A barrel is full of water. All the water in the barrel is put in equal quantities into three buckets of different sizes. When this operation is completed, it is noted that the first bucket is half full, the second is two-thirds full, while the third is three-quarters full.

If the capacity (in gallons) of the barrel and each of the buckets is a whole number, which of the following options can be the minimum capacity of the barrel?

Option 1  – 6 gallons Three buckets contain 6/3 = 2 gallons each The capacity of the three buckets will be: 1^st bucket = 2 x 2 = 4 gallons, 2^nd bucket = 3/2 x 2 gallons = 3 gallons, 3^rd bucket = 4/3 x 2 gallons = 8/3 gallons (False) The capacity of the buckets should be in whole numbers. Option 2 – 12 gallons Three buckets contain 12/3 = 4 gallons each 1^st bucket = 4 x 2 = 8 gallons, 2^nd bucket = 3/2 x 4 = 6 gallons, 3^rd bucket = 4/3 x 4 = 16/3 gallons (False) Option 3 – 15 gallons Three buckets contain 15/3 = 5 gallons each 1^st bucket = 5 x 2 = 10 gallons, 2^nd bucket = 3/2 x 5 = 15/2 gallons (False) Option 4 – 18 gallons Three buckets contain 18/3 = 6 gallons each 1^st bucket = 6 x 2 = 12 gallons, 2^nd bucket = 3/2 x 6 = 9 gallons, 3^rd bucket = 4/3 x 6 = 8 gallons All conditions are satisfied by option 4.