A vessel contains mixture of petrol and kerosene oil in the ratio 4 : 3. When 105 liters of the mixture is taken out from the vessel and completely replaced by kerosene oil, then the ratio of petrol to kerosene oil in the resulting mixture gets reversed. Find initial quantity of mixture in the vessel.

Applying the replacement formula, the final ratio of petrol to kerosene is the initial ratio multiplied by the fraction representing the remaining mixture after replacement. Let the initial quantity be V liters; the final ratio becomes (4/3) multiplied by ((V minus 105) divided by V). The new ratio is the reverse of the initial ratio, meaning 3 divided by 4. Solving (4/3) multiplied by ((V minus 105) divided by V) equals 3/4 gives ((V minus 105) divided by V) equals 9/16. Solving 16V minus 1680 equals 9V gives 7V equals 1680, so the initial quantity is 420 liters.

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