Four friends went to a restaurant- When the bill arrived- Jon paid 15 as much as Jackey- Jackey paid 12 as much as Jenny paid- and Jenny paid 12 as much as Roy paid- What fraction did Jackey pay-

Let Roy's share = x Jenny's share = x2 Jackey's share = nbsp;x2×12 = x4 Jon's share = nbsp;x2×12×15 = x20 Total bill = Sum of all their shares = x + x2 ...

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Byju's Answer

Standard IX

Mathematics

Ratio and Proportion

Four friends ...

Question

Four friends went to a restaurant. When the bill arrived, Jon paid $\frac{1}{5}$ as much as Jackey, Jackey paid $\frac{1}{2}$ as much as Jenny paid, and Jenny paid $\frac{1}{2}$ as much as Roy paid. What fraction did Jackey pay?

\frac{5}{36}

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\frac{9}{20}

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\frac{1}{5}

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\frac{5}{30}

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Solution

The correct option is A $\frac{5}{36}$
Let Roy's share = x

Jenny's share = $\frac{x}{2}$

Jackey's share = $\frac{x}{2} \times \frac{1}{2} = \frac{x}{4}$

Jon's share = $\frac{x}{2} \times \frac{1}{2} \times \frac{1}{5} = \frac{x}{20}$

Total bill = Sum of all their shares

$= x + \frac{x}{2} + \frac{x}{4} + \frac{x}{20}$

$= \frac{20 x + 10 x + 5 x + x}{20}$

$= \frac{36 x}{20}$

$= \frac{9 x}{5}$

Let's find the fraction of the money paid by Jackey.

We know that Jackey's share is $\frac{x}{4}$ .

$Fraction that Jackey paid = \frac{Jackey's share}{Total bill}$

$= \frac{\frac{x}{4}}{\frac{9 x}{5}}$

$= \frac{x}{4} \times \frac{5}{9 x}$

$= \frac{5}{36}$

$= \frac{5}{36}$

Therefore, the fraction of amount Jackey paid is $\frac{5}{36} .$

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Four friends went to a restaurant. When the bill arrived, Jon paid 15 as much as Jackey, Jackey paid 12 as much as Jenny paid, and Jenny paid 12 as much as Roy paid. What fraction did Jackey pay?

Four friends went to a restaurant. When the bill arrived, Jon paid $\frac{1}{5}$ as much as Jackey, Jackey paid $\frac{1}{2}$ as much as Jenny paid, and Jenny paid $\frac{1}{2}$ as much as Roy paid. What fraction did Jackey pay?