Puzzle | Camel and Banana Puzzle

A person owns a banana plantation and needs to transport 3000 bananas to a market located 1000 km away. The only available means of transportation is a camel.

The camel has the following limitations:

• It can carry a maximum of 1000 bananas at a time.
• It consumes 1 banana per kilometre travelled.

The camel may make multiple trips and can store bananas at intermediate points.

Determine the maximum number of bananas that can be delivered to the market.

Check if you were right - full answer with solution below.

Approach

To minimise the loss of bananas, the journey is divided into three stages: P1, P2, and P3. At each stage, bananas are transported in parts, and the number of trips determines how many bananas are consumed per kilometre.

The diagram above shows how the number of bananas reduces from 3000 to 2000 to 1000 across the three stages before reaching the destination.

Solution

Step 1: From 3000 to 2000 Bananas

The camel must transport 3000 bananas, but it can carry only 1000 at a time. Therefore, 3 trips are required.

For each kilometre:

• Two trips involve moving forward and returning, consuming 2 bananas each
• One trip involves only moving forward, consuming 1 banana

Total consumption = 5 bananas per kilometer

3000 − 5x = 2000
x = 200 km

After this stage:

• Distance covered = 200 km
• Bananas remaining = 2000

Step 2: From 2000 to 1000 Bananas

Now, 2 trips are required.

For each kilometre:

• One trip involves moving forward and returning, consuming 2 bananas
• One trip involves only moving forward, consuming 1 banana

Total consumption = 3 bananas per kilometer

2000 − 3y = 1000
y = 333.33 km

After this stage:

• Total distance covered = 533.33 km
• Bananas remaining = 1000

Step 3: Final Stage

At this stage, the camel carries 1000 bananas in a single trip.

Remaining distance:
1000 − 533.33 = 466.67 km

Bananas consumed:
466.67

Bananas remaining at destination:
1000 − 466.67 = 533.33

The maximum number of bananas that can reach the destination is approximately 533 bananas.