A rectangular box measures internally 1.6 m in length, 1 m in breadth and 60 cm in depth. How many solid cubical boxes, each with edge 20 cm, can be packed completely inside the box?

Introduction / Context:
Packing problems ask how many smaller solids fit inside a larger solid without overlapping. Here, a large rectangular box must be filled with smaller cubes. Because the edges align neatly, the number of cubes along each dimension is given by division of the corresponding lengths, and the total count is the product of these numbers.

Given Data / Assumptions:

• Internal dimensions of big box: length = 1.6 m, breadth = 1 m, depth = 60 cm.
• Edge of each small cube = 20 cm.
• Cubes are packed without gaps, with edges parallel to box edges.

Concept / Approach:
We first convert all dimensions to a common unit, preferably centimetres, because the cube edge is given in centimetres. Then we find the number of cubes along each dimension by integer division (floor), and finally multiply these three counts to get the total number of cubes that fit inside.

Step-by-Step Solution:
Step 1: Convert dimensions to centimetres. Length = 1.6 m = 160 cm. Breadth = 1 m = 100 cm. Depth = 60 cm (already in centimetres). Edge of each cube = 20 cm. Step 2: Number of cubes along length = 160 / 20 = 8. Step 3: Number of cubes along breadth = 100 / 20 = 5. Step 4: Number of cubes along depth = 60 / 20 = 3. Step 5: Total cubes = 8 * 5 * 3 = 120.

Verification / Alternative check:
The volume method also confirms this result. Volume of big box = 160 * 100 * 60 = 960000 cm^3. Volume of each cube = 20 * 20 * 20 = 8000 cm^3. Dividing gives 960000 / 8000 = 120 cubes, which agrees with the count from dimensions.

Why Other Options Are Wrong:
30 cubes and 60 cubes are too few and would fill only a fraction of the volume.
90 cubes fill three quarters of the full 120 cube capacity and would leave significant empty space.
150 cubes would require more volume than the box provides, so they cannot all fit without overlapping.

Common Pitfalls:
Some learners forget to convert all dimensions into the same units and may incorrectly divide metres by centimetres. Others may mistakenly add or average the dimensions instead of taking products. For packing problems with exact cube fitting, ensure that the box dimensions are multiples of the cube edge and always work in a consistent unit system.

Final Answer:
The maximum number of cubical boxes that can be packed is 120 cubes.