Question

There are five containers A, B, C, D and E each containing 1200 litres of water. The water is being pumped from one tank to another as follows:
From A to B at 30 litres/minute
From C to A at 60 litres/minute
From A to E at 20 litres/minute
From C to D at 50 litres/minute
From D to B at 80 litres/minute
From B to C at 60 litres/minute
From E to D at 10 litres/minute
From E to A at 10 litres/minute
Which tank gets emptied first?

• A. A
• B. B
• C. C
• D. D
• E. E

Answer 1

The Correct Option is C

To determine which tank gets emptied first, we need to analyze the water inflow and outflow for each tank.

Each tank initially contains 1200 liters. Let's look at the water flow for each tank: 

1. Tank A:
   • Inflow: 60 liters/min from C, 10 liters/min from E.
   • Outflow: 30 liters/min to B, 20 liters/min to E.
   • \(\text{Net flow for A} = (60 + 10) - (30 + 20) = 20 \text{ liters/min} \text{ (increase)}\)
2. Tank B:
   • Inflow: 30 liters/min from A, 80 liters/min from D.
   • Outflow: 60 liters/min to C.
   • \(\text{Net flow for B} = (30 + 80) - 60 = 50 \text{ liters/min} \text{ (increase)}\)
3. Tank C:
   • Inflow: 60 liters/min from B.
   • Outflow: 60 liters/min to A, 50 liters/min to D.
   • \(\text{Net flow for C} = 60 - (60 + 50) = -50 \text{ liters/min} \text{ (decrease)}\)
4. Tank D:
   • Inflow: 50 liters/min from C, 10 liters/min from E.
   • Outflow: 80 liters/min to B.
   • \(\text{Net flow for D} = (50 + 10) - 80 = -20 \text{ liters/min} \text{ (decrease)}\)
5. Tank E:
   • Inflow: 20 liters/min from A.
   • Outflow: 10 liters/min to D, 10 liters/min to A.
   • \(\text{Net flow for E} = 20 - (10 + 10) = 0 \text{ liters/min} \text{ (neutral)}\)

Based on the calculations, Tank C is losing water at the highest rate of \(50 \text{ liters/min}\). Let's calculate how long it takes for Tank C to empty:

\(\text{Time for C to empty} = \frac{1200 \text{ liters}}{50 \text{ liters/min}} = 24 \text{ minutes}\)

Therefore, Tank C will be the first one to get emptied.