Question

$\text{A jug contains}4\frac{5}{7}\text{litre of water. From this,}2\frac{3}{14}\text{litres are used and further}\frac{3}{7}\text{litres of}\text{water are drained off. Calculate the final volume}\text{of water remaining in the jug.}$

• A. $2\frac{3}{14}\text{L}$
• B. $2\frac{3}{7}\text{L}$
• C. $2\frac{1}{14}\text{L}$
• D. $2\frac{1}{7}\text{L}$

Answer 1

The correct option is C $2\frac{1}{14}\text{L}$

$\text{Initial volume of water}=4\frac{5}{7}\text{L}\text{Volume of water used}=2\frac{3}{14}\text{L}\text{∴ Volume of water remaining after using:}=(4\frac{5}{7}-2\frac{3}{14})\text{L}$

$\text{Calculating}4\frac{5}{7}-2\frac{3}{14}\text{we get:}$

$Wholenumberpart=4-2=2$

$Fractionalpart=\frac{5}{7}-\frac{3}{14}=\frac{5\times 2}{7\times 2}-\frac{3}{14}=\frac{10}{14}-\frac{3}{14}=\frac{7}{14}=\frac{7÷7}{14÷7}=\frac{1}{2}$

$\text{Combining the whole number and the}\text{fractional parts, we get:}$

$4\frac{5}{7}-2\frac{3}{14}=2\frac{1}{2}$

$\text{So, the volume of water remaining in}\text{the jug after usage is}2\frac{1}{2}\text{L}$

$\text{Now, from this}2\frac{1}{2}\text{litres, further}\frac{3}{7}\text{litres of water are drained off.}$

$\text{So, the volume of water remaining after}\text{draining is}=(2\frac{1}{2}-\frac{3}{7})\text{L}$


$\text{Calculating}2\frac{1}{2}-\frac{3}{7}\text{we get:}$

$Wholenumberpart=2-0=2$

$Fractionalpart=\frac{1}{2}-\frac{3}{7}=\frac{1\times 7}{2\times 7}-\frac{3\times 2}{7\times 2}=\frac{7}{14}-\frac{6}{14}=\frac{(7-6)}{14}=\frac{1}{14}$

$\text{Combining both the whole number}\text{and fractional parts, we get:}$

$2\frac{1}{2}-\frac{3}{7}=2\frac{1}{14}$

$\therefore \text{The volume of water finally remaining}\text{in the jug is}2\frac{1}{14}\text{L}$