There is a vessel that contains 4L of water.
By pumping 1L out of the vessel and put in 1L of soy sauce instead.
Then, pumping 1L out of the vessel and put in 1L of soy sauce instead.
When I repeat this operation four times in total, how many does the soy sauce remain in this vessel ?
By pumping 1L out of the vessel and put in 1L of soy sauce instead.
Then, pumping 1L out of the vessel and put in 1L of soy sauce instead.
When I repeat this operation four times in total, how many does the soy sauce remain in this vessel ?
Answer
The amount of the water which will remain in the 4th time can be calculated in the same way is calculated that 4 × (1 - 1/4) × (1 - 1/4) × (1 - 1/4) × (1 - 1/4) = 81/64L.
Therefore, the amount of the soy sauce which remains is 4L - 81/64L = 175/64L.
175/64 L
Solution
The amount of the liquid (water + soy sauce) at the time of four operations finishing is 4L.
The amount of the remaining soy sauce should just subtract the amount of the water remaining from the whole amount.
Then the amount of the remaining water should be calculated.
The amount of the water which remains in a container by the 1st operation is 4L × (1 - 1/4) =3L.
The amount of the water pumped out by the 2nd operation is 3L × 1/4 and remains 3L × (1 - 1/4) = 9/4 L.
The amount of the water remains by the 3rd time becomes 9/4 × (1 - 1/4).
The amount of the remaining soy sauce should just subtract the amount of the water remaining from the whole amount.
Then the amount of the remaining water should be calculated.
The amount of the water which remains in a container by the 1st operation is 4L × (1 - 1/4) =3L.
The amount of the water pumped out by the 2nd operation is 3L × 1/4 and remains 3L × (1 - 1/4) = 9/4 L.
The amount of the water remains by the 3rd time becomes 9/4 × (1 - 1/4).
The amount of the water which will remain in the 4th time can be calculated in the same way is calculated that 4 × (1 - 1/4) × (1 - 1/4) × (1 - 1/4) × (1 - 1/4) = 81/64L.
Therefore, the amount of the soy sauce which remains is 4L - 81/64L = 175/64L.
