Subject: General Aptitude · Chapter: Area · Exam: 2010 · Marks: · Difficulty:
The length, breadth and height of the room are in the ratio 3 : 2 : 1. The breadth and height of the room are halved and length of the room is doubled. The area of the four walls of the room will
(a)decrease by 13.64\%
(b)decrease by 15\%
(c)decrease by 18.75\%
(d)decrease by 30\%
Answer
Answer (as printed): D
Explanation
Let the length, breadth and height of the room be $3 x, 2 x$ and $x$ respectively. Area of 4 walls $=2(l+b) \times h=2(3 x+2 x) \times x=10 x^{2}$. New length $=6 x$, New breadth $=x$, New height $=\frac{x}{2}$. New area of four walls $=\left[2(6 x+x) \times \frac{x}{2}\right]=7 x^{2}$. Decrease in area $=\left(10 x^{2}-7 x^{2}\right)=3 x^{2}$. ∴ Decrease $\%=\left(\frac{3 x^{2}}{10 x^{2}} \times 100\right) \%=30 \%$.
Explanation as extracted from the printed page; notation may be imperfect.