Two pipes. A and B. can fill a tank in X minutes and 6 minutes, respectively. If both the pipes are used together, then they take 1.5 minute To fill the tank. Find the value of X.
(a)1 min
(b)4 min
(c)5 min
(d)2 min

Options

A. 1 min
B. 4 min
C. 5 min
D. 2 min

Answer

To solve the problem of finding the value of X, we will follow these steps:

### Step 1: Determine the filling rates of pipes A and B
- Pipe B can fill the tank in 6 minutes. Therefore, the filling rate of pipe B is:
\[ \text{Rate of B} = \frac{1 \text{ tank}}{6 \text{ minutes}} = \frac{1}{6} \text{ tanks per minute} \]

### Step 2: Determine the combined filling rate of pipes A and B
- When both pipes A and B are used together, they can fill the tank in 1.5 minutes. Therefore, the combined filling rate of pipes A and B is:
\[ \text{Rate of A + B} = \frac{1 \text{ tank}}{1.5 \text{ minutes}} = \frac{2}{3} \text{ tanks per minute} \]

### Step 3: Express the filling rate of pipe A
- Let the filling time for pipe A be X minutes. Therefore, the filling rate of pipe A is:
\[ \text{Rate of A} = \frac{1 \text{ tank}}{X \text{ minutes}} = \frac{1}{X} \text{ tanks per minute} \]

### Step 4: Set up the equation for the combined rates
- The combined rate of pipes A and B can be expressed as:
\[ \text{Rate of A} + \text{Rate of B} = \text{Rate of A + B} \]
Substituting the rates we found:
\[ \frac{1}{X} + \frac{1}{6} = \frac{2}{3} \]

### Step 5: Solve for X
- To solve the equation, first find a common denominator for the left side, which is 6X:
\[ \frac{6}{6X} + \frac{X}{6X} = \frac{2}{3} \]
This simplifies to:
\[ \frac{6 + X}{6X} = \frac{2}{3} \]
- Cross-multiply to eliminate the fractions:
\[ 3(6 + X) = 2(6X) \]
Expanding both sides gives:
\[ 18 + 3X = 12X \]
- Rearranging the equation:
\[ 18 = 12X - 3X \]
\[ 18 = 9X \]
\[ X = 2 \]

### Conclusion
The value of X is 2 minutes.

### Answer
(d) 2 min

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