Question

16 litres are drawn from a container full of wine and replaced with water. This operation is performed three more times. The ratio of the quantity of wine now left in the container to that of water is 256:369. How much wine did the container actually hold?

Answer 1

The container actually held approximately 27.09 liters of wine. Hence 27.09 is the right answer to this question.

Step-by-step explanation:

Let's assume that the container initially holds x liters of wine. After the first operation, 16 liters of wine are drawn and replaced with water. So, the quantity of wine left in the container is x - 16 liters, and the quantity of water is 16 liters.

This ratio of wine to water is (x - 16):16.After three more operations, the ratio of wine left in the container to water becomes 256:369. So, we can set up the following proportion:

(x - 16)/16 = 256/369. Cross multiplying gives us: 369(x - 16) = 16 * 256. Simplifying the equation: 369x - 5904 = 4096. Adding 5904 to both sides: 369x = 10000. Dividing both sides by 369: x = 27.09. Therefore, the container actually held approximately 27.09 liters of wine.