There are two buckets A and B. Initially A has 2 litres of water and B...
From the given data, we get
When T = 0 hr, A has 2 liters and B has 0 liters
When T = 1 hr, A has 1 liter and B has 1 liter
When T = 1.5 hr, A has 1.5 liters and B has 0.5 liters
When T = 2 hr, A has 0.5 liters and B has 1.5 liters
When T = 2.5 hr, A has 1 liter and B has 1 liter
When T = 3 hr, A has 0 liters and B has 2 liters
∴ Earliest A will get empty it in 3 hours
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There are two buckets A and B. Initially A has 2 litres of water and B...
The problem states that there are two buckets, A and B, initially A has 2 liters of water and B is empty. The process involves transferring 1 liter of water from A to B every hour, followed by returning 1/2 liter back to A from B half an hour later.
To find out when bucket A will become empty, let's analyze the process step by step:
1. First Hour:
- A: 2 liters
- B: 1 liter
2. After Half an Hour:
- A: 2 liters + 1/2 liter = 2.5 liters
- B: 1 liter - 1/2 liter = 1/2 liter
3. Second Hour:
- A: 2.5 liters - 1 liter = 1.5 liters
- B: 1/2 liter + 1 liter = 1.5 liters
4. After Half an Hour:
- A: 1.5 liters + 1/2 liter = 2 liters
- B: 1.5 liters - 1 liter = 1/2 liter
5. Third Hour:
- A: 2 liters - 1 liter = 1 liter
- B: 1/2 liter + 1 liter = 1.5 liters
From the above analysis, we can observe that after every hour, the amount of water in bucket A decreases by 1 liter. And after every half an hour, the amount of water in bucket A increases by 1/2 liter.
To find out when bucket A will become empty, we can calculate the time it takes for A to reach 0 liters:
- After 1 hour, A has 1 liter remaining
- After 2 hours, A has 0 liters remaining
Therefore, the earliest A will get empty is in 2 hours, which corresponds to option (d) in the given choices.