The length of a cuboid has increased by 20%, the breadth has increased by 50%. How much should you reduce the height to keep the volume constant?

To keep the volume of the cuboid constant, we need to adjust the height based on the changes in length and breadth.

Step 1: Calculate the new volume based on the increased length and breadth.

If the original length is L, the new length is 1.2L (increased by 20%). If the original breadth is B, the new breadth is 1.5B (increased by 50%).

So, the new volume (V') based on the increased length and breadth is V' = 1.2L * 1.5B * H = 1.8LBH.

Step 2: Compare the new volume with the original volume.

The original volume (V) is LBH.

To keep the volume constant, we want V' = V.

So, 1.8LBH = LBH.

Step 3: Solve for the new height.

Divide both sides of the equation by LBH to solve for the new height (H').

1.8 = H'/H.

So, H' = H/1.8.

This means the new height is approximately 55.56% of the original height.

Step 4: Calculate the reduction in height.

The reduction in height is 100% - 55.56% = 44.44%.

So, you should reduce the height by approximately 44.44% to keep the volume constant.