A can was full of olive oil. Lata draws each time 20% of the volume from the can and replaceswith groundnut oil. Usha draws 10% of the volume and replaces with mustard oil. Starting with Lata, bothrepeats the procedure alternatively two times each. What is the ratio of olive oil, groundnut oil and mustardoil in the end?

Let the amount of olive oil in the jar be 1000 units.

After Lata drew 20% and replaced it with groundnut oil, the amount of olive oil in the mixture will be 800 units, and that of groundnut oil will be 200 units.

Now, Usha will draw 10% of the volume; thus, the amount of olive oil left will be $$800\times\ 0.9\ =\ 720$$. Similarly, the amount of groundnut oil will be 180 units, and the amount of mustard oil will be 100 units.

Again after Lata's draw, the amount of olive oil will become $$720\times\ 0.8=576$$. Similarly, the amount of mustard oil will become 80 units, and the amount of groundnut oil will become  $$180\times\ 0.8+200=344$$ units.

Lastly, Usha will again draw 10% of the volume. Thus, the volume of olive oil will become $$576\times\ 0.9=518.4$$. Similarly, the amount of groundnut oil will become 309.6, and the amount of mustard oil will become $$80\times\ 0.9+100\ =\ 172$$

Thus, the ratio will be 5184 : 3096 : 1720

The correct option is B.

Alternative solution:

Percentage of olive oil in the mixture = $$100\times\ \left(\frac{8}{10}\right)\times\ \left(\frac{9}{10}\right)\times\ \left(\frac{8}{10}\right)\times\ \left(\frac{9}{10}\right)=51.84\%$$.