A water tank has three taps A, B and C. A fills four buckets in 24 minutes, B fills 8 buckets in 1 hour and C fills 2 buckets in 20 minutes. If all the taps are opened together a full tank is emptied in 2 hours. If a bucket can hold 5 litres of water, what is the capacity of the tank?

Options

A. 120 litres
B. 240 litres
C. 180 litres
D. 60 litres

Answer

To solve the problem step by step, we will first determine the rate at which each tap fills the buckets, then calculate the total discharge when all taps are opened together, and finally, find the capacity of the tank.

### Step 1: Calculate the filling rate of each tap

1. **Tap A**:
- Fills 4 buckets in 24 minutes.
- Each bucket holds 5 litres, so 4 buckets = 4 * 5 = 20 litres.
- Rate of Tap A = 20 litres / 24 minutes = \( \frac{20}{24} = \frac{5}{6} \) litres per minute.

2. **Tap B**:
- Fills 8 buckets in 1 hour (60 minutes).
- 8 buckets = 8 * 5 = 40 litres.
- Rate of Tap B = 40 litres / 60 minutes = \( \frac{40}{60} = \frac{2}{3} \) litres per minute.

3. **Tap C**:
- Fills 2 buckets in 20 minutes.
- 2 buckets = 2 * 5 = 10 litres.
- Rate of Tap C = 10 litres / 20 minutes = \( \frac{10}{20} = \frac{1}{2} \) litres per minute.

### Step 2: Calculate the total discharge rate when all taps are opened together

- Total discharge rate = Rate of Tap A + Rate of Tap B + Rate of Tap C
- Total discharge rate = \( \frac{5}{6} + \frac{2}{3} + \frac{1}{2} \)

To add these fractions, we need a common denominator. The least common multiple of 6, 3, and 2 is 6.

- Convert each fraction:
- \( \frac{5}{6} \) remains \( \frac{5}{6} \)
- \( \frac{2}{3} = \frac{4}{6} \)
- \( \frac{1}{2} = \frac{3}{6} \)

Now, we can add them:
- Total discharge rate = \( \frac{5}{6} + \frac{4}{6} + \frac{3}{6} = \frac{12}{6} = 2 \) litres per minute.

### Step 3: Calculate the total amount of water discharged in 2 hours

- Since 2 hours = 120 minutes, the total discharge in 120 minutes is:
- Total discharge = Discharge rate * Time = 2 litres/minute * 120 minutes = 240 litres.

### Step 4: Determine the capacity of the tank

- Since the tank is emptied in 2 hours when all taps are opened, the capacity of the tank is equal to the total amount of water discharged.
- Therefore, the capacity of the tank = 240 litres.

### Final Answer:
The capacity of the tank is **240 litres**.

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