A bottle is full of dettol. 1/3 of it is taken out and replaced by water. This operation is done four times. Find the ratio of dettol and water in the bottle. Group of answer choices 16:65 81:16 16:81 65:16

Let's denote the initial volume of dettol as 1 (it doesn't matter what unit we use, since we're interested in the ratio).

After the first operation, 1/3 of the dettol is taken out, so we're left with 2/3 of the dettol. Then, the same volume of water is added, but this doesn't change the volume of dettol.

After the second operation, again 1/3 of the mixture is taken out. But now, the mixture is not pure dettol, it's 2/3 dettol and 1/3 water. So, we're taking out 1/3 * 2/3 = 2/9 of the dettol. We're left with 2/3 - 2/9 = 4/9 of the dettol.

We repeat this operation two more times. Each time, we take out 1/3 of the mixture, which means we take out 1/3 * 4/9 = 4/27 of the dettol after the third operation, and 1/3 * 4/27 = 4/81 of the dettol after the fourth operation.

So, after four operations, the volume of dettol left in the bottle is:

2/3 * 4/9 * 4/27 * 4/81 = 16/729

Since the total volume of the mixture in the bottle is 1, the volume of water is:

1 - 16/729 = 713/729

So, the ratio of dettol to water is 16:713. However, this is not one of the options. Let's check the calculations again.

The mistake is in the calculation of the volume of dettol left after each operation. After the first operation, we're left with 2/3 of the dettol. After the second operation, we're left with 2/3 * 2/3 = 4/9 of the dettol. After the third operation, we're left with 2/3 * 4/9 = 8/27 of the dettol. And after the fourth operation, we're left with 2/3 * 8/27 = 16/81 of the dettol.

So, the correct ratio of dettol to water is 16:65.