A tap supplies water at `15^@C` and another tap connected to geyser supplies water at `95^@C`. How much hot water must be taken so as to get 60 kg of water at `35^@C`?

Options

A. 15 kg
B. 5 kg
C. 10 kg
D. 20 kg

Explanation

To solve the problem, we need to use the principle of calorimetry, which states that the heat lost by the hot water will be equal to the heat gained by the cold water.

### Step-by-Step Solution:

1. **Define Variables:**
Let \( x \) be the mass of hot water taken from the geyser (in kg).
Therefore, the mass of cold water taken from the tap will be \( 60 - x \) kg, since the total mass of water is 60 kg.

2. **Identify Temperatures:**
- Temperature of hot water from the geyser, \( T_h = 95^\circ C \)
- Temperature of cold water from the tap, \( T_c = 15^\circ C \)
- Final temperature of the mixture, \( T_f = 35^\circ C \)

3. **Set Up the Heat Transfer Equation:**
According to the principle of calorimetry:
\[ \text{Heat lost by hot water} = \text{Heat gained by cold water} \]
This can be expressed as:
\[ m_h \cdot c \cdot (T_h - T_f) = m_c \cdot c \cdot (T_f - T_c) \]
Where \( m_h = x \) (mass of hot water), \( m_c = 60 - x \) (mass of cold water), and \( c \) is the specific heat capacity of water (which cancels out).

4. **Substituting Values:**
Substituting the values into the equation:
\[ x \cdot (95 - 35) = (60 - x) \cdot (35 - 15) \]
Simplifying the temperature differences:
\[ x \cdot 60 = (60 - x) \cdot 20 \]

5. **Expanding the Equation:**
Expanding the right side:
\[ 60x = 1200 - 20x \]

6. **Rearranging the Equation:**
Bringing all terms involving \( x \) to one side:
\[ 60x + 20x = 1200 \]
\[ 80x = 1200 \]

7. **Solving for \( x \):**
Dividing both sides by 80:
\[ x = \frac{1200}{80} = 15 \]

8. **Conclusion:**
Therefore, the mass of hot water required is \( x = 15 \) kg.

### Final Answer:
The required mass of hot water is **15 kg**.