Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
Length of a rectangular solid is increased by 10\% and breadth is decreased by 10\%. Then the volume of the solid
(a)remains unchanged
(b)decreases by 1\%
(c)decreases by 10\%
(d)increases by 10\%
Answer
Answer (as printed): B
Explanation
Let the original length, breadth and height of the solid be $l, b$ and $h$ respectively. Original volume $=(l b h)$ cu. units. New length $=110 \%$ of $l=\frac{11 l}{10}$. New breadth $=90 \%$ of $b=\frac{9 b}{10}$. New volume $=\left(\frac{11 l}{10} \times \frac{9 b}{10} \times h\right)$ cu. units $=\left(\frac{99}{100} l b h\right)$ cu. units. Decrease $=\left(l b h-\frac{99}{100} l b h\right)=\frac{l b h}{100}$. ∴ Decrease\% $=\left(\frac{l b h}{100} \times \frac{1}{l b h} \times 100\right) \%=1 \%$.
Explanation as extracted from the printed page; notation may be imperfect.