Tap D can fill 4 buckets in 36 min and tap E can fill 2 buckets in 12 min and tap D and top E can fill a tank in 1 hour. Find Capacity of tank if capacity of a bucket is 12 lit?

Options

A. 240 lit
B. 180 lit
C. 200 lit
D. 160 lit

Answer

To solve the problem step by step, we will first determine the filling rates of taps D and E, and then calculate the total capacity of the tank.

### Step 1: Determine the filling rate of Tap D
Tap D can fill 4 buckets in 36 minutes.
- Time taken to fill 1 bucket = 36 minutes / 4 = 9 minutes.

**Hint:** To find the time taken to fill one bucket, divide the total time by the number of buckets filled.

### Step 2: Determine the filling rate of Tap E
Tap E can fill 2 buckets in 12 minutes.
- Time taken to fill 1 bucket = 12 minutes / 2 = 6 minutes.

**Hint:** Similar to Tap D, divide the total time by the number of buckets to find the time for one bucket.

### Step 3: Calculate the efficiency of both taps
- Efficiency of Tap D = 1 bucket / 9 minutes = 1/9 buckets per minute.
- Efficiency of Tap E = 1 bucket / 6 minutes = 1/6 buckets per minute.

**Hint:** Efficiency is calculated as the reciprocal of the time taken to fill one bucket.

### Step 4: Find the combined efficiency of both taps
To find the combined efficiency of both taps, we need to add their individual efficiencies:
- Combined efficiency = (1/9 + 1/6) buckets per minute.

To add these fractions, we need a common denominator:
- The least common multiple (LCM) of 9 and 6 is 18.
- Convert the fractions:
- 1/9 = 2/18
- 1/6 = 3/18
- Combined efficiency = (2/18 + 3/18) = 5/18 buckets per minute.

**Hint:** When adding fractions, find a common denominator to make the addition easier.

### Step 5: Calculate the total buckets filled in 1 hour
Since both taps together can fill at a rate of 5/18 buckets per minute, in 60 minutes (1 hour):
- Total buckets filled = (5/18) * 60 = 100/3 buckets.

**Hint:** Multiply the combined efficiency by the total time (in minutes) to find the total work done.

### Step 6: Calculate the total capacity of the tank
Given that the capacity of one bucket is 12 liters:
- Total capacity of the tank = (100/3 buckets) * 12 liters/bucket = 400 liters.

**Hint:** To find the total capacity, multiply the number of buckets filled by the capacity of each bucket.

### Conclusion
The capacity of the tank is **400 liters**.

### Final Answer
The correct option is not listed in the provided options. However, based on the calculations, the capacity of the tank is **400 liters**.