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?

ABC26GN1130 · Simplification

Subject: General Aptitude · Chapter: Simplification · Exam: 2005 · Marks: · Difficulty:

Three friends had dinner at a restaurant. When the bill was received, Amita paid $\frac{2}{3}$ as much as Veena paid and Veena paid $\frac{1}{2}$ as much as Tanya paid. What fraction of the bill did Veena pay?

(a)$\frac{1}{3}$

(b)$\frac{3}{11}$

(c)$\frac{12}{31}$

(d)$\frac{5}{8}$

Answer

Answer (as printed): B

Explanation

Let Tanya's share $=₹ x$. Then, Veena's share $$\begin{gathered} =₹\left(\frac{x}{2}\right), \text { Amita's share }=₹\left(\frac{2}{3} \times \frac{x}{2}\right)=₹\left(\frac{x}{3}\right) . \\ \text { Total bill }=₹\left(x+\frac{x}{2}+\frac{x}{3}\right)=₹\left(\frac{11 x}{6}\right) . \\ \therefore \quad \text { Required fraction }=\left(\frac{x}{2} \times \frac{6}{11 x}\right)=\frac{3}{11} . \end{gathered}$$

Explanation as extracted from the printed page; notation may be imperfect.

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