Discussion
Dean has a cardboard box whose length, breadth and height are in the ratio 1:2:3. He makes a new box such that the length, breadth and height got increased by 100%, 200% and 200% respectively. How much less is volume of old box than the new box?
Answer: C
Take the original dimensions as \( 1k, 2k, 3k \).
\[ V_{\text{old}} = 1k \times 2k \times 3k = 6k^{3} \]
An increase of 100% doubles a length, and 200% triples it:
\[ 1k \to 2k, \qquad 2k \to 6k, \qquad 3k \to 9k \]
\[ V_{\text{new}} = 2k \times 6k \times 9k = 108k^{3} \]
\[ V_{\text{new}} - V_{\text{old}} = 102k^{3} = 17 \times 6k^{3} \]
So the old box falls short by 17 times its own volume. Note that a 200% increase means the length becomes three times the original, not two - that single slip turns the answer into 7.
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