In a hall there are seven children (including girls and boys) P, Q, R, S, T, U and V. They sit on three benches I, II and III. Such that at least two children on each bench and at least one girl on each bench. R who is a girl child, does not sit with P, T and S. U the boy child sits with only Q. P sits on the bench I with his best friends. V sits on the bench III. T is the brother of R. Who sits with R?
- AS
- BU
- CQ
- DV
Solution & Step-by-step Explanation
Let's logically break down the rules and constraints given:
Total children = 7 (P, Q, R, S, T, U, V).
Benches = I, II, III.
Distribution constraint: At least 2 children per bench. Since total children = 7, the allocation across the three benches must be 3,2,2.
Gender constraint: At least 1 girl on each bench.
U (boy) sits with only Q. This implies that the bench containing U has exactly 2 people: U and Q.
P sits on Bench I. Since U and Q occupy a bench entirely by themselves, that bench must be Bench II or Bench III.
V sits on Bench III.
Since U and Q are alone together on a bench, and Bench III contains V, U and Q must be on Bench II.
Bench II: U, Q
Now we are left with Benches I and III, and children P, R, S, T, V.
Bench I has P.
Bench III has V.
R is a girl and does not sit with P, T, or S.
Since R cannot sit with P, she cannot be on Bench I.
Since U and Q are alone on Bench II, R cannot be on Bench II.
Therefore, R must sit on Bench III.
Let's look at who sits on Bench III: V is already on Bench III. So R sits with V.
Let's double-check the remaining positions to ensure consistency:
Bench I: P, T, S (3 people)
Bench II: U, Q (2 people)
Bench III: V, R (2 people)
This fulfills all conditions perfectly. Thus, V sits with R.
Total children = 7 (P, Q, R, S, T, U, V).
Benches = I, II, III.
Distribution constraint: At least 2 children per bench. Since total children = 7, the allocation across the three benches must be 3,2,2.
Gender constraint: At least 1 girl on each bench.
U (boy) sits with only Q. This implies that the bench containing U has exactly 2 people: U and Q.
P sits on Bench I. Since U and Q occupy a bench entirely by themselves, that bench must be Bench II or Bench III.
V sits on Bench III.
Since U and Q are alone together on a bench, and Bench III contains V, U and Q must be on Bench II.
Bench II: U, Q
Now we are left with Benches I and III, and children P, R, S, T, V.
Bench I has P.
Bench III has V.
R is a girl and does not sit with P, T, or S.
Since R cannot sit with P, she cannot be on Bench I.
Since U and Q are alone on Bench II, R cannot be on Bench II.
Therefore, R must sit on Bench III.
Let's look at who sits on Bench III: V is already on Bench III. So R sits with V.
Let's double-check the remaining positions to ensure consistency:
Bench I: P, T, S (3 people)
Bench II: U, Q (2 people)
Bench III: V, R (2 people)
This fulfills all conditions perfectly. Thus, V sits with R.