Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
A rectangle becomes a square when its length is reduced by 10 units and its breadth is increased by 5 units. But by this process the area of the rectangle is reduced by 210 sq. units. The area of the rectangle
(a)in square units is
(b)$2900>A>2875$
(c)$2925<A>2875$
(d)$2925>A>2900$
Answer
Answer (as printed): D
Explanation
Let the length and breadth of the rectangle be $l$ and $b$ units respectively. Then, $$\begin{aligned} & l-10=b+5 \\ & \Rightarrow l-b=15 \end{aligned}$$ And, $l b-(l-10)(b+5)=210$ $$\begin{aligned} & \Rightarrow l b-(l b+5 l-10 b-50)=210 \\ & \Rightarrow-5 l+10 b=160 \Rightarrow-l+2 b=32 \end{aligned}$$ Adding (i) and (ii), we get: $b=47$. Putting $b=47$ in (i), we get: $l=62$. Hence, area of the rectangle $=l b=(62 \times 47)$ sq. units = 2914 sq.units. Clearly, 2925 > A > 2900.
Explanation as extracted from the printed page; notation may be imperfect.