Question

$A,B,C,D$ and $E$ went to a restaurant. $A$ paid $\frac{1}{2}$ of the bill, $B$ paid $\frac{1}{5}$ of the bill and rest of the bill was shared equally by $C,D,\mathrm{and}E$ .What fraction of the bill was paid by each?

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Solution

**Finding the fraction of the bill was paid by each **$C,D,\mathrm{and}E$**:**

As the bill is paid by all together so let consider the whole bill as $1$

Bill paid by $A=\frac{1}{2}\times 1=\frac{1}{2}$

Bill paid by $B=\frac{1}{5}\times 1=\frac{1}{5}$

Remaining bill$=$Total bill $-$Sum of bill paid by $A$ and $B$.

Therefore, Remaining bill is

$=1-\left(\frac{1}{2}+\frac{1}{5}\right)\phantom{\rule{0ex}{0ex}}=1-\left(\frac{5+2}{10}\right)\phantom{\rule{0ex}{0ex}}=1-\frac{7}{10}\phantom{\rule{0ex}{0ex}}=\frac{10-7}{10}\phantom{\rule{0ex}{0ex}}=\frac{3}{10}$

As, rest of the bill was shared equally by $C,D,\mathrm{and}E$.

Therefore, fractions of the bill was paid by each

$=\frac{3}{10}\xf73\phantom{\rule{0ex}{0ex}}=\frac{3}{10}\times \frac{1}{3}\phantom{\rule{0ex}{0ex}}=\frac{1}{10}$

**Hence, the fraction of bill paid by each **$C,D,\mathrm{and}E$** is **$\frac{1}{10}$.

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