Let the length and the breadth of the rectangle be x m and y m, respectively.
Case 1: When length is increased by 3m and the breadth is decreased by 4m:
xy – (x + 3) (y – 4) = 67
⇒ xy – xy + 4x – 3y + 12 = 67
⇒ 4x – 3y = 55 ………(i)
Case 2: When length is reduced by 1m and breadth is increased by 4m:
(x – 1) (y + 4) – xy = 89
⇒ xy + 4x – y – 4 – xy = 89
⇒ 4x – y = 93 ………(ii)
Subtracting (i) and (ii), we get:
2y = 38
⇒ y = 19
On substituting y = 19 in (ii), we have
4x – 19 = 93
⇒4x = 93 + 19 = 112
⇒x = 28
Hence, the length = 28m and breadth = 19m.
