Six taps can fill an empty cistern in 8 hours. How much more time will be taken, if two taps go out of order ? Assume, all the taps supply water at the same rate.

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Determine the total work done by the taps
Given that 6 taps can fill the cistern in 8 hours, we can calculate the total work done in terms of "tap-hours."

**Calculation:**
Total work = Number of taps × Time taken
Total work = 6 taps × 8 hours = 48 tap-hours

### Step 2: Calculate the work done by one tap
Since the total work is 48 tap-hours, we can find out how much work one tap can do.

**Calculation:**
Work done by 1 tap = Total work / Number of taps
Work done by 1 tap = 48 tap-hours / 6 taps = 8 hours per tap

### Step 3: Calculate the time taken by 4 taps
Now, if 2 taps go out of order, we are left with 4 taps. We need to find out how long it will take for 4 taps to fill the cistern.

**Calculation:**
Time taken by 4 taps = Total work / Number of working taps
Time taken by 4 taps = 48 tap-hours / 4 taps = 12 hours

### Step 4: Determine the additional time taken
We need to find out how much more time is taken when 2 taps are out of order compared to when all 6 taps are working.

**Calculation:**
Additional time taken = Time taken by 4 taps - Time taken by 6 taps
Additional time taken = 12 hours - 8 hours = 4 hours

### Conclusion
Thus, if 2 taps go out of order, it will take an additional 4 hours to fill the cistern.

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