Discussion
Three friends had dinner at a restaurant. When the bill was received, Amita paid 2/3 as much as Veena paid and Veena paid 1/2 as much as Tanya paid. What fraction of the bill did Veena pay?
Answer: C
Veena paid 3/11 of the bill.
Let Tanya pay \(t\). Veena paid half of that, and Amita two-thirds of Veena's share:
\[ \begin{aligned} V &= t/2,\quad A = \tfrac{2}{3} \cdot \tfrac{t}{2} = \tfrac{t}{3} \\ \text{total} &= t + \tfrac{t}{2} + \tfrac{t}{3} = \tfrac{11t}{6} \end{aligned} \]
Veena's fraction is \((t/2) \div (11t/6) = 3/11\). In whole numbers, Tanya 6, Veena 3, Amita 2, total 11. 1/3 would mean the three paid equally.
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