Two pipes N and g can fill a water tank in 90 and 10 hours respectively. If they are opened together, then in how many hours will the tank be filled?

Options

A. 9
B. 18
C. 20
D. 6

Answer

To solve the problem of how long it will take for two pipes, N and G, to fill a water tank when opened together, we can follow these steps:

### Step 1: Determine the filling rates of each pipe.
- Pipe N can fill the tank in 90 hours. Therefore, its filling rate is:
\[ \text{Rate of Pipe N} = \frac{1 \text{ tank}}{90 \text{ hours}} = \frac{1}{90} \text{ tanks per hour} \]

- Pipe G can fill the tank in 10 hours. Therefore, its filling rate is:
\[ \text{Rate of Pipe G} = \frac{1 \text{ tank}}{10 \text{ hours}} = \frac{1}{10} \text{ tanks per hour} \]

### Step 2: Combine the rates of both pipes.
When both pipes are opened together, their combined filling rate is:
\[ \text{Combined Rate} = \text{Rate of Pipe N} + \text{Rate of Pipe G} = \frac{1}{90} + \frac{1}{10} \]

To add these fractions, we need a common denominator. The least common multiple of 90 and 10 is 90. Therefore, we can rewrite \(\frac{1}{10}\) as \(\frac{9}{90}\):
\[ \text{Combined Rate} = \frac{1}{90} + \frac{9}{90} = \frac{10}{90} = \frac{1}{9} \text{ tanks per hour} \]

### Step 3: Calculate the time taken to fill the tank.
To find out how long it takes to fill one tank, we take the reciprocal of the combined rate:
\[ \text{Time to fill the tank} = \frac{1 \text{ tank}}{\frac{1}{9} \text{ tanks per hour}} = 9 \text{ hours} \]

### Final Answer:
The tank will be filled in **9 hours** when both pipes N and G are opened together.

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