Question Details

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.

How many persons are lighter than S?

Options

A

Two

B

One

C

Four

D

Three

E

None

Show Answer

Correct Answer :

Option A

Two

Two

Solution :

Step-by-step Explanation:

Let the six persons be arranged in descending order of their weight from left to right (from the heaviest to the lightest):
Position 1 (Heaviest) > Position 2 > Position 3 > Position 4 > Position 5 > Position 6 (Lightest)

Step 1: Determine the positions of Q and T
The problem states: "Only T is lighter than Q whose weight is 17kg."
This means T is the lightest person (at Position 6) and Q is the second lightest person (at Position 5) with a weight of 17 kg.
So, the arrangement is:
_ > _ > _ > _ > Q (17 kg) > T

Step 2: Calculate the weights of S and N
We are given:
- "S is twice heavier than Q"

Weight of S = 2 * Weight of Q = 2 * 17 = 34 kg

- "S is 14 kg lighter than N"

Weight of N = Weight of S + 14 = 34 + 14 = 48 kg

Step 3: Analyze the positions of M and S
We are given: "Two persons between M and S."
Since Q is at Position 5 and T is at Position 6, S can only be placed at Position 1, 2, 3, or 4.
- If S is at Position 1, then M must be at Position 4 (with Positions 2 and 3 in between). However, since Weight of N (48 kg) > Weight of S (34 kg), N must be to the left of S. If S is at Position 1, no one can be heavier than S. Thus, S cannot be at Position 1.
- Therefore, S must be at Position 4, and M must be at Position 1.
The arrangement now looks like:
M > _ > _ > S (34 kg) > Q (17 kg) > T

Step 4: Place the remaining persons N and R
We need to place N and R in the vacant Positions 2 and 3.
We are given: "R is not the second heaviest among all."
Position 2 represents the second heaviest person, so R cannot be at Position 2. Thus, R must be at Position 3, and N must be at Position 2.
The final arrangement from heaviest to lightest is:
M > N (48 kg) > R > S (34 kg) > Q (17 kg) > T

Conclusion:
Looking at the final arrangement, the persons lighter than S are Q and T. Thus, there are exactly two persons lighter than S.

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