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Three friends, Vinitha, Mira and Neethu, had lunch at a hotel. When the bill was received. Vinitha paid \(\frac{2}{3}\) as much as Mira paid and Mira paid \(\frac{1}{2}\) as much as Neethu paid. What fraction of the bill did Mira pay?

Three friends, Vinitha, Mira and Neethu, had lunch at a hotel. When the bill was received. Vinitha paid \(\frac{2}{3}\) as much as Mira paid and Mira paid \(\frac{1}{2}\) as much as Neethu paid. What fraction of the bill did Mira pay? Correct Answer <span class="math-tex">\(\frac{3}{11}\)</span>

1. Three friends, Vinitha, Mira and Neethu, had lunch at a hotel.

2. When the bill was received, Vinitha paid 2/3 as much as Mira paid and Mira paid 1/2 as much as Neethu paid.

Vinitha = 2/3 × Mira       ---(i)

Mira = 1/2 × Neethu

2 × Mira = Neethu       ---(ii)

As, the total bill was divided among them

So, Vinitha + Mira + Neethu = 1       ---(iii)

Substituting the value of (i) and (ii) in (iii), we get:

Assume total bill is X.

2/3 × Mira + Mira + 2 × Mira = X

Mira = 3/11 × X

Hence, Mira paid ‘3/11th’ fraction of the bill.

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