Answer the question given below based on the given information. A jeweler has five gold articles 'P', 'Q', 'R', 'S' and 'T', each of which weighs differently. 'T' weighs thrice as much as 'S'. 'S' weighs four times as much as 'R'. 'R' weighs half as much as 'Q'. 'Q' weighs half as much as 'P'. 'P' weighs less than 'T' but more than 'R'. Which of the following gold articles is the lightest in weight?
Identifying the Lightest Gold Article
The problem asks us to find the lightest among five gold articles (P, Q, R, S, T) based on given weight relationships.
Analyzing Weight Relationships
We are given the following information:
- 'T' weighs thrice as much as 'S': $ T = 3S $
- 'S' weighs four times as much as 'R': $ S = 4R $
- 'R' weighs half as much as 'Q': $ R = \frac{Q}{2} $ which implies $ Q = 2R $
- 'Q' weighs half as much as 'P': $ Q = \frac{P}{2} $ which implies $ P = 2Q $
- 'P' weighs less than 'T' but more than 'R': $ R < P < T $
Calculating Relative Weights
Let's express the weights of all articles in terms of the lightest possible base unit, which appears to be 'R'.
- Weight of R: $ W_R = R $
- Weight of Q: Since $ Q = 2R $, $ W_Q = 2R $
- Weight of P: Since $ P = 2Q $ and $ Q = 2R $, then $ P = 2(2R) = 4R $. So, $ W_P = 4R $
- Weight of S: Since $ S = 4R $, $ W_S = 4R $
- Weight of T: Since $ T = 3S $ and $ S = 4R $, then $ T = 3(4R) = 12R $. So, $ W_T = 12R $
The relative weights are:
- $ R = 1R $
- $ Q = 2R $
- $ P = 4R $
- $ S = 4R $
- $ T = 12R $
We verify the condition $ R < P < T $. Since $ R $ must be a positive weight, $ 1R < 4R < 12R $ is true.
Determining the Lightest Article
Comparing the relative weights:
- R weighs $ 1R $
- Q weighs $ 2R $
- P weighs $ 4R $
- S weighs $ 4R $
- T weighs $ 12R $
The smallest weight is $ 1R $, which corresponds to article 'R'. Note that 'P' and 'S' have equal weight ($ 4R $).
Final Answer
The lightest gold article is 'R'. This corresponds to Option A.
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