Answer:
(a) Let \['x'\] marks be the lowest score Then according to the question, we get \[2x+7=87\] \[\Rightarrow \] \[2x=87-7\] \[\Rightarrow \] \[x=\frac{80}{2}=40\] Therefore, the lowest score is 40 marks. (b) Let\['x'\] be the base angle of an isosceles triangle. Then according to the question, we get \[2{{x}^{\text{o}}}+{{40}^{\text{o}}}={{180}^{\text{o}}}\] \[\Rightarrow \] \[2{{x}^{\text{o}}}={{180}^{\text{o}}}-{{40}^{\text{o}}}\] \[\Rightarrow \] \[{{x}^{\text{o}}}=\frac{{{140}^{\text{o}}}}{2}={{70}^{\text{o}}}\] Therefore the base angles of the triangle are \[\text{7}0{}^\circ \] and \[\text{7}0{}^\circ \]. (c) Let \['x'\] runs be the score of Rahul. Then according to the question, we get \[2x+x=198\] \[\Rightarrow \] \[3x=198\] \[\Rightarrow \] \[x=\frac{198}{3}=66\] Therefore, Rahul scores 66 runs, and Sachin scores \[\text{2}\times \text{66}=\text{132}\] runs.
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