A heater boils certain amount of water in 15 minutes. Another heater boils same amount of water in 10 minutes. Time taken to boil same amount of water when both are used in parallel is

Options

A. 25 minute
B. 6 minute
C. 12 minute
D. 12.5 minute

Answer

To solve the problem of how long it takes to boil the same amount of water when both heaters are used in parallel, we can follow these steps:

### Step 1: Understand the relationship between power and time
The power of a heater is inversely proportional to the time it takes to boil the water. This means:
\[ P \propto \frac{1}{t} \]
Where \( P \) is power and \( t \) is time.

### Step 2: Determine the power of each heater
Let’s denote:
- Heater 1 takes 15 minutes to boil water, so we can say its power \( P_1 \) is proportional to \( \frac{1}{15} \).
- Heater 2 takes 10 minutes to boil water, so its power \( P_2 \) is proportional to \( \frac{1}{10} \).

### Step 3: Calculate the total power when both heaters are used in parallel
When two heaters are used in parallel, their powers add up:
\[ P_{total} = P_1 + P_2 \]
Substituting the values we have:
\[ P_{total} \propto \frac{1}{15} + \frac{1}{10} \]

### Step 4: Find a common denominator and add the fractions
The least common multiple of 15 and 10 is 30. Thus:
\[ P_{total} \propto \frac{2}{30} + \frac{3}{30} = \frac{5}{30} = \frac{1}{6} \]

### Step 5: Relate total power back to time
Since power is inversely proportional to time, we can relate the total power to the time taken to boil the water when both heaters are used:
\[ t_{total} \propto \frac{1}{P_{total}} \]
Thus:
\[ t_{total} = 6 \text{ minutes} \]

### Conclusion
The time taken to boil the same amount of water when both heaters are used in parallel is **6 minutes**.

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