A family has 5 members P, Q, R, S, and T, each having a different weight. The following conditions are given:

P weighs twice as much as Q.

Q weighs four and a half times as much as R.

R weighs half as much as S.

S weighs half as much as T.

T weighs less than P but more than R.

Question

A family has 5 members P, Q, R, S, and T, each having a different weight. The following conditions are given:

P weighs twice as much as Q.

Q weighs four and a half times as much as R.

R weighs half as much as S.

S weighs half as much as T.

T weighs less than P but more than R.

Accepted Answer

#### Step 1: Represent Relationships Mathematically
Let the weight of R be $$ x $$. Then, based on the given conditions:  
1. $$ Q = 4.5x $$ (Q weighs 4.5 times as much as R).  
2. $$ P = 2Q = 2(4.5x) = 9x $$ (P weighs twice as much as Q).  
3. $$ S = 2R = 2x $$ (R weighs half as much as S).  
4. $$ T = 2S = 2(2x) = 4x $$ (S weighs half as much as T).

#### Step 2: Compare Weights
From the above relationships:  
- $$ P = 9x $$  
- $$ Q = 4.5x $$  
- $$ R = x $$  
- $$ S = 2x $$  
- $$ T = 4x $$

#### Step 3: Determine the Lightest Member
The weights in ascending order are:  
$$ R (x), S (2x), T (4x), Q (4.5x), P (9x) $$.

Thus, **R is the lightest member**.

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### Final Answer:
The lightest member is **(c) R**.

Answer

Answer

Answer