There are four water tanks each with equal capacity of 1200 liters. The water is being pumped from one tank to another as per the following scheme. From P to Q @ 52 liters/second. From P to S @ 48 liters/second From Q to R @ 36 liters/second From R to P @ 76 liters/second From R to S @ 24 liters/second From S to Q @ 48 liters/second If all the pumps are started simultaneously, when each of the tanks has 384 liters of water which tank would get emptied first?

Options

A. P
B. Q
C. R
D. S

Answer

To solve the problem of which tank will get emptied first, we need to analyze the inflow and outflow of water for each tank. Let's break it down step by step.

### Step 1: Identify the inflow and outflow rates for each tank.

1. **Tank P:**
- Outflow:
- To Q: 52 liters/second
- To S: 48 liters/second
- Inflow:
- From R: 76 liters/second
- Net flow for P = Inflow - Outflow = 76 - (52 + 48) = 76 - 100 = -24 liters/second (P is losing water)

2. **Tank Q:**
- Outflow:
- To R: 36 liters/second
- Inflow:
- From P: 52 liters/second
- From S: 48 liters/second
- Net flow for Q = Inflow - Outflow = (52 + 48) - 36 = 100 - 36 = 64 liters/second (Q is gaining water)

3. **Tank R:**
- Outflow:
- To P: 76 liters/second
- To S: 24 liters/second
- Inflow:
- From Q: 36 liters/second
- Net flow for R = Inflow - Outflow = 36 - (76 + 24) = 36 - 100 = -64 liters/second (R is losing water)

4. **Tank S:**
- Outflow:
- To Q: 48 liters/second
- Inflow:
- From P: 48 liters/second
- From R: 24 liters/second
- Net flow for S = Inflow - Outflow = (48 + 24) - 48 = 72 - 48 = 24 liters/second (S is gaining water)

### Step 2: Determine the initial amount of water in each tank.

Each tank starts with 384 liters of water.

### Step 3: Calculate the time taken for each tank to empty.

1. **Tank P:**
- Initial water: 384 liters
- Rate of loss: 24 liters/second
- Time to empty = Initial water / Rate of loss = 384 / 24 = 16 seconds

2. **Tank Q:**
- Initial water: 384 liters
- Rate of gain: 64 liters/second (Q will not empty)
- Time to empty = Not applicable (Q will never empty)

3. **Tank R:**
- Initial water: 384 liters
- Rate of loss: 64 liters/second
- Time to empty = Initial water / Rate of loss = 384 / 64 = 6 seconds

4. **Tank S:**
- Initial water: 384 liters
- Rate of gain: 24 liters/second (S will not empty)
- Time to empty = Not applicable (S will never empty)

### Step 4: Conclusion

From the calculations, Tank R will empty first in 6 seconds.

### Final Answer:
**Tank R will get emptied first.**

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