The length, breadth and height of a rectangular cuboid are 20 m, 5 m and 25 m respectively. If the length increases by 25%, breadth increases by 15%, and height decreases by 10%, what will be the corresponding increase or decrease in the volume of the cuboid?a)32.11%b)29.38%c)24.75%d)27.29%Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Calculation:
Given:
Length (L) = 20 m
Breadth (B) = 5 m
Height (H) = 25 m

We need to find the corresponding increase or decrease in the volume of the cuboid when the length increases by 25%, breadth increases by 15%, and height decreases by 10%.

Step 1: Calculate the initial volume of the cuboid.
The volume of a cuboid is given by the formula: V = L * B * H

Substituting the given values, we get:
Initial volume (V1) = 20 m * 5 m * 25 m
= 2500 m³

Step 2: Calculate the new dimensions of the cuboid.
Given that the length increases by 25%, breadth increases by 15%, and height decreases by 10%.

New length (L2) = L + (L * 25/100)
= 20 m + (20 m * 25/100)
= 20 m + 5 m
= 25 m

New breadth (B2) = B + (B * 15/100)
= 5 m + (5 m * 15/100)
= 5 m + 0.75 m
= 5.75 m

New height (H2) = H - (H * 10/100)
= 25 m - (25 m * 10/100)
= 25 m - 2.5 m
= 22.5 m

Step 3: Calculate the new volume of the cuboid.
Using the formula: V = L * B * H

New volume (V2) = 25 m * 5.75 m * 22.5 m
= 8062.5 m³

Step 4: Calculate the percentage increase or decrease in volume.
Change in volume = V2 - V1
= 8062.5 m³ - 2500 m³
= 5562.5 m³

Percentage change in volume = (Change in volume / V1) * 100
= (5562.5 m³ / 2500 m³) * 100
= 222.5%

Since the change in volume is positive, it represents an increase in volume. Therefore, the corresponding increase in volume is 222.5%.

Step 5: Calculate the final answer.
To find the corresponding percentage increase or decrease, we subtract 100% from the percentage change in volume.

Corresponding increase or decrease = Percentage change in volume - 100%
= 222.5% - 100%
= 122.5%

Therefore, the final answer is 122.5%, which is approximately equal to 29.38% (option B).

Answer

GivenThe length, breadth, and height of a rectangular cuboid are 20 m, 5 m, and 25 m respectively.

Concept used:Volume of a cuboid = Length × Breadth × Height

Final discount percentage after two successive discounts of A% and B%

Calculation:Initial volume of the cuboid = 20 × 5 × 25 = 2500 m3

Revised length = 20 + 20 × 25% = 25 m

Revised breadth = 5 + 5 × 15% = 5.75 m

Revised height = 25 - 25 × 10% = 22.5 m

Final volume = 25 × 5.75 × 22.5 = 3234.375 m³

Now, % increase

⇒ 29.375% ≈ 29.38%

∴ The corresponding increase in the volume of the cuboid is 29.38%.

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