Question

An oil container had $2\frac{3}{5}L$ of oil . Ananya put $1\frac{1}{3}L$ more oil in it .But later she found that there was a leakage in the container. She transferred the remaining oil into a new container and found that it was only $2\frac{3}{4}L$. How much oil had leaked ?

Answer 1

Step 1: Converting mixed fractions into improper fractions

Oil in the container $=2\frac{3}{5}L$

$$\begin{gathered} =\frac{5\times 2+3}{5} \\ =\frac{13}{5}L \end{gathered}$$

Ananya put in the container $=1\frac{1}{3}L$

$$\begin{gathered} =\frac{3\times 1+1}{3} \\ =\frac{4}{3}L \end{gathered}$$

Oil left after leakage$=2\frac{3}{4}L$

$$\begin{gathered} =\frac{2\times 4+3}{4} \\ =\frac{11}{4}L \end{gathered}$$

Step 2: Finding the total oil in the container before leakage

Total oil in the container before leakage

$$\begin{gathered} =\frac{13}{5}L+\frac{4}{3}L \\ =\frac{39+20}{15}[\because LCM(5,3)=15] \\ =\frac{59}{15}L \end{gathered}$$

Step 3: Amount of oil leaked

Amount of oil leaked can be found by subtracting amount of oil left after leakage from total oil in container before leakage

$$\begin{gathered} =\frac{59}{15}L-\frac{11}{4}L \\ =\frac{59\times 4-11\times 15}{60}[\because LCM(15,4)=60] \\ =\frac{236-165}{60} \\ =\frac{71}{60}L \end{gathered}$$

Hence, amount of oil leaked is $\frac{71}{60}L$