a thief steals four gallons of liquid soap kept in a train compartment's bathroom from a container that is

Question

full of liquid soap. he then fills it with water to avoid detection. unable to resist the temptation, he steals 4 gallons of mixture again, and fills it with water. when the liquid soap is checked , it is found that ratio of soap left to that of the water is 36:13. what was the initial amount of the soap in the container. .

please explain, me in detail,
and tell me if any technique related to allegations,
how to solve this type of question.
try to solve in the shorter way.

ans should be in litres,

Answer 1

FIRST filching: Let V be the volume of the container in gallons. After the robbery and the filling with water, the AMOUNT of soap in the container is V-4, and the fractional concentration of soap is ... V-4/V. The amount of water is 4 gallons and fractional conc is 4/V.
SECOND filching: The amount of soap taken is
4(V-4)/V, leaving (V-4)(1-4/V) as the amount behind. The amount of water taken is. The amount of water taken is 4(4/V), leaving 4-4(4/V) behind.
So to find V, 13* [(V-4)(1-4/V)] = 36*[4-4(4/V)]
You can express V in liter by multipling by 3.78.