Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
The area of a rectangle gets reduced by $9 \mathrm{m}^{2}$ if its length is reduced by 5 m and breadth is increased by 3 m . If we increase the length by 3 m and breadth by 2 m, the area is increased by $67 \mathrm{m}^{2}$. The length of the rectangle is
(a)9 m
(b)15.6 m
(c)17 m
(d)18.5 m
Answer
Answer (as printed): C
Explanation
Let the length and breadth of the rectangle be $l$ and $b$ metres respectively. Then, area of the rectangle $=l b$. $$\begin{aligned} & l b-(l-5)(b+3)=9 \\ & \Rightarrow l b-(l b+3 l-5 b-15)=9 \\ & \Rightarrow l b-l b-3 l+5 b+15=9 \\ & \Rightarrow 3 l-5 b=6 \end{aligned}$$ And, $(l+3)(b+2)-l b=67$
Explanation as extracted from the printed page; notation may be imperfect.