10 pipes of the same diameter can fill a tank in 24 minutes.If 2 pipes gp out of order.how long will the remaining pipe take to fill the tank?

Options

A. 40 min
B. 45 min
C. 30 min
D. `19. 1/5` min

Answer

To solve the problem step by step, let's break it down:

**Step 1: Understand the problem.**
We know that 10 pipes can fill a tank in 24 minutes. We need to find out how long it will take for the remaining 8 pipes to fill the tank after 2 pipes go out of order.

**Step 2: Calculate the work done by one pipe.**
If 10 pipes can fill the tank in 24 minutes, then the work done by 10 pipes in 24 minutes is equivalent to filling 1 tank.

To find out how much work one pipe does in one minute, we can use the formula:
- Work done by 10 pipes in 1 minute = 1 tank / 24 minutes = 1/24 tank per minute.

Now, to find the work done by 1 pipe in 1 minute:
- Work done by 1 pipe in 1 minute = (1/24) / 10 = 1/240 tank per minute.

**Step 3: Calculate the work done by 8 pipes.**
Now, if we have 8 pipes working together, the work done by 8 pipes in 1 minute will be:
- Work done by 8 pipes in 1 minute = 8 * (1/240) = 8/240 = 1/30 tank per minute.

**Step 4: Calculate the time taken by 8 pipes to fill the tank.**
To find out how long it will take for 8 pipes to fill the tank, we can use the formula:
- Time = Total work / Work done in one minute.

Since filling the tank is considered as 1 unit of work:
- Time taken by 8 pipes = 1 tank / (1/30 tank per minute) = 30 minutes.

Thus, the remaining 8 pipes will take **30 minutes** to fill the tank.