Pipes A and B can fill a tank in 36 hours and 48 hours, respectively. Both pipes are opened together for 9 hours and then A is closed. Pipe B alone will fill the remaining part of the tank now in:

Options

A. 27 hours
B. 25 hours
C. 25 hours
D. 24 hours

Answer

To solve the problem step by step, we will first determine how much of the tank each pipe can fill in one hour, then calculate how much they fill together in 9 hours, and finally find out how long it will take for pipe B to fill the remaining part of the tank alone.

### Step 1: Determine the filling rates of pipes A and B.
- Pipe A can fill the tank in 36 hours.
- Pipe B can fill the tank in 48 hours.

To find their rates:
- Rate of Pipe A = 1 tank / 36 hours = 1/36 tanks per hour.
- Rate of Pipe B = 1 tank / 48 hours = 1/48 tanks per hour.

### Step 2: Calculate the combined filling rate of pipes A and B.
- Combined rate = Rate of Pipe A + Rate of Pipe B
- Combined rate = (1/36 + 1/48)

To add these fractions, we need a common denominator. The least common multiple (LCM) of 36 and 48 is 144.

- (1/36) = 4/144
- (1/48) = 3/144

Now, add them:
- Combined rate = (4/144 + 3/144) = 7/144 tanks per hour.

### Step 3: Calculate how much of the tank is filled in 9 hours.
- Amount filled in 9 hours = Combined rate × Time
- Amount filled in 9 hours = (7/144) × 9 = 63/144 = 7/16 of the tank.

### Step 4: Determine the remaining part of the tank to be filled.
- Remaining part of the tank = 1 - (7/16) = 16/16 - 7/16 = 9/16 of the tank.

### Step 5: Calculate how long it will take for pipe B to fill the remaining part.
- Pipe B's rate is 1/48 tanks per hour.
- Time taken by Pipe B to fill 9/16 of the tank = Remaining part / Rate of Pipe B
- Time = (9/16) / (1/48) = (9/16) × (48/1) = 9 × 3 = 27 hours.

### Final Answer:
Pipe B alone will fill the remaining part of the tank in **27 hours**.

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