A ship is full of cargo containers. It drops 2/3 of cargo containers at the first port and takes 60 more, at the second port it drops two third of the new total and takes eleven more. On arriving at the third port it is found that it have 48 cargo containers. Find the number of cargo containers in the ship at the starting?

Options

A. 189
B. 159
C. 161
D. 153

Answer

To find the number of cargo containers on the ship at the start, we can break down the problem step by step.

### Step-by-Step Solution:

1. **Let the initial number of cargo containers be \( x \)**.
- This is our starting point.

2. **At the first port:**
- The ship drops \( \frac{2}{3} \) of its cargo containers.
- Therefore, the remaining cargo containers after dropping is:
\[ x - \frac{2}{3}x = \frac{1}{3}x \]
- Then, the ship takes on 60 more containers:
\[ \text{Total after first port} = \frac{1}{3}x + 60 \]

3. **At the second port:**
- The ship drops \( \frac{2}{3} \) of the new total:
\[ \text{New total before dropping} = \frac{1}{3}x + 60 \]
- After dropping \( \frac{2}{3} \), the remaining cargo containers are:
\[ \left(\frac{1}{3}x + 60\right) - \frac{2}{3}\left(\frac{1}{3}x + 60\right) = \frac{1}{3}\left(\frac{1}{3}x + 60\right) = \frac{1}{9}x + 20 \]
- The ship then takes on 11 more containers:
\[ \text{Total after second port} = \frac{1}{9}x + 20 + 11 = \frac{1}{9}x + 31 \]

4. **At the third port:**
- It is given that the ship has 48 cargo containers:
\[ \frac{1}{9}x + 31 = 48 \]

5. **Solving for \( x \):**
- Subtract 31 from both sides:
\[ \frac{1}{9}x = 48 - 31 \]
\[ \frac{1}{9}x = 17 \]
- Multiply both sides by 9 to isolate \( x \):
\[ x = 17 \times 9 \]
\[ x = 153 \]

### Conclusion:
The initial number of cargo containers on the ship was **153**.