The average weight of a shipment containing 30 heavy crates and 20 light boxes is 60 kg. When all the light boxes are removed, the average weight of the remaining heavy crates increases by 10 kg. What is the average weight of the 20 light boxes?

The correct answer is 45 kg.

Step 1: Calculate the total weight of the shipment.
The shipment contains 30 heavy crates and 20 light boxes, giving a total of 50 items. Given that the average weight of these 50 items is 60 kg, we can calculate the total weight of the entire shipment as follows:

$\text{Total number of items}=30+20=50$

$\text{Total weight of shipment}=50\times 60\text{kg}=3000\text{kg}$

Step 2: Calculate the total weight of the 30 heavy crates.
When all 20 light boxes are removed, only the 30 heavy crates remain. The average weight of these remaining heavy crates increases by 10 kg over the original average of 60 kg, making their new average weight 70 kg.

$\text{Average weight of heavy crates}=60+10=70\text{kg}$

$\text{Total weight of heavy crates}=30\times 70\text{kg}=2100\text{kg}$

Step 3: Calculate the total weight of the 20 light boxes.
To find the total weight of the 20 light boxes, subtract the total weight of the heavy crates from the total weight of the shipment:

$\text{Total weight of light boxes}=3000\text{kg}-2100\text{kg}=900\text{kg}$

Step 4: Calculate the average weight of the 20 light boxes.
Finally, divide the total weight of the light boxes by the number of light boxes (20):

$\text{Average weight of light boxes}=\frac{900\text{kg}}{20}=45\text{kg}$

Thus, the average weight of the 20 light boxes is 45 kg.