Question

a flask was \\(\frac{5}{8}\\) filled with water. ravi poured \\(95\text{ cm}^3\\) of water into the flask and it was \\(\frac{5}{6}\\) full. what was the capacity of the flask?

Explanation:

Identify the given values

We are given:

• Initial water level: \(\frac{5}{8}\) of the flask capacity.
• Added water volume: \(95\text{ cm}^3\).
• Final water level: \(\frac{5}{6}\) of the flask capacity.

Find the fraction difference

To find what fraction of the flask \(95\text{ cm}^3\) represents, we subtract the initial fraction from the final fraction:

$$ \frac{5}{6} - \frac{5}{8} $$

Find a common denominator, which is \(24\):

$$ \frac{5 \times 4}{6 \times 4} - \frac{5 \times 3}{8 \times 3} = \frac{20}{24} - \frac{15}{24} = \frac{5}{24} $$

Set up the unit equation

The difference of \(\frac{5}{24}\) of the total capacity corresponds to the added \(95\text{ cm}^3\).
Let \(24\text{ units}\) represent the total capacity of the flask.
Thus, \(5\text{ units}\) represent the added water:

$$ 5\text{ units} = 95\text{ cm}^3 $$

Calculate the value of one unit

Divide the added volume by the number of units it represents:

$$ 1\text{ unit} = 95 \div 5 = 19\text{ cm}^3 $$

Calculate the total capacity

Multiply the value of one unit by the total number of units (\(24\)):

$$ 24\text{ units} = 24 \times 19 = 456\text{ cm}^3 $$

Answer:

\(456\text{ cm}^3\)