Question
If x = 3t, y = $$\frac{1}{2}$$(t + 1), then the value of t for which x = 2y is?
Answer: Option B
$$\eqalign{
& x = 3t\,......(i) \cr
& y = \frac{1}{2}\left( {t + 1} \right) \cr
& x = 2y \cr
& \Rightarrow x = 2 \times \frac{1}{2}\left( {t + 1} \right) \cr
& \Rightarrow x = t + 1\,......(ii) \cr
& \therefore 3t = t + 1 \cr
& \left( {{\text{From equation (i) and (ii)}}} \right) \cr
& \Rightarrow 2t = 1 \cr
& \Rightarrow t = \frac{1}{2} \cr} $$
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$$\eqalign{
& x = 3t\,......(i) \cr
& y = \frac{1}{2}\left( {t + 1} \right) \cr
& x = 2y \cr
& \Rightarrow x = 2 \times \frac{1}{2}\left( {t + 1} \right) \cr
& \Rightarrow x = t + 1\,......(ii) \cr
& \therefore 3t = t + 1 \cr
& \left( {{\text{From equation (i) and (ii)}}} \right) \cr
& \Rightarrow 2t = 1 \cr
& \Rightarrow t = \frac{1}{2} \cr} $$
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