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.
Which of the following statement is true?
I. U is younger to W
II. R does not belong to Manipur
III. Sum of the ages of Q and T is more than 35 years
- A.
Both I and II
- B.
Only III
- C.
All I, II and III
- D.
Both II and III
- E.
Only I
Attempted by 3 students.
Show answer & explanation
Correct answer: C
Concept
This is a combined age-and-grouping puzzle. The method is to first pin down every age from the arithmetic relations (each "X is k years younger/older" or "twice older" fixes a number), then use the grouping clues to place each person into a state. A key device is the "same-state" note: when a clue says a person and "the one who is N years old" share a state, that person is themselves not N years old, but they sit in the same state as whoever is N. Solve ages fully, then assign states, then read off the truth of each statement.
Step 1 — fix the ages
R is 29; Q is 3 years older, so Q = 32.
S is twice Q, so S = 64.
V is 61; W is 7 years younger, so W = 54.
The 35-year-old must be P or U. If P were 35 it would be a multiple of 5, which is forbidden, so U = 35; then P = U + 2 = 37, which is not a multiple of 5 — consistent.
X is the youngest, so X = 18. The remaining unfixed person is T; W must share a state with the 51-year-old, and the only age still free is 51, so T = 51.
The complete, forced age list is:
Person | P | Q | R | S | T | U | V | W | X |
|---|---|---|---|---|---|---|---|---|---|
Age | 37 | 32 | 29 | 64 | 51 | 35 | 61 | 54 | 18 |
Step 2 — place the states
S is neither Assam nor Tripura, so S is in Manipur.
The 64-year-old is S; both V (61) and T must share that state, so V and T join Manipur.
W shares a state with the 51-year-old (T), so W is in Manipur too — Manipur is now full with S, T, V, W (four, the maximum).
The 35-year-old (U) is in Tripura; U shares a state with the 29-year-old (R), so R is in Tripura.
P is not in Assam and is in a different state from V and S, so P is in Tripura.
Q shares a state with the 18-year-old (X); the only state left for the two of them is Assam.
State | Members |
|---|---|
Manipur | S, T, V, W |
Tripura | P, R, U |
Assam | Q, X |
Step 3 — test each statement
I. U younger than W: U = 35, W = 54, so U is younger — TRUE.
II. R does not belong to Manipur: R is in Tripura — TRUE.
III. Sum of ages of Q and T > 35: 32 + 51 = 83 > 35 — TRUE.
Cross-check
All nine ages are distinct and lie in 18–68, each state holds between two and four persons (Manipur 4, Tripura 3, Assam 2), and every grouping clue is consistent with this single arrangement. Since all three statements hold, the option naming all three is the answer.