An electric kettle has tow heating coils. When one of the coils connected to an AC source, the water in the kettle boils in `10` min. when the other coil is used the water boils in `40` min. if both the coils are connected in parallel, the time taken by the same quantity of water of boil will be

Options

A. 25 min
B. 15 min
C. 8 min
D. 4 min

Answer

To solve the problem, we need to determine the time taken for the water to boil when both heating coils of the electric kettle are connected in parallel. We will use the concept of power and the relationship between time, power, and heat.

### Step-by-Step Solution:

1. **Understand the Problem**:
- We have two heating coils in an electric kettle.
- Coil 1 boils water in 10 minutes.
- Coil 2 boils water in 40 minutes.
- We need to find the time taken to boil the same quantity of water when both coils are connected in parallel.

2. **Define Variables**:
- Let \( t_1 = 10 \) minutes (time taken by coil 1).
- Let \( t_2 = 40 \) minutes (time taken by coil 2).

3. **Calculate Power for Each Coil**:
- The power \( P \) of a heating coil can be expressed as:
\[ P = \frac{H}{t} \]
where \( H \) is the heat required to boil the water and \( t \) is the time taken.

- For Coil 1:
\[ P_1 = \frac{H}{t_1} = \frac{H}{10} \]

- For Coil 2:
\[ P_2 = \frac{H}{t_2} = \frac{H}{40} \]

4. **Calculate Total Power When Both Coils Are Connected in Parallel**:
- When coils are connected in parallel, the total power \( P_{total} \) is the sum of the individual powers:
\[ P_{total} = P_1 + P_2 = \frac{H}{10} + \frac{H}{40} \]

- To add these fractions, find a common denominator (which is 40):
\[ P_{total} = \frac{4H}{40} + \frac{H}{40} = \frac{5H}{40} = \frac{H}{8} \]

5. **Calculate Time Taken to Boil Water with Both Coils**:
- Using the power formula again, we have:
\[ P_{total} = \frac{H}{t_{total}} \]
- Setting the two expressions for power equal gives:
\[ \frac{H}{t_{total}} = \frac{H}{8} \]
- Solving for \( t_{total} \):
\[ t_{total} = 8 \text{ minutes} \]

### Final Answer:
The time taken by the same quantity of water to boil when both coils are connected in parallel is **8 minutes**.

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