Study the following information carefully and answer the questions given below-
Six persons are arranged in descending order according to their weight from left to right. Only T is lighter than Q whose weight is 17kg. S is twice heavier than Q and 14 kg lighter than N. Two persons between M and S. R is not the second heaviest among all.
Who is the heaviest among all?
Correct Answer :
M
Solution :
To find the heaviest person among the six, let us analyze the given information step-by-step.
We are arranging six persons in descending order of their weight from left to right:
1st (Heaviest) > 2nd > 3rd > 4th > 5th > 6th (Lightest)
Step 1: Place T and Q.
The problem states: "Only T is lighter than Q".
This means Q is heavier than only one person (which is T), so Q must be in the 5th position and T must be in the 6th (lightest) position.
Arrangement so far: _ > _ > _ > _ > Q > T
We are also given that the weight of Q is 17 kg.
Step 2: Determine the weights of S and N.
- "S is twice heavier than Q" ⇒ Weight of S = 2 �� 17 kg = 34 kg.
- "S is 14 kg lighter than N" ⇒ Weight of N = Weight of S + 14 kg = 34 kg + 14 kg = 48 kg.
Since N (48 kg) > S (34 kg) > Q (17 kg), N must be placed to the left of S, and S must be placed to the left of Q.
Step 3: Analyze the positions of M and S.
We have 4 vacant positions left: 1st, 2nd, 3rd, and 4th.
The problem states: "Two persons between M and S."
Let's look at the remaining slots: _ (1st) > _ (2nd) > _ (3rd) > _ (4th) > Q (5th) > T (6th).
Since S must be heavier than Q (17 kg), S can only be in the 1st, 2nd, 3rd, or 4th position.
If S is in the 4th position, then M must be in the 1st position (leaving 2nd and 3rd between them).
If S is in the 3rd position, M cannot be placed because we need two positions between S and M, which is impossible in the remaining slots.
If S is in the 2nd position, M cannot be placed either.
If S is in the 1st position, M must be in the 4th position.
Thus, we have two possibilities for S and M:
Case A: M (1st) > _ (2nd) > _ (3rd) > S (4th) > Q (5th) > T (6th)
Case B: S (1st) > _ (2nd) > _ (3rd) > M (4th) > Q (5th) > T (6th)
Step 4: Place N and R to find the correct case.
We know that N (48 kg) is heavier than S (34 kg), so N must be to the left of S.
In Case B, S is in the 1st position, so N cannot be placed to the left of S. Therefore, Case B is invalid.
This leaves us with Case A: M (1st) > _ (2nd) > _ (3rd) > S (4th) > Q (5th) > T (6th).
Since N must be to the left of S (4th), the two available slots for N are the 2nd and 3rd positions. Hence, N must be either 2nd or 3rd.
The remaining person is R. R must occupy the other slot among the 2nd and 3rd positions.
The constraint states: "R is not the second heaviest among all."
This means R cannot be in the 2nd position. Therefore, R must be in the 3rd position, and N must be in the 2nd position.
Final Arrangement:
M (1st) > N (2nd) > R (3rd) > S (4th) > Q (5th) > T (6th)
Therefore, M is the heaviest person among all.
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