A chemical plant has four tanks (A, B, C and D), each containing 1000 litres of a chemical. The chemical is being pumped from one tank to anther as follows.
From A to B @ 20 litres/minute
From C to A @ 90 litres/minute
From A to D @ 10 litres/minute
From C to D @ 50 litres/minute
From B to C @ 100 litres/minute
From D to B @ 110 litres/minute
Which tank gets emptied first, and how long does it take (in minutes)to get empty after pumping starts?

Options

A. A, 16.66
B. C, 20
C. D, 20
D. D, 25

Answer

To solve the problem, we need to analyze the flow of the chemical between the tanks and determine how much chemical is in each tank after every minute. We will calculate the net change in volume for each tank after one minute and then find out which tank gets emptied first.

### Step-by-Step Solution:

1. **Identify the flow rates:**
- From A to B: 20 litres/minute (A loses 20 litres)
- From C to A: 90 litres/minute (A gains 90 litres)
- From A to D: 10 litres/minute (A loses 10 litres)
- From C to D: 50 litres/minute (C loses 50 litres)
- From B to C: 100 litres/minute (B loses 100 litres)
- From D to B: 110 litres/minute (D gains 110 litres)

2. **Calculate the net change for each tank after 1 minute:**
- For Tank A:
\[ \text{Net change in A} = -20 + 90 - 10 = 60 \text{ litres} \]
- For Tank B:
\[ \text{Net change in B} = -100 + 110 + 20 = 30 \text{ litres} \]
- For Tank C:
\[ \text{Net change in C} = -50 - 90 + 100 = -40 \text{ litres} \]
- For Tank D:
\[ \text{Net change in D} = -110 + 10 + 50 = -50 \text{ litres} \]

3. **Determine which tank empties first:**
- The net changes are:
- Tank A: +60 litres
- Tank B: +30 litres
- Tank C: -40 litres
- Tank D: -50 litres
- Since Tank D has the highest negative change (-50 litres), it will empty first.

4. **Calculate the time taken for Tank D to empty:**
- Let \( X \) be the time in minutes for Tank D to empty.
- The initial volume in Tank D is 1000 litres.
- The equation for Tank D is:
\[ 1000 - 50X = 0 \]
- Solving for \( X \):
\[ 50X = 1000 \implies X = \frac{1000}{50} = 20 \text{ minutes} \]

5. **Conclusion:**
- Tank D will be the first to empty, and it will take 20 minutes to do so.

### Final Answer:
Tank D gets emptied first, and it takes 20 minutes to empty.