If the length of a cuboid is increased by 20% and its breadth is decreased by 20%, then the volume of cuboid

decreases by 4%

The correct answer is Option (3) → decreases by 4%

Step 1: Understand the Formula

The volume ($V$) of a cuboid is calculated as:

$V = \text{Length} (L) \times \text{Breadth} (B) \times \text{Height} (H)$

Step 2: Apply the Changes

Let the original dimensions be $L$, $B$, and $H$. The original volume is $V_1 = L \times B \times H$.

• New Length ($L'$): Increased by 20% $\Rightarrow L' = L + 0.20L = 1.20L$
• New Breadth ($B'$): Decreased by 20% $\Rightarrow B' = B - 0.20B = 0.80B$
• New Height ($H'$): Remains the same $\Rightarrow H' = H$

Step 3: Calculate the New Volume

Now, we find the new volume ($V_2$):

$V_2 = (1.20L) \times (0.80B) \times H$

$V_2 = (1.20 \times 0.80) \times (L \times B \times H)$

$V_2 = 0.96 \times V_1$

Step 4: Determine the Percentage Change

The new volume is 0.96 (or 96%) of the original volume.

$\text{Change} = 100\% - 96\% = 4\%$

Since the result is less than the original volume, it represents a decrease.

Conclusion

The volume of the cuboid decreases by 4%.