GATE2018 ME-1: GA-4

Question

A rectangle becomes a square when its length and breadth are reduced by $10$ m and $5$ m, respectively. During this process, the rectangle loses $650$ m$^2$ of area. What is the area of the original rectangle in square meters?

• A. $1125$
• B. $2250$
• C. $2924$
• D. $4500$

Answer 1

Answer: $B$. 2250

Let $l$ and $b$ be the length & breadth of rectangle.

Area of rectangle, $A = l\times b   \qquad \to (1)$

Given, rectangle becomes square when $l$ reduces by $10$ and $b$ reduces by $5$

$\implies  l-10 = b-5\qquad \to (2)$

Then, area of square $= (l-10)\times (b-5) = A-650$

$\implies (l-10)\times(b-5) = (l\times b) - 650 \qquad \to (3)$ 

Solving, $(ii)$ & $(iii)$ we get $b=45,l=50.$

Thus, area of rectangle $= 45\times 50 = 2250\;m^2$