-check
Re-add independently: 51 + 54 = 105, and 105 + 37 = 142. This matches, and no other age assignment satisfies all the relational and grouping constraints simultaneously, so the sum is uniquely 142.