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?

Answer 1

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

$$\begin{gathered} =1-\left(\frac{1}{2}+\frac{1}{5}\right) \\ =1-\left(\frac{5+2}{10}\right) \\ =1-\frac{7}{10} \\ =\frac{10-7}{10} \\ =\frac{3}{10} \end{gathered}$$

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

Therefore, fractions of the bill was paid by each

$$\begin{gathered} =\frac{3}{10}÷3 \\ =\frac{3}{10}\times \frac{1}{3} \\ =\frac{1}{10} \end{gathered}$$

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