The length and breadth of a cuboid are increased by 50 percent and 20 percent respectively. If its height is decreased by 30 percent, then what will be percentage increase in the volume of cuboid?

Length increased by 50%.

Breadth increased by 20%.

Height decreased by 30%.

To find the percentage increase in the volume of the cuboid.

The volume V of a cuboid is given by:

V = Length × Breadth × Height

The percentage increase in volume is calculated as:

​$$\text{Percentage Increase} = \left(\frac{V_{\text{new}} - V_{\text{original}}}{V_{\text{original}}}\right) \times 100$$​​

Let the original dimensions be L, B, and H. After changes:

New length = 1.5L

New breadth = 1.2B

New height = 0.7H​​

​$$V_{\text{original}} = L \times B \times H$$​​

New volume:

​$$V_{\text{new}} = 1.5L \times 1.2B \times 0.7H = 1.26 \times (L \times B \times H)$$​​

​$$\text{Percentage Increase} = \left(\frac{1.26V - V}{V}\right) \times 100 = (1.26 - 1) \times 100 = 0.26 \times 100 = 26\%$$​​

Thus, The percentage increase in the volume of the cuboid is 26%.