A warehouse initially contains 210 gift boxes, and 150 additional gift boxes are received. If all these gift boxes are distributed between Department A and Department B in the ratio of 5:3, what is the difference between the total number of gift boxes received by Department A and Department B?

The correct answer is 90.

Step 1: Calculate the total number of gift boxes.
The warehouse initially contains 210 gift boxes and receives 150 additional boxes.
Total gift boxes = Initial boxes + Additional boxes

$\text{Total gift boxes}=210+150=360$

Step 2: Determine the total ratio parts.
The gift boxes are distributed between Department A and Department B in the ratio of 5 : 3.
Total ratio parts = 5 + 3 = 8 parts.

$\text{Total ratio parts}=5+3=8$

Step 3: Calculate the number of boxes per ratio part.
Divide the total number of gift boxes by the total number of ratio parts:

$\text{Value of 1 part}=\frac{360}{8}=45$

Step 4: Calculate the difference between Department A and Department B.
Department A receives 5 parts and Department B receives 3 parts.
Difference in ratio parts = 5 - 3 = 2 parts.

$\text{Difference in parts}=5-3=2$

To find the difference in the number of gift boxes, multiply the difference in ratio parts by the value of 1 part:

$\text{Difference in boxes}=2\times 45=90$

Alternative Verification:
Calculate the boxes received by each department individually:
Department A = 5 × 45 = 225 boxes
Department B = 3 × 45 = 135 boxes
Difference = 225 - 135 = 90 boxes.

Therefore, the difference between the total number of gift boxes received by Department A and Department B is 90.