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. (a)25 minute
B. (b) 6 minute
C. (c) 12 minute
D. (d) 12.5 minute

Answer

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

### Step 1: Determine the rates of each heater
- The first heater boils a certain amount of water in 15 minutes. Therefore, its rate of boiling water is:
\[ \text{Rate of Heater 1} = \frac{1 \text{ (amount of water)}}{15 \text{ minutes}} = \frac{1}{15} \text{ (amount/minute)} \]
- The second heater boils the same amount of water in 10 minutes. Thus, its rate is:
\[ \text{Rate of Heater 2} = \frac{1 \text{ (amount of water)}}{10 \text{ minutes}} = \frac{1}{10} \text{ (amount/minute)} \]

### Step 2: Combine the rates when both heaters are used in parallel
When both heaters are used together, their rates add up:
\[ \text{Combined Rate} = \text{Rate of Heater 1} + \text{Rate of Heater 2} = \frac{1}{15} + \frac{1}{10} \]

### Step 3: Find a common denominator and add the rates
To add these fractions, we need a common denominator. The least common multiple of 15 and 10 is 30:
\[ \frac{1}{15} = \frac{2}{30}, \quad \frac{1}{10} = \frac{3}{30} \]
Now we can add the rates:
\[ \text{Combined Rate} = \frac{2}{30} + \frac{3}{30} = \frac{5}{30} = \frac{1}{6} \text{ (amount/minute)} \]

### Step 4: Calculate the time taken to boil the same amount of water
Let \( x \) be the time taken to boil the same amount of water using both heaters in parallel. Since the combined rate is \( \frac{1}{6} \) amount per minute, we can set up the equation:
\[ \frac{1}{x} = \frac{1}{6} \]
To find \( x \), we take the reciprocal:
\[ x = 6 \text{ minutes} \]

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