To determine the height of Tank X, let's follow the problem step-by-step:
1. Initial Condition of Tank Y:
Tank Y is initially half filled with water. The given options for the height of Tank Y are [60 cm, 35 cm, 40 cm, 45 cm, 70 cm]. Here, let’s consider the correct height of Tank Y, which is 70 cm.
Therefore, the initial water height in Tank Y is:
[tex]\[
\text{Current water height in Tank Y} = \frac{1}{2} \times 70 \, \text{cm} = 35 \, \text{cm}
\][/tex]
2. Final Condition of Tank Y:
When all the water from Tank X is poured into Tank Y, Tank Y becomes 3/4 full. Hence, the final water height in Tank Y is:
[tex]\[
\text{Final water height in Tank Y} = \frac{3}{4} \times 70 \, \text{cm} = 52.5 \, \text{cm}
\][/tex]
3. Water Poured from Tank X:
The amount of water poured from Tank X is the difference in the water levels of Tank Y before and after pouring the water in. Thus:
[tex]\[
\text{Water poured from Tank X} = \text{Final water height} - \text{Initial water height}
\][/tex]
[tex]\[
\text{Water poured from Tank X} = 52.5 \, \text{cm} - 35 \, \text{cm} = 17.5 \, \text{cm}
\][/tex]
4. Height of Tank X:
Because all the water in Tank X was transferred to Tank Y and the volume of water is based on the height of Tank X, the height of Tank X must be equivalent to the volume of water poured into Tank Y. Therefore:
[tex]\[
\text{Height of Tank X} = 17.5 \, \text{cm}
\][/tex]
Thus, the height of Tank X is 17.5 cm.
