Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
The length, breadth and height of a cuboid are in the ratio 1 : 2 : 3. The length, breadth and height of the cuboid are increased by 100\%, 200\% and 200\% respectively. Then the increase in the volume of the cuboid is
(a)5 times
(b)6 times
(c)12 times
(d)17 times
Answer
Answer (as printed): D
Explanation
Let the original length, breadth and height of the cuboid be $x, 2 x$ and $3 x$ units respectively. Then, original volume $=(x \times 2 x \times 3 x)$ cu. units $=6 x^{3}$ cu. units. New length $=200 \%$ of $x=2 x$, New breadth $=300 \%$ of $2 x=6 x$, New height $=300 \%$ of $3 x=9 x$. ∴ New volume $=(2 x \times 6 x \times 9 x)$ cu. units $$=108 x^{3} \text { cu. units. }$$ Increase in volume $=\left(108 x^{3}-6 x^{3}\right)$ cu. units $$=\left(102 x^{3}\right) \text { cu. units }$$ ∴ Required ratio $=\frac{102 x^{3}}{6 x^{3}}=17$.
Explanation as extracted from the printed page; notation may be imperfect.