The length, breadth and height of a room in the shape of a cuboid are increased by 10%, 20% and 50% respectively. Find the percentage increase in the volume of the cuboid.

Volume of a cuboid is V = l × b × h. When each dimension changes by a factor, the volume changes by the product of those factors, not by the sum of the percentages. So the new volume is 1.10 × 1.20 × 1.50 times the old one.

Step by step: 1.10 × 1.20 = 1.32, and 1.32 × 1.50 = 1.98. The volume becomes 1.98 times the original, which is a 98% increase. Option C is correct.

• A (77): Does not match the product of the factors. It is not a standard result of these three changes.
• B (87): Also does not match the product. It is a near miss that comes from arithmetic slips.
• D (55): Far too small. It does not account for the 50% rise in height.

The core concept is successive percentage change for multiplicative quantities. For a product of independent factors, the overall change is found by multiplying (1+x)(1+y)(1+z), and the cross-terms matter. This links to Mensuration and to quick estimation in the Prelims Quantitative Aptitude section, and the same logic applies to questions on compound growth and population or area changes.

Trap: Adding the percentages (10 + 20 + 50 = 80) and then choosing the nearest option. Aspirants who rush for the nearest value may also pick 87 by mixing up the cross-terms.